// Copyright 2015-2021 The Khronos Group, Inc. // // SPDX-License-Identifier: CC-BY-4.0 [[textures]] = Image Operations == Image Operations Overview Vulkan Image Operations are operations performed by those SPIR-V Image Instructions which take an code:OpTypeImage (representing a sname:VkImageView) or code:OpTypeSampledImage (representing a (sname:VkImageView, sname:VkSampler) pair). Read, write, and atomic operations also take texel coordinates as operands, and return a value based on a neighborhood of texture elements (_texels_) within the image. Query operations return properties of the bound image or of the lookup itself. The "`Depth`" operand of code:OpTypeImage is ignored. [NOTE] .Note ==== Texel is a term which is a combination of the words texture and element. Early interactive computer graphics supported texture operations on textures, a small subset of the image operations on images described here. The discrete samples remain essentially equivalent, however, so we retain the historical term texel to refer to them. ==== Image Operations include the functionality of the following SPIR-V Image Instructions: * code:OpImageSample* and code:OpImageSparseSample* read one or more neighboring texels of the image, and <> the texel values based on the state of the sampler. ** Instructions with code:ImplicitLod in the name <> the LOD used in the sampling operation based on the coordinates used in neighboring fragments. ** Instructions with code:ExplicitLod in the name <> the LOD used in the sampling operation based on additional coordinates. ** Instructions with code:Proj in the name apply homogeneous <> to the coordinates. * code:OpImageFetch and code:OpImageSparseFetch return a single texel of the image. No sampler is used. * code:OpImage*Gather and code:OpImageSparse*Gather read neighboring texels and <> of each. * code:OpImageRead (and code:OpImageSparseRead) and code:OpImageWrite read and write, respectively, a texel in the image. No sampler is used. ifdef::VK_NV_shader_image_footprint[] * code:OpImageSampleFootprintNV identifies and returns information about the set of texels in the image that would be accessed by an equivalent code:OpImageSample* instruction. endif::VK_NV_shader_image_footprint[] * Instructions with code:Dref in the name apply <> on the texel values. * Instructions with code:Sparse in the name additionally return a <> code. * code:OpImageQuerySize, code:OpImageQuerySizeLod, code:OpImageQueryLevels, and code:OpImageQuerySamples return properties of the image descriptor that would be accessed. The image itself is not accessed. * code:OpImageQueryLod returns the lod parameters that would be used in a sample operation. The actual operation is not performed. [[textures-texel-coordinate-systems]] === Texel Coordinate Systems Images are addressed by _texel coordinates_. There are three _texel coordinate systems_: * normalized texel coordinates [eq]#[0.0, 1.0]# * unnormalized texel coordinates [eq]#[0.0, width / height / depth)# * integer texel coordinates [eq]#[0, width / height / depth)# SPIR-V code:OpImageFetch, code:OpImageSparseFetch, code:OpImageRead, code:OpImageSparseRead, and code:OpImageWrite instructions use integer texel coordinates. Other image instructions can: use either normalized or unnormalized texel coordinates (selected by the pname:unnormalizedCoordinates state of the sampler used in the instruction), but there are <> on what operations, image state, and sampler state is supported. Normalized coordinates are logically <> to unnormalized as part of image operations, and <> are only performed on normalized coordinates. The array layer coordinate is always treated as unnormalized even when other coordinates are normalized. Normalized texel coordinates are referred to as [eq]#(s,t,r,q,a)#, with the coordinates having the following meanings: * [eq]#s#: Coordinate in the first dimension of an image. * [eq]#t#: Coordinate in the second dimension of an image. * [eq]#r#: Coordinate in the third dimension of an image. ** [eq]#(s,t,r)# are interpreted as a direction vector for Cube images. * [eq]#q#: Fourth coordinate, for homogeneous (projective) coordinates. * [eq]#a#: Coordinate for array layer. The coordinates are extracted from the SPIR-V operand based on the dimensionality of the image variable and type of instruction. For code:Proj instructions, the components are in order [eq]#(s, [t,] [r,] q)#, with [eq]#t# and [eq]#r# being conditionally present based on the code:Dim of the image. For non-code:Proj instructions, the coordinates are [eq]#(s [,t] [,r] [,a])#, with [eq]#t# and [eq]#r# being conditionally present based on the code:Dim of the image and [eq]#a# being conditionally present based on the code:Arrayed property of the image. Projective image instructions are not supported on code:Arrayed images. Unnormalized texel coordinates are referred to as [eq]#(u,v,w,a)#, with the coordinates having the following meanings: * [eq]#u#: Coordinate in the first dimension of an image. * [eq]#v#: Coordinate in the second dimension of an image. * [eq]#w#: Coordinate in the third dimension of an image. * [eq]#a#: Coordinate for array layer. Only the [eq]#u# and [eq]#v# coordinates are directly extracted from the SPIR-V operand, because only 1D and 2D (non-code:Arrayed) dimensionalities support unnormalized coordinates. The components are in order [eq]#(u [,v])#, with [eq]#v# being conditionally present when the dimensionality is 2D. When normalized coordinates are converted to unnormalized coordinates, all four coordinates are used. Integer texel coordinates are referred to as [eq]#(i,j,k,l,n)#, with the coordinates having the following meanings: * [eq]#i#: Coordinate in the first dimension of an image. * [eq]#j#: Coordinate in the second dimension of an image. * [eq]#k#: Coordinate in the third dimension of an image. * [eq]#l#: Coordinate for array layer. * [eq]#n#: Index of the sample within the texel. They are extracted from the SPIR-V operand in order [eq]#(i [,j] [,k] [,l] [,n])#, with [eq]#j# and [eq]#k# conditionally present based on the code:Dim of the image, and [eq]#l# conditionally present based on the code:Arrayed property of the image. [eq]#n# is conditionally present and is taken from the code:Sample image operand. For all coordinate types, unused coordinates are assigned a value of zero. [[textures-texel-coordinate-systems-diagrams]] image::{images}/vulkantexture0-ll.svg[align="center",title="Texel Coordinate Systems, Linear Filtering",opts="{imageopts}"] The Texel Coordinate Systems - For the example shown of an 8{times}4 texel two dimensional image. * Normalized texel coordinates: ** The [eq]#s# coordinate goes from 0.0 to 1.0. ** The [eq]#t# coordinate goes from 0.0 to 1.0. * Unnormalized texel coordinates: ** The [eq]#u# coordinate within the range 0.0 to 8.0 is within the image, otherwise it is outside the image. ** The [eq]#v# coordinate within the range 0.0 to 4.0 is within the image, otherwise it is outside the image. * Integer texel coordinates: ** The [eq]#i# coordinate within the range 0 to 7 addresses texels within the image, otherwise it is outside the image. ** The [eq]#j# coordinate within the range 0 to 3 addresses texels within the image, otherwise it is outside the image. * Also shown for linear filtering: ** Given the unnormalized coordinates [eq]#(u,v)#, the four texels selected are [eq]#i~0~j~0~#, [eq]#i~1~j~0~#, [eq]#i~0~j~1~#, and [eq]#i~1~j~1~#. ** The fractions [eq]#{alpha}# and [eq]#{beta}#. ** Given the offset [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~#, the four texels selected by the offset are [eq]#i~0~j'~0~#, [eq]#i~1~j'~0~#, [eq]#i~0~j'~1~#, and [eq]#i~1~j'~1~#. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [NOTE] .Note ==== For formats with reduced-resolution components, [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~# are relative to the resolution of the highest-resolution component, and therefore may be divided by two relative to the unnormalized coordinate space of the lower-resolution components. ==== endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] image::{images}/vulkantexture1-ll.svg[align="center",title="Texel Coordinate Systems, Nearest Filtering",opts="{imageopts}"] The Texel Coordinate Systems - For the example shown of an 8{times}4 texel two dimensional image. * Texel coordinates as above. Also shown for nearest filtering: ** Given the unnormalized coordinates [eq]#(u,v)#, the texel selected is [eq]#ij#. ** Given the offset [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~#, the texel selected by the offset is [eq]#ij'#. ifdef::VK_NV_corner_sampled_image[] For corner-sampled images, the texel samples are located at the grid intersections instead of the texel centers. image::{images}/vulkantexture0-corner-alternative-a-ll.svg[align="center",title="Texel Coordinate Systems, Corner Sampling",opts="{imageopts}"] endif::VK_NV_corner_sampled_image[] == Conversion Formulas ifdef::editing-notes[] [NOTE] .editing-note ==== (Bill) These Conversion Formulas will likely move to Section 2.7 Fixed-Point Data Conversions (RGB to sRGB and sRGB to RGB) and section 2.6 Numeric Representation and Computation (RGB to Shared Exponent and Shared Exponent to RGB) ==== endif::editing-notes[] [[textures-RGB-sexp]] === RGB to Shared Exponent Conversion An RGB color [eq]#(red, green, blue)# is transformed to a shared exponent color [eq]#(red~shared~, green~shared~, blue~shared~, exp~shared~)# as follows: First, the components [eq]#(red, green, blue)# are clamped to [eq]#(red~clamped~, green~clamped~, blue~clamped~)# as: {empty}:: [eq]#red~clamped~ = max(0, min(sharedexp~max~, red))# {empty}:: [eq]#green~clamped~ = max(0, min(sharedexp~max~, green))# {empty}:: [eq]#blue~clamped~ = max(0, min(sharedexp~max~, blue))# where: [latexmath] +++++++++++++++++++ \begin{aligned} N & = 9 & \text{number of mantissa bits per component} \\ B & = 15 & \text{exponent bias} \\ E_{max} & = 31 & \text{maximum possible biased exponent value} \\ sharedexp_{max} & = \frac{(2^N-1)}{2^N} \times 2^{(E_{max}-B)} \end{aligned} +++++++++++++++++++ [NOTE] .Note ==== [eq]#NaN#, if supported, is handled as in <> `minNum()` and `maxNum()`. This results in any [eq]#NaN# being mapped to zero. ==== The largest clamped component, [eq]#max~clamped~# is determined: {empty}:: [eq]#max~clamped~ = max(red~clamped~, green~clamped~, blue~clamped~)# A preliminary shared exponent [eq]#exp'# is computed: [latexmath] +++++++++++++++++++ \begin{aligned} exp' = \begin{cases} \left \lfloor \log_2(max_{clamped}) \right \rfloor + (B+1) & \text{for}\ max_{clamped} > 2^{-(B+1)} \\ 0 & \text{for}\ max_{clamped} \leq 2^{-(B+1)} \end{cases} \end{aligned} +++++++++++++++++++ The shared exponent [eq]#exp~shared~# is computed: [latexmath] +++++++++++++++++++ \begin{aligned} max_{shared} = \left \lfloor { \frac{max_{clamped}}{2^{(exp'-B-N)}} + \frac{1}{2} } \right \rfloor \end{aligned} +++++++++++++++++++ [latexmath] +++++++++++++++++++ \begin{aligned} exp_{shared} = \begin{cases} exp' & \text{for}\ 0 \leq max_{shared} < 2^N \\ exp'+1 & \text{for}\ max_{shared} = 2^N \end{cases} \end{aligned} +++++++++++++++++++ Finally, three integer values in the range [eq]#0# to [eq]#2^N^# are computed: [latexmath] +++++++++++++++++++ \begin{aligned} red_{shared} & = \left \lfloor { \frac{red_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \\ green_{shared} & = \left \lfloor { \frac{green_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \\ blue_{shared} & = \left \lfloor { \frac{blue_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \end{aligned} +++++++++++++++++++ [[textures-sexp-RGB]] === Shared Exponent to RGB A shared exponent color [eq]#(red~shared~, green~shared~, blue~shared~, exp~shared~)# is transformed to an RGB color [eq]#(red, green, blue)# as follows: {empty}:: latexmath:[red = red_{shared} \times {2^{(exp_{shared}-B-N)}}] {empty}:: latexmath:[green = green_{shared} \times {2^{(exp_{shared}-B-N)}}] {empty}:: latexmath:[blue = blue_{shared} \times {2^{(exp_{shared}-B-N)}}] where: {empty}:: [eq]#N = 9# (number of mantissa bits per component) {empty}:: [eq]#B = 15# (exponent bias) == Texel Input Operations _Texel input instructions_ are SPIR-V image instructions that read from an image. _Texel input operations_ are a set of steps that are performed on state, coordinates, and texel values while processing a texel input instruction, and which are common to some or all texel input instructions. They include the following steps, which are performed in the listed order: * <> ** <> ** <> ** <> ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] ** <> endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] * <> * <> * <> * <> * <> ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] * <> * <> endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] For texel input instructions involving multiple texels (for sampling or gathering), these steps are applied for each texel that is used in the instruction. Depending on the type of image instruction, other steps are conditionally performed between these steps or involving multiple coordinate or texel values. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] If <> is implicit, <> instead takes place during chroma reconstruction, before <> occurs. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-input-validation]] === Texel Input Validation Operations _Texel input validation operations_ inspect instruction/image/sampler state or coordinates, and in certain circumstances cause the texel value to be replaced or become undefined:. There are a series of validations that the texel undergoes. [[textures-operation-validation]] ==== Instruction/Sampler/Image View Validation There are a number of cases where a SPIR-V instruction can: mismatch with the sampler, the image view, or both, and a number of further cases where the sampler can: mismatch with the image view. In such cases the value of the texel returned is undefined:. These cases include: * The sampler pname:borderColor is an integer type and the image view pname:format is not one of the elink:VkFormat integer types or a stencil component of a depth/stencil format. * The sampler pname:borderColor is a float type and the image view pname:format is not one of the elink:VkFormat float types or a depth component of a depth/stencil format. ifndef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is one of the opaque black colors (ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK or ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>. endif::VK_EXT_border_color_swizzle[] ifdef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is one of the opaque black colors (ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK or ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>, and slink:VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::pname:borderColorSwizzleFromImage feature is not enabled, and slink:VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified. * slink:VkSamplerBorderColorComponentMappingCreateInfoEXT::pname:components, if specified, has a component swizzle that does not match the component swizzle of the image view, and either component swizzle is not a form of identity swizzle. * slink:VkSamplerBorderColorComponentMappingCreateInfoEXT::pname:srgb, if specified, does not match the sRGB encoding of the image view. endif::VK_EXT_border_color_swizzle[] ifdef::VK_EXT_custom_border_color[] * The sampler pname:borderColor is a custom color (ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or ename:VK_BORDER_COLOR_INT_CUSTOM_EXT) and the supplied slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:customBorderColor is outside the bounds of the values representable in the image view's pname:format. ifndef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is a custom color (ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or ename:VK_BORDER_COLOR_INT_CUSTOM_EXT) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>. endif::VK_EXT_border_color_swizzle[] ifdef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is a custom color (ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or ename:VK_BORDER_COLOR_INT_CUSTOM_EXT) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>, and slink:VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::pname:borderColorSwizzleFromImage feature is not enabled, and slink:VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified. endif::VK_EXT_border_color_swizzle[] endif::VK_EXT_custom_border_color[] * The elink:VkImageLayout of any subresource in the image view does not match the slink:VkDescriptorImageInfo::pname:imageLayout used to write the image descriptor. * The SPIR-V Image Format is not <> with the image view's pname:format. * The sampler pname:unnormalizedCoordinates is ename:VK_TRUE and any of the <> are violated. ifdef::VK_EXT_fragment_density_map[] * The sampler was created with pname:flags containing ename:VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and the image was not created with pname:flags containing ename:VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT. * The sampler was not created with pname:flags containing ename:VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and the image was created with pname:flags containing ename:VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT. * The sampler was created with pname:flags containing ename:VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and is used with a function that is not code:OpImageSampleImplicitLod or code:OpImageSampleExplicitLod, or is used with operands code:Offset or code:ConstOffsets. endif::VK_EXT_fragment_density_map[] * The SPIR-V instruction is one of the code:OpImage*Dref* instructions and the sampler pname:compareEnable is ename:VK_FALSE * The SPIR-V instruction is not one of the code:OpImage*Dref* instructions and the sampler pname:compareEnable is ename:VK_TRUE ifndef::VK_KHR_format_feature_flags2[] * The SPIR-V instruction is one of the code:OpImage*Dref* instructions and the image view pname:format is not one of the depth/stencil formats with a depth component, or the image view aspect is not ename:VK_IMAGE_ASPECT_DEPTH_BIT. endif::VK_KHR_format_feature_flags2[] ifdef::VK_KHR_format_feature_flags2[] * The SPIR-V instruction is one of the code:OpImage*Dref* instructions, the image view pname:format is one of the depth/stencil formats, and the image view aspect is not ename:VK_IMAGE_ASPECT_DEPTH_BIT. endif::VK_KHR_format_feature_flags2[] * The SPIR-V instruction's image variable's properties are not compatible with the image view: ** Rules for pname:viewType: *** ename:VK_IMAGE_VIEW_TYPE_1D must: have code:Dim = 1D, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_2D must: have code:Dim = 2D, code:Arrayed = 0. *** ename:VK_IMAGE_VIEW_TYPE_3D must: have code:Dim = 3D, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_CUBE must: have code:Dim = Cube, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_1D_ARRAY must: have code:Dim = 1D, code:Arrayed = 1, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_2D_ARRAY must: have code:Dim = 2D, code:Arrayed = 1. *** ename:VK_IMAGE_VIEW_TYPE_CUBE_ARRAY must: have code:Dim = Cube, code:Arrayed = 1, code:MS = 0. ** If the image was created with slink:VkImageCreateInfo::pname:samples equal to ename:VK_SAMPLE_COUNT_1_BIT, the instruction must: have code:MS = 0. ** If the image was created with slink:VkImageCreateInfo::pname:samples not equal to ename:VK_SAMPLE_COUNT_1_BIT, the instruction must: have code:MS = 1. ** If the code:Sampled code:Type of the code:OpTypeImage does not match the numeric format of the image, as shown in the _SPIR-V Sampled Type_ column of the <> table. ** If the <> does not match the signedness of the image's format. ifdef::VK_NV_corner_sampled_image[] * If the image was created with slink:VkImageCreateInfo::pname:flags containing ename:VK_IMAGE_CREATE_CORNER_SAMPLED_BIT_NV, the sampler addressing modes must: only use a elink:VkSamplerAddressMode of ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. endif::VK_NV_corner_sampled_image[] ifdef::VK_NV_shader_image_footprint[] * The SPIR-V instruction is code:OpImageSampleFootprintNV with code:Dim = 2D and pname:addressModeU or pname:addressModeV in the sampler is not ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. * The SPIR-V instruction is code:OpImageSampleFootprintNV with code:Dim = 3D and pname:addressModeU, pname:addressModeV, or pname:addressModeW in the sampler is not ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. endif::VK_NV_shader_image_footprint[] ifdef::VK_EXT_custom_border_color[] * The sampler was created with a specified slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:format which does not match the elink:VkFormat of the image view(s) it is sampling. * The sampler is sampling an image view of ename:VK_FORMAT_B4G4R4A4_UNORM_PACK16, ename:VK_FORMAT_B5G6R5_UNORM_PACK16, or ename:VK_FORMAT_B5G5R5A1_UNORM_PACK16 format without a specified slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:format. endif::VK_EXT_custom_border_color[] ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] Only code:OpImageSample* and code:OpImageSparseSample* can: be used with a sampler that enables <>. code:OpImageFetch, code:OpImageSparseFetch, code:OpImage*Gather, and code:OpImageSparse*Gather must: not be used with a sampler that enables <>. The code:ConstOffset and code:Offset operands must: not be used with a sampler that enables <>. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-integer-coordinate-validation]] ==== Integer Texel Coordinate Validation Integer texel coordinates are validated against the size of the image level, and the number of layers and number of samples in the image. For SPIR-V instructions that use integer texel coordinates, this is performed directly on the integer coordinates. For instructions that use normalized or unnormalized texel coordinates, this is performed on the coordinates that result after <> to integer texel coordinates. If the integer texel coordinates do not satisfy all of the conditions {empty}:: [eq]#0 {leq} i < w~s~# {empty}:: [eq]#0 {leq} j < h~s~# {empty}:: [eq]#0 {leq} k < d~s~# {empty}:: [eq]#0 {leq} l < layers# {empty}:: [eq]#0 {leq} n < samples# where: {empty}:: [eq]#w~s~ =# width of the image level {empty}:: [eq]#h~s~ =# height of the image level {empty}:: [eq]#d~s~ =# depth of the image level {empty}:: [eq]#layers =# number of layers in the image {empty}:: [eq]#samples =# number of samples per texel in the image then the texel fails integer texel coordinate validation. There are four cases to consider: . Valid Texel Coordinates + * If the texel coordinates pass validation (that is, the coordinates lie within the image), + then the texel value comes from the value in image memory. . Border Texel + * If the texel coordinates fail validation, and * If the read is the result of an image sample instruction or image gather instruction, and * If the image is not a cube image, + then the texel is a border texel and <> is performed. . Invalid Texel + * If the texel coordinates fail validation, and * If the read is the result of an image fetch instruction, image read instruction, or atomic instruction, + then the texel is an invalid texel and <> is performed. . Cube Map Edge or Corner + Otherwise the texel coordinates lie beyond the edges or corners of the selected cube map face, and <> is performed. [[textures-cubemapedge]] ==== Cube Map Edge Handling If the texel coordinates lie beyond the edges or corners of the selected cube map face, the following steps are performed. Note that this does not occur when using ename:VK_FILTER_NEAREST filtering within a mip level, since ename:VK_FILTER_NEAREST is treated as using ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. * Cube Map Edge Texel + ** If the texel lies beyond the selected cube map face in either only [eq]#i# or only [eq]#j#, then the coordinates [eq]#(i,j)# and the array layer [eq]#l# are transformed to select the adjacent texel from the appropriate neighboring face. * Cube Map Corner Texel + ** If the texel lies beyond the selected cube map face in both [eq]#i# and [eq]#j#, then there is no unique neighboring face from which to read that texel. The texel should: be replaced by the average of the three values of the adjacent texels in each incident face. However, implementations may: replace the cube map corner texel by other methods. ifndef::VK_EXT_filter_cubic[] The methods are subject to the constraint that if the three available texels have the same value, the resulting filtered texel must: have that value. endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] The methods are subject to the constraint that for linear filtering if the three available texels have the same value, the resulting filtered texel must: have that value, and for cubic filtering if the twelve available samples have the same value, the resulting filtered texel must: have that value. endif::VK_EXT_filter_cubic[] [[textures-sparse-validation]] ==== Sparse Validation If the texel reads from an unbound region of a sparse image, the texel is a _sparse unbound texel_, and processing continues with <>. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-layout-validation]] ==== Layout Validation If all planes of a _disjoint_ _multi-planar_ image are not in the same <>, the image must: not be sampled with <> enabled. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-format-conversion]] === Format Conversion Texels undergo a format conversion from the elink:VkFormat of the image view to a vector of either floating point or signed or unsigned integer components, with the number of components based on the number of components present in the format. * Color formats have one, two, three, or four components, according to the format. * Depth/stencil formats are one component. The depth or stencil component is selected by the pname:aspectMask of the image view. Each component is converted based on its type and size (as defined in the <> section for each elink:VkFormat), using the appropriate equations in <>, <>, <>, <>, and <>. Signed integer components smaller than 32 bits are sign-extended. If the image view format is sRGB, the color components are first converted as if they are UNORM, and then sRGB to linear conversion is applied to the R, G, and B components as described in the "`sRGB EOTF`" section of the <>. The A component, if present, is unchanged. If the image view format is block-compressed, then the texel value is first decoded, then converted based on the type and number of components defined by the compressed format. [[textures-texel-replacement]] === Texel Replacement A texel is replaced if it is one (and only one) of: * a border texel, * an invalid texel, or * a sparse unbound texel. Border texels are replaced with a value based on the image format and the pname:borderColor of the sampler. The border color is: [[textures-border-replacement-color]] ifdef::VK_EXT_custom_border_color[] .Border Color [eq]#B#, Custom Border Color slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:customBorderColor [eq]#U# endif::VK_EXT_custom_border_color[] ifndef::VK_EXT_custom_border_color[] .Border Color [eq]#B# endif::VK_EXT_custom_border_color[] [options="header",cols="60%,40%"] |==== | Sampler pname:borderColor | Corresponding Border Color | ename:VK_BORDER_COLOR_FLOAT_TRANSPARENT_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0.0, 0.0, 0.0, 0.0]# | ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0.0, 0.0, 0.0, 1.0]# | ename:VK_BORDER_COLOR_FLOAT_OPAQUE_WHITE | [eq]#[B~r~, B~g~, B~b~, B~a~] = [1.0, 1.0, 1.0, 1.0]# | ename:VK_BORDER_COLOR_INT_TRANSPARENT_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0, 0, 0, 0]# | ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0, 0, 0, 1]# | ename:VK_BORDER_COLOR_INT_OPAQUE_WHITE | [eq]#[B~r~, B~g~, B~b~, B~a~] = [1, 1, 1, 1]# ifdef::VK_EXT_custom_border_color[] | ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT | [eq]#[B~r~, B~g~, B~b~, B~a~] = [U~r~, U~g~, U~b~, U~a~]# | ename:VK_BORDER_COLOR_INT_CUSTOM_EXT | [eq]#[B~r~, B~g~, B~b~, B~a~] = [U~r~, U~g~, U~b~, U~a~]# endif::VK_EXT_custom_border_color[] |==== ifdef::VK_EXT_custom_border_color[] The custom border color ([eq]#U#) may: be rounded by implementations prior to texel replacement, but the error introduced by such a rounding must: not exceed one ULP of the image's pname:format. endif::VK_EXT_custom_border_color[] [NOTE] .Note ==== The names etext:VK_BORDER_COLOR_*\_TRANSPARENT_BLACK, etext:VK_BORDER_COLOR_*\_OPAQUE_BLACK, and etext:VK_BORDER_COLOR_*_OPAQUE_WHITE are meant to describe which components are zeros and ones in the vocabulary of compositing, and are not meant to imply that the numerical value of ename:VK_BORDER_COLOR_INT_OPAQUE_WHITE is a saturating value for integers. ==== This is substituted for the texel value by replacing the number of components in the image format [[textures-border-replacement-table]] .Border Texel Components After Replacement [width="100%",options="header"] |==== | Texel Aspect or Format | Component Assignment | Depth aspect | [eq]#D = B~r~# | Stencil aspect | [eq]#S = B~r~# | One component color format | [eq]#Color~r~ = B~r~# | Two component color format | [eq]#[Color~r~,Color~g~] = [B~r~,B~g~]# | Three component color format| [eq]#[Color~r~,Color~g~,Color~b~] = [B~r~,B~g~,B~b~]# | Four component color format | [eq]#[Color~r~,Color~g~,Color~b~,Color~a~] = [B~r~,B~g~,B~b~,B~a~]# |==== The value returned by a read of an invalid texel is undefined:, unless that read operation is from a buffer resource and the pname:robustBufferAccess feature is enabled. In that case, an invalid texel is replaced as described by the <>. ifdef::VK_EXT_image_robustness,VK_EXT_robustness2[] If the access is to an image resource and the x, y, z, or layer coordinate validation fails and ifdef::VK_EXT_image_robustness[] <> is enabled then zero must: be returned for the R, G, and B components, if present. Either zero or one must: be returned for the A component, if present. endif::VK_EXT_image_robustness[] ifdef::VK_EXT_image_robustness+VK_EXT_robustness2[If] ifdef::VK_EXT_robustness2[] <> is enabled, zero values must: be returned. endif::VK_EXT_robustness2[] If only the sample index was invalid, the values returned are undefined:. endif::VK_EXT_image_robustness,VK_EXT_robustness2[] ifdef::VK_EXT_image_robustness[] Additionally, if <> is enabled, ifdef::VK_EXT_robustness2[] but <> is not, endif::VK_EXT_robustness2[] any invalid texels may: be expanded to four components prior to texel replacement. This means that components not present in the image format may be replaced with 0 or may undergo <> as normal. endif::VK_EXT_image_robustness[] ifdef::VK_EXT_robustness2[] Loads from a null descriptor return a four component color value of all zeros. However, for storage images and storage texel buffers using an explicit SPIR-V Image Format, loads from a null descriptor may: return an alpha value of 1 (float or integer, depending on format) if the format does not include alpha. endif::VK_EXT_robustness2[] If the slink:VkPhysicalDeviceSparseProperties::pname:residencyNonResidentStrict property is ename:VK_TRUE, a sparse unbound texel is replaced with 0 or 0.0 values for integer and floating-point components of the image format, respectively. If pname:residencyNonResidentStrict is ename:VK_FALSE, the value of the sparse unbound texel is undefined:. [[textures-depth-compare-operation]] === Depth Compare Operation If the image view has a depth/stencil format, the depth component is selected by the pname:aspectMask, and the operation is a code:Dref instruction, a depth comparison is performed. The value of the result [eq]#D# is [eq]#1.0# if the result of the compare operation is [eq]#true#, and [eq]#0.0# otherwise. The compare operation is selected by the pname:compareOp member of the sampler. [latexmath] +++++++++++++++++++ \begin{aligned} D & = 1.0 & \begin{cases} D_{\textit{ref}} \leq D_{\textit{tex}} & \text{for LEQUAL} \\ D_{\textit{ref}} \geq D_{\textit{tex}} & \text{for GEQUAL} \\ D_{\textit{ref}} < D_{\textit{tex}} & \text{for LESS} \\ D_{\textit{ref}} > D_{\textit{tex}} & \text{for GREATER} \\ D_{\textit{ref}} = D_{\textit{tex}} & \text{for EQUAL} \\ D_{\textit{ref}} \neq D_{\textit{tex}} & \text{for NOTEQUAL} \\ \textit{true} & \text{for ALWAYS} \\ \textit{false} & \text{for NEVER} \end{cases} \\ D & = 0.0 & \text{otherwise} \end{aligned} +++++++++++++++++++ where [eq]#D~tex~# is the texel depth value and [eq]#D~ref~# is the reference value from the SPIR-V operand. If the image being sampled has a fixed-point format then the reference value is clamped to [0, 1] before the comparison operation. [[textures-conversion-to-rgba]] === Conversion to RGBA The texel is expanded from one, two, or three components to four components based on the image base color: [[textures-texel-color-rgba-conversion-table]] .Texel Color After Conversion To RGBA [width="100%", options="header", cols="<4,<6"] |==== | Texel Aspect or Format | RGBA Color | Depth aspect | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [D,0,0,one]# | Stencil aspect | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [S,0,0,one]# | One component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,0,0,one]# | Two component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,Color~g~,0,one]# | Three component color format| [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,Color~g~,Color~b~,one]# | Four component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,Color~g~,Color~b~,Color~a~]# |==== where [eq]#one = 1.0f# for floating-point formats and depth aspects, and [eq]#one = 1# for integer formats and stencil aspects. [[textures-component-swizzle]] === Component Swizzle ifndef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] All texel input instructions apply a _swizzle_ based on the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkImageViewCreateInfo structure for the image being read. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] All texel input instructions apply a _swizzle_ based on: * the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkImageViewCreateInfo structure for the image being read if <> is not enabled, and * the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkSamplerYcbcrConversionCreateInfo structure for the <> if sampler {YCbCr} conversion is enabled. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] The swizzle can: rearrange the components of the texel, or substitute zero or one for any components. It is defined as follows for each color [eq]#component#: [latexmath] +++++++++++++++++++ \begin{aligned} Color'_{component} & = \begin{cases} Color_r & \text{for RED swizzle} \\ Color_g & \text{for GREEN swizzle} \\ Color_b & \text{for BLUE swizzle} \\ Color_a & \text{for ALPHA swizzle} \\ 0 & \text{for ZERO swizzle} \\ one & \text{for ONE swizzle} \\ identity & \text{for IDENTITY swizzle} \end{cases} \end{aligned} +++++++++++++++++++ where: [latexmath] +++++++++++++++++++ \begin{aligned} one & = \begin{cases} & 1.0\text{f} & \text{for floating point components} \\ & 1 & \text{for integer components} \\ \end{cases} \\ identity & = \begin{cases} & Color_r & \text{for}\ component = r \\ & Color_g & \text{for}\ component = g \\ & Color_b & \text{for}\ component = b \\ & Color_a & \text{for}\ component = a \\ \end{cases} \end{aligned} +++++++++++++++++++ If the border color is one of the etext:VK_BORDER_COLOR_*_OPAQUE_BLACK enums and the elink:VkComponentSwizzle is not the <> for all components, the value of the texel after swizzle is undefined:. [[textures-sparse-residency]] === Sparse Residency code:OpImageSparse* instructions return a structure which includes a _residency code_ indicating whether any texels accessed by the instruction are sparse unbound texels. This code can: be interpreted by the code:OpImageSparseTexelsResident instruction which converts the residency code to a boolean value. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-chroma-reconstruction]] === Chroma Reconstruction In some color models, the color representation is defined in terms of monochromatic light intensity (often called "`luma`") and color differences relative to this intensity, often called "`chroma`". It is common for color models other than RGB to represent the chroma components at lower spatial resolution than the luma component. This approach is used to take advantage of the eye's lower spatial sensitivity to color compared with its sensitivity to brightness. Less commonly, the same approach is used with additive color, since the green component dominates the eye's sensitivity to light intensity and the spatial sensitivity to color introduced by red and blue is lower. Lower-resolution components are "`downsampled`" by resizing them to a lower spatial resolution than the component representing luminance. This process is also commonly known as "`chroma subsampling`". There is one luminance sample in each texture texel, but each chrominance sample may be shared among several texels in one or both texture dimensions. * "`etext:_444`" formats do not spatially downsample chroma values compared with luma: there are unique chroma samples for each texel. * "`etext:_422`" formats have downsampling in the x dimension (corresponding to _u_ or _s_ coordinates): they are sampled at half the resolution of luma in that dimension. * "`etext:_420`" formats have downsampling in the x dimension (corresponding to _u_ or _s_ coordinates) and the y dimension (corresponding to _v_ or _t_ coordinates): they are sampled at half the resolution of luma in both dimensions. The process of reconstructing a full color value for texture access involves accessing both chroma and luma values at the same location. To generate the color accurately, the values of the lower-resolution components at the location of the luma samples must be reconstructed from the lower-resolution sample locations, an operation known here as "`chroma reconstruction`" irrespective of the actual color model. The location of the chroma samples relative to the luma coordinates is determined by the pname:xChromaOffset and pname:yChromaOffset members of the slink:VkSamplerYcbcrConversionCreateInfo structure used to create the sampler {YCbCr} conversion. The following diagrams show the relationship between unnormalized (_u_,_v_) coordinates and (_i_,_j_) integer texel positions in the luma component (shown in black, with circles showing integer sample positions) and the texel coordinates of reduced-resolution chroma components, shown as crosses in red. [NOTE] .Note ==== If the chroma values are reconstructed at the locations of the luma samples by means of interpolation, chroma samples from outside the image bounds are needed; these are determined according to <>. These diagrams represent this by showing the bounds of the "`chroma texel`" extending beyond the image bounds, and including additional chroma sample positions where required for interpolation. The limits of a sample for etext:NEAREST sampling is shown as a grid. ==== image::{images}/chromasamples_422_cosited.svg[align="center",title="422 downsampling, xChromaOffset=COSITED_EVEN",opts="{imageopts}"] image::{images}/chromasamples_422_midpoint.svg[align="center",title="422 downsampling, xChromaOffset=MIDPOINT",opts="{imageopts}"] image::{images}/chromasamples_420_xcosited_ycosited.svg[align="center",title="420 downsampling, xChromaOffset=COSITED_EVEN, yChromaOffset=COSITED_EVEN",opts="{imageopts}"] image::{images}/chromasamples_420_xmidpoint_ycosited.svg[align="center",title="420 downsampling, xChromaOffset=MIDPOINT, yChromaOffset=COSITED_EVEN",opts="{imageopts}"] image::{images}/chromasamples_420_xcosited_ymidpoint.svg[align="center",title="420 downsampling, xChromaOffset=COSITED_EVEN, yChromaOffset=MIDPOINT",opts="{imageopts}"] image::{images}/chromasamples_420_xmidpoint_ymidpoint.svg[align="center",title="420 downsampling, xChromaOffset=MIDPOINT, yChromaOffset=MIDPOINT",opts="{imageopts}"] Reconstruction is implemented in one of two ways: If the format of the image that is to be sampled sets ename:VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT, or the slink:VkSamplerYcbcrConversionCreateInfo's pname:forceExplicitReconstruction is set to ename:VK_TRUE, reconstruction is performed as an explicit step independent of filtering, described in the <> section. If the format of the image that is to be sampled does not set ename:VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT and if the slink:VkSamplerYcbcrConversionCreateInfo's pname:forceExplicitReconstruction is set to ename:VK_FALSE, reconstruction is performed as an implicit part of filtering prior to color model conversion, with no separate post-conversion texel filtering step, as described in the <> section. [[textures-explicit-reconstruction]] ==== Explicit Reconstruction * If the pname:chromaFilter member of the slink:VkSamplerYcbcrConversionCreateInfo structure is ename:VK_FILTER_NEAREST: ** If the format's R and B components are reduced in resolution in just width by a factor of two relative to the G component (i.e. this is a "`etext:_422`" format), the latexmath:[\tau_{ijk}[level\]] values accessed by <> are reconstructed as follows: + [latexmath] ++++++++++++++ \begin{aligned} \tau_R'(i, j) & = \tau_R(\left\lfloor{i\times 0.5}\right\rfloor, j)[level] \\ \tau_B'(i, j) & = \tau_B(\left\lfloor{i\times 0.5}\right\rfloor, j)[level] \end{aligned} ++++++++++++++ ** If the format's R and B components are reduced in resolution in width and height by a factor of two relative to the G component (i.e. this is a "`etext:_420`" format), the latexmath:[\tau_{ijk}[level\]] values accessed by <> are reconstructed as follows: + [latexmath] ++++++++++++++ \begin{aligned} \tau_R'(i, j) & = \tau_R(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)[level] \\ \tau_B'(i, j) & = \tau_B(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)[level] \end{aligned} ++++++++++++++ + [NOTE] .Note ==== pname:xChromaOffset and pname:yChromaOffset have no effect if pname:chromaFilter is ename:VK_FILTER_NEAREST for explicit reconstruction. ==== * If the pname:chromaFilter member of the slink:VkSamplerYcbcrConversionCreateInfo structure is ename:VK_FILTER_LINEAR: ** If the format's R and B components are reduced in resolution in just width by a factor of two relative to the G component (i.e. this is a "`etext:_422`" format): *** If pname:xChromaOffset is ename:VK_CHROMA_LOCATION_COSITED_EVEN: + [latexmath] +++++ \tau_{RB}'(i,j) = \begin{cases} \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\ 0.5\times\tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level] + \\ 0.5\times\tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases} +++++ + *** If pname:xChromaOffset is ename:VK_CHROMA_LOCATION_MIDPOINT: + [latexmath] +++++ \tau_{RB}'(i,j) = \begin{cases} 0.25 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor - 1,j)[level] + \\ 0.75 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\ 0.75 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level] + \\ 0.25 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases} +++++ ** If the format's R and B components are reduced in resolution in width and height by a factor of two relative to the G component (i.e. this is a "`etext:_420`" format), a similar relationship applies. Due to the number of options, these formulae are expressed more concisely as follows: + [latexmath] +++++ \begin{aligned} i_{RB} & = \begin{cases} 0.5 \times (i) & \textrm{xChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5 \times (i - 0.5) & \textrm{xChromaOffset = MIDPOINT} \end{cases}\\ j_{RB} & = \begin{cases} 0.5 \times (j) & \textrm{yChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5 \times (j - 0.5) & \textrm{yChromaOffset = MIDPOINT} \end{cases}\\ \\ i_{floor} & = \left\lfloor i_{RB} \right\rfloor \\ j_{floor} & = \left\lfloor j_{RB} \right\rfloor \\ \\ i_{frac} & = i_{RB} - i_{floor} \\ j_{frac} & = j_{RB} - j_{floor} \end{aligned} +++++ + [latexmath] +++++ \begin{aligned} \tau_{RB}'(i,j) = & \tau_{RB}( i_{floor}, j_{floor})[level] & \times & ( 1 - i_{frac} ) & & \times & ( 1 - j_{frac} ) & + \\ & \tau_{RB}( 1 + i_{floor}, j_{floor})[level] & \times & ( i_{frac} ) & & \times & ( 1 - j_{frac} ) & + \\ & \tau_{RB}( i_{floor}, 1 + j_{floor})[level] & \times & ( 1 - i_{frac} ) & & \times & ( j_{frac} ) & + \\ & \tau_{RB}( 1 + i_{floor}, 1 + j_{floor})[level] & \times & ( i_{frac} ) & & \times & ( j_{frac} ) & \end{aligned} +++++ [NOTE] .Note ==== In the case where the texture itself is bilinearly interpolated as described in <>, thus requiring four full-color samples for the filtering operation, and where the reconstruction of these samples uses bilinear interpolation in the chroma components due to pname:chromaFilter=ename:VK_FILTER_LINEAR, up to nine chroma samples may be required, depending on the sample location. ==== [[textures-implict-reconstruction]] ==== Implicit Reconstruction Implicit reconstruction takes place by the samples being interpolated, as required by the filter settings of the sampler, except that pname:chromaFilter takes precedence for the chroma samples. If pname:chromaFilter is ename:VK_FILTER_NEAREST, an implementation may: behave as if pname:xChromaOffset and pname:yChromaOffset were both ename:VK_CHROMA_LOCATION_MIDPOINT, irrespective of the values set. [NOTE] .Note ==== This will not have any visible effect if the locations of the luma samples coincide with the location of the samples used for rasterization. ==== The sample coordinates are adjusted by the downsample factor of the component (such that, for example, the sample coordinates are divided by two if the component has a downsample factor of two relative to the luma component): [latexmath] ++++++ \begin{aligned} u_{RB}' (422/420) &= \begin{cases} 0.5\times (u + 0.5), & \textrm{xChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5\times u, & \textrm{xChromaOffset = MIDPOINT} \end{cases} \\ v_{RB}' (420) &= \begin{cases} 0.5\times (v + 0.5), & \textrm{yChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5\times v, & \textrm{yChromaOffset = MIDPOINT} \end{cases} \end{aligned} ++++++ [[textures-sampler-YCbCr-conversion]] === Sampler {YCbCr} Conversion Sampler {YCbCr} conversion performs the following operations, which an implementation may: combine into a single mathematical operation: * <> * <> [[textures-sampler-YCbCr-conversion-rangeexpand]] ==== Sampler {YCbCr} Range Expansion Sampler {YCbCr} range expansion is applied to color component values after all texel input operations which are not specific to sampler {YCbCr} conversion. For example, the input values to this stage have been converted using the normal <> rules. Sampler {YCbCr} range expansion is not applied if pname:ycbcrModel is ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY. That is, the shader receives the vector C'~rgba~ as output by the Component Swizzle stage without further modification. For other values of pname:ycbcrModel, range expansion is applied to the texel component values output by the <> defined by the pname:components member of slink:VkSamplerYcbcrConversionCreateInfo. Range expansion applies independently to each component of the image. For the purposes of range expansion and {YCbCr} model conversion, the R and B components contain color difference (chroma) values and the G component contains luma. The A component is not modified by sampler {YCbCr} range expansion. The range expansion to be applied is defined by the pname:ycbcrRange member of the slink:VkSamplerYcbcrConversionCreateInfo structure: * If pname:ycbcrRange is ename:VK_SAMPLER_YCBCR_RANGE_ITU_FULL, the following transformations are applied: + [latexmath] +++++++++++++++++++ \begin{aligned} Y' &= C'_{rgba}[G] \\ C_B &= C'_{rgba}[B] - {{2^{(n-1)}}\over{(2^n) - 1}} \\ C_R &= C'_{rgba}[R] - {{2^{(n-1)}}\over{(2^n) - 1}} \end{aligned} +++++++++++++++++++ + [NOTE] .Note ==== These formulae correspond to the "`full range`" encoding in the "`Quantization schemes`" chapter of the <>. Should any future amendments be made to the ITU specifications from which these equations are derived, the formulae used by Vulkan may: also be updated to maintain parity. ==== * If pname:ycbcrRange is ename:VK_SAMPLER_YCBCR_RANGE_ITU_NARROW, the following transformations are applied: + [latexmath] +++++++++++++++++++ \begin{aligned} Y' &= {{C'_{rgba}[G] \times (2^n-1) - 16\times 2^{n-8}}\over{219\times 2^{n-8}}} \\ C_B &= {{C'_{rgba}[B] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \\ C_R &= {{C'_{rgba}[R] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \end{aligned} +++++++++++++++++++ + [NOTE] .Note ==== These formulae correspond to the "`narrow range`" encoding in the "`Quantization schemes`" chapter of the <>. ==== * _n_ is the bit-depth of the components in the format. The precision of the operations performed during range expansion must: be at least that of the source format. An implementation may: clamp the results of these range expansion operations such that Y{prime} falls in the range [0,1], and/or such that C~B~ and C~R~ fall in the range [-0.5,0.5]. [[textures-sampler-YCbCr-conversion-modelconversion]] ==== Sampler {YCbCr} Model Conversion The range-expanded values are converted between color models, according to the color model conversion specified in the pname:ycbcrModel member: ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY:: The color components are not modified by the color model conversion since they are assumed already to represent the desired color model in which the shader is operating; {YCbCr} range expansion is also ignored. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_IDENTITY:: The color components are not modified by the color model conversion and are assumed to be treated as though in {YCbCr} form both in memory and in the shader; {YCbCr} range expansion is applied to the components as for other {YCbCr} models, with the vector (C~R~,Y{prime},C~B~,A) provided to the shader. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_709:: The color components are transformed from a {YCbCr} representation to an {RGBprime} representation as described in the "`BT.709 {YCbCr} conversion`" section of the <>. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_601:: The color components are transformed from a {YCbCr} representation to an {RGBprime} representation as described in the "`BT.601 {YCbCr} conversion`" section of the <>. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_2020:: The color components are transformed from a {YCbCr} representation to an {RGBprime} representation as described in the "`BT.2020 {YCbCr} conversion`" section of the <>. In this operation, each output component is dependent on each input component. An implementation may: clamp the {RGBprime} results of these conversions to the range [0,1]. The precision of the operations performed during model conversion must: be at least that of the source format. The alpha component is not modified by these model conversions. [NOTE] .Note ==== Sampling operations in a non-linear color space can introduce color and intensity shifts at sharp transition boundaries. To avoid this issue, the technically precise color correction sequence described in the "`Introduction to Color Conversions`" chapter of the <> may be performed as follows: * Calculate the <> corresponding to the desired sample position. * For a pname:minFilter or pname:magFilter of ename:VK_FILTER_NEAREST: . Calculate (_i_,_j_) for the sample location as described under the "`nearest filtering`" formulae in <> . Calculate the normalized texel coordinates corresponding to these integer coordinates. . Sample using <> at this location. * For a pname:minFilter or pname:magFilter of ename:VK_FILTER_LINEAR: . Calculate (_i~[0,1]~_,_j~[0,1]~_) for the sample location as described under the "`linear filtering`" formulae in <> . Calculate the normalized texel coordinates corresponding to these integer coordinates. . Sample using <> at each of these locations. . Convert the non-linear A{prime}{RGBprime} outputs of the {YCbCr} conversions to linear ARGB values as described in the "`Transfer Functions`" chapter of the <>. . Interpolate the linear ARGB values using the [eq]#{alpha}# and [eq]#{beta}# values described in the "`linear filtering`" section of <> and the equations in <>. The additional calculations and, especially, additional number of sampling operations in the ename:VK_FILTER_LINEAR case can be expected to have a performance impact compared with using the outputs directly. Since the variations from "`correct`" results are subtle for most content, the application author should determine whether a more costly implementation is strictly necessary. If pname:chromaFilter, and pname:minFilter or pname:magFilter are both ename:VK_FILTER_NEAREST, these operations are redundant and sampling using <> at the desired sample coordinates will produce the "`correct`" results without further processing. ==== endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] == Texel Output Operations _Texel output instructions_ are SPIR-V image instructions that write to an image. _Texel output operations_ are a set of steps that are performed on state, coordinates, and texel values while processing a texel output instruction, and which are common to some or all texel output instructions. They include the following steps, which are performed in the listed order: * <> ** <> ** <> ** <> ** <> * <> [[textures-output-validation]] === Texel Output Validation Operations _Texel output validation operations_ inspect instruction/image state or coordinates, and in certain circumstances cause the write to have no effect. There are a series of validations that the texel undergoes. [[textures-format-validation]] ==== Texel Format Validation If the image format of the code:OpTypeImage is not <> with the sname:VkImageView's pname:format, the write causes the contents of the image's memory to become undefined:. [[textures-type-validation]] ==== Texel Type Validation If the code:Sampled code:Type of the code:OpTypeImage does not match the type defined for the format, as specified in the _SPIR-V Sampled Type_ column of the <> table, the write causes the value of the texel to become undefined:. For integer types, if the <> does not match the signedness of the accessed resource, the write causes the value of the texel to become undefined:. [[textures-output-coordinate-validation]] === Integer Texel Coordinate Validation The integer texel coordinates are validated according to the same rules as for texel input <>. If the texel fails integer texel coordinate validation, then the write has no effect. [[textures-output-sparse-validation]] === Sparse Texel Operation If the texel attempts to write to an unbound region of a sparse image, the texel is a sparse unbound texel. In such a case, if the slink:VkPhysicalDeviceSparseProperties::pname:residencyNonResidentStrict property is ename:VK_TRUE, the sparse unbound texel write has no effect. If pname:residencyNonResidentStrict is ename:VK_FALSE, the write may: have a side effect that becomes visible to other accesses to unbound texels in any resource, but will not be visible to any device memory allocated by the application. [[textures-output-format-conversion]] === Texel Output Format Conversion If the image format is sRGB, a linear to sRGB conversion is applied to the R, G, and B components as described in the "`sRGB EOTF`" section of the <>. The A component, if present, is unchanged. Texels then undergo a format conversion from the floating point, signed, or unsigned integer type of the texel data to the elink:VkFormat of the image view. Any unused components are ignored. Each component is converted based on its type and size (as defined in the <> section for each elink:VkFormat). Floating-point outputs are converted as described in <> and <>. Integer outputs are converted such that their value is preserved. The converted value of any integer that cannot be represented in the target format is undefined:. [[textures-normalized-operations]] == Normalized Texel Coordinate Operations If the image sampler instruction provides normalized texel coordinates, some of the following operations are performed. [[textures-projection]] === Projection Operation For code:Proj image operations, the normalized texel coordinates [eq]#(s,t,r,q,a)# and (if present) the [eq]#D~ref~# coordinate are transformed as follows: [latexmath] +++++++++++++++++++ \begin{aligned} s & = \frac{s}{q}, & \text{for 1D, 2D, or 3D image} \\ \\ t & = \frac{t}{q}, & \text{for 2D or 3D image} \\ \\ r & = \frac{r}{q}, & \text{for 3D image} \\ \\ D_{\textit{ref}} & = \frac{D_{\textit{ref}}}{q}, & \text{if provided} \end{aligned} +++++++++++++++++++ [[textures-derivative-image-operations]] === Derivative Image Operations Derivatives are used for LOD selection. These derivatives are either implicit (in an code:ImplicitLod image instruction in a fragment shader) or explicit (provided explicitly by shader to the image instruction in any shader). For implicit derivatives image instructions, the derivatives of texel coordinates are calculated in the same manner as <>. That is: [latexmath] +++++++++++++++++++ \begin{aligned} \partial{s}/\partial{x} & = dPdx(s), & \partial{s}/\partial{y} & = dPdy(s), & \text{for 1D, 2D, Cube, or 3D image} \\ \partial{t}/\partial{x} & = dPdx(t), & \partial{t}/\partial{y} & = dPdy(t), & \text{for 2D, Cube, or 3D image} \\ \partial{r}/\partial{x} & = dPdx(r), & \partial{r}/\partial{y} & = dPdy(r), & \text{for Cube or 3D image} \end{aligned} +++++++++++++++++++ Partial derivatives not defined above for certain image dimensionalities are set to zero. For explicit LOD image instructions, if the optional: SPIR-V operand code:Grad is provided, then the operand values are used for the derivatives. The number of components present in each derivative for a given image dimensionality matches the number of partial derivatives computed above. If the optional: SPIR-V operand code:Lod is provided, then derivatives are set to zero, the cube map derivative transformation is skipped, and the scale factor operation is skipped. Instead, the floating point scalar coordinate is directly assigned to [eq]#{lambda}~base~# as described in <>. ifdef::VK_VERSION_1_2,VK_EXT_descriptor_indexing[] If the image or sampler object used by an implicit derivative image instruction is not uniform across the quad and <> is not supported, then the derivative and LOD values are undefined:. Implicit derivatives are well-defined when the image and sampler and control flow are uniform across the quad, even if they diverge between different quads. If <> is supported, then derivatives and implicit LOD values are well-defined even if the image or sampler object are not uniform within a quad. The derivatives are computed as specified above, and the implicit LOD calculation proceeds for each shader invocation using its respective image and sampler object. endif::VK_VERSION_1_2,VK_EXT_descriptor_indexing[] === Cube Map Face Selection and Transformations For cube map image instructions, the [eq]#(s,t,r)# coordinates are treated as a direction vector [eq]#(r~x~,r~y~,r~z~)#. The direction vector is used to select a cube map face. The direction vector is transformed to a per-face texel coordinate system [eq]#(s~face~,t~face~)#, The direction vector is also used to transform the derivatives to per-face derivatives. === Cube Map Face Selection The direction vector selects one of the cube map's faces based on the largest magnitude coordinate direction (the major axis direction). Since two or more coordinates can: have identical magnitude, the implementation must: have rules to disambiguate this situation. The rules should: have as the first rule that [eq]#r~z~# wins over [eq]#r~y~# and [eq]#r~x~#, and the second rule that [eq]#r~y~# wins over [eq]#r~x~#. An implementation may: choose other rules, but the rules must: be deterministic and depend only on [eq]#(r~x~,r~y~,r~z~)#. The layer number (corresponding to a cube map face), the coordinate selections for [eq]#s~c~#, [eq]#t~c~#, [eq]#r~c~#, and the selection of derivatives, are determined by the major axis direction as specified in the following two tables. .Cube map face and coordinate selection [width="75%",frame="all",options="header"] |==== | Major Axis Direction | Layer Number | Cube Map Face | [eq]#s~c~# | [eq]#t~c~# | [eq]#r~c~# | [eq]#+r~x~# | [eq]#0# | Positive X | [eq]#-r~z~# | [eq]#-r~y~# | [eq]#r~x~# | [eq]#-r~x~# | [eq]#1# | Negative X | [eq]#+r~z~# | [eq]#-r~y~# | [eq]#r~x~# | [eq]#+r~y~# | [eq]#2# | Positive Y | [eq]#+r~x~# | [eq]#+r~z~# | [eq]#r~y~# | [eq]#-r~y~# | [eq]#3# | Negative Y | [eq]#+r~x~# | [eq]#-r~z~# | [eq]#r~y~# | [eq]#+r~z~# | [eq]#4# | Positive Z | [eq]#+r~x~# | [eq]#-r~y~# | [eq]#r~z~# | [eq]#-r~z~# | [eq]#5# | Negative Z | [eq]#-r~x~# | [eq]#-r~y~# | [eq]#r~z~# |==== .Cube map derivative selection [width="75%",frame="all",options="header"] |==== | Major Axis Direction | [eq]#{partial}s~c~ / {partial}x# | [eq]#{partial}s~c~ / {partial}y# | [eq]#{partial}t~c~ / {partial}x# | [eq]#{partial}t~c~ / {partial}y# | [eq]#{partial}r~c~ / {partial}x# | [eq]#{partial}r~c~ / {partial}y# | [eq]#+r~x~# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-r~x~# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#-{partial}r~x~ / {partial}x# | [eq]#-{partial}r~x~ / {partial}y# | [eq]#+r~y~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#+{partial}r~y~ / {partial}x# | [eq]#+{partial}r~y~ / {partial}y# | [eq]#-r~y~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+r~z~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#-r~z~# | [eq]#-{partial}r~x~ / {partial}x# | [eq]#-{partial}r~x~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# |==== === Cube Map Coordinate Transformation [latexmath] ++++++++++++++++++++++++ \begin{aligned} s_{\textit{face}} & = \frac{1}{2} \times \frac{s_c}{|r_c|} + \frac{1}{2} \\ t_{\textit{face}} & = \frac{1}{2} \times \frac{t_c}{|r_c|} + \frac{1}{2} \\ \end{aligned} ++++++++++++++++++++++++ === Cube Map Derivative Transformation [latexmath] ++++++++++++++++++++++++ \begin{aligned} \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{\partial}{\partial{x}} \left ( \frac{1}{2} \times \frac{s_{c}}{|r_{c}|} + \frac{1}{2}\right ) \\ \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \frac{\partial}{\partial{x}} \left ( \frac{s_{c}}{|r_{c}|} \right ) \\ \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{s_c}/\partial{x} -s_c \times {\partial{r_{c}}}/{\partial{x}}} {\left ( r_{c} \right )^2} \right ) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \frac{\partial{s_{\textit{face}}}}{\partial{y}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{s_c}/\partial{y} -s_c \times {\partial{r_{c}}}/{\partial{y}}} {\left ( r_{c} \right )^2} \right )\\ \frac{\partial{t_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{t_c}/\partial{x} -t_c \times {\partial{r_{c}}}/{\partial{x}}} {\left ( r_{c} \right )^2} \right ) \\ \frac{\partial{t_{\textit{face}}}}{\partial{y}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{t_c}/\partial{y} -t_c \times {\partial{r_{c}}}/{\partial{y}}} {\left ( r_{c} \right )^2} \right ) \end{aligned} ++++++++++++++++++++++++ ifdef::editing-notes[] [NOTE] .editing-note ==== (Bill) Note that we never revisited ARB_texture_cubemap after we introduced dependent texture fetches (ARB_fragment_program and ARB_fragment_shader). The derivatives of [eq]#s~face~# and [eq]#t~face~# are only valid for non-dependent texture fetches (pre OpenGL 2.0). ==== endif::editing-notes[] [[textures-lod-and-scale-factor]] === Scale Factor Operation, Level-of-Detail Operation and Image Level(s) Selection LOD selection can: be either explicit (provided explicitly by the image instruction) or implicit (determined from a scale factor calculated from the derivatives). The LOD must: be computed with pname:mipmapPrecisionBits of accuracy. [[textures-scale-factor]] ==== Scale Factor Operation The magnitude of the derivatives are calculated by: {empty}:: [eq]#m~ux~ = {vert}{partial}s/{partial}x{vert} {times} w~base~# {empty}:: [eq]#m~vx~ = {vert}{partial}t/{partial}x{vert} {times} h~base~# {empty}:: [eq]#m~wx~ = {vert}{partial}r/{partial}x{vert} {times} d~base~# {empty}:: [eq]#m~uy~ = {vert}{partial}s/{partial}y{vert} {times} w~base~# {empty}:: [eq]#m~vy~ = {vert}{partial}t/{partial}y{vert} {times} h~base~# {empty}:: [eq]#m~wy~ = {vert}{partial}r/{partial}y{vert} {times} d~base~# where: {empty}:: [eq]#{partial}t/{partial}x = {partial}t/{partial}y = 0# (for 1D images) {empty}:: [eq]#{partial}r/{partial}x = {partial}r/{partial}y = 0# (for 1D, 2D or Cube images) and: {empty}:: [eq]#w~base~ = image.w# {empty}:: [eq]#h~base~ = image.h# {empty}:: [eq]#d~base~ = image.d# (for the pname:baseMipLevel, from the image descriptor). ifdef::VK_NV_corner_sampled_image[] For corner-sampled images, the [eq]#w~base~#, [eq]#h~base~#, and [eq]#d~base~# are instead: {empty}:: [eq]#w~base~ = image.w - 1# {empty}:: [eq]#h~base~ = image.h - 1# {empty}:: [eq]#d~base~ = image.d - 1# endif::VK_NV_corner_sampled_image[] A point sampled in screen space has an elliptical footprint in texture space. The minimum and maximum scale factors [eq]#({rho}~min~, {rho}~max~)# should: be the minor and major axes of this ellipse. The _scale factors_ [eq]#{rho}~x~# and [eq]#{rho}~y~#, calculated from the magnitude of the derivatives in x and y, are used to compute the minimum and maximum scale factors. [eq]#{rho}~x~# and [eq]#{rho}~y~# may: be approximated with functions [eq]#f~x~# and [eq]#f~y~#, subject to the following constraints: [latexmath] ++++++++++++++++++++++++ \begin{aligned} & f_x \text{\ is\ continuous\ and\ monotonically\ increasing\ in\ each\ of\ } m_{ux}, m_{vx}, \text{\ and\ } m_{wx} \\ & f_y \text{\ is\ continuous\ and\ monotonically\ increasing\ in\ each\ of\ } m_{uy}, m_{vy}, \text{\ and\ } m_{wy} \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \max(|m_{ux}|, |m_{vx}|, |m_{wx}|) \leq f_{x} \leq \sqrt{2} (|m_{ux}| + |m_{vx}| + |m_{wx}|) \\ \max(|m_{uy}|, |m_{vy}|, |m_{wy}|) \leq f_{y} \leq \sqrt{2} (|m_{uy}| + |m_{vy}| + |m_{wy}|) \end{aligned} ++++++++++++++++++++++++ ifdef::editing-notes[] [NOTE] .editing-note ==== (Bill) For reviewers only - anticipating questions. We only support implicit derivatives for normalized texel coordinates. So we are documenting the derivatives in s,t,r (normalized texel coordinates) rather than u,v,w (unnormalized texel coordinates) as in OpenGL and OpenGL ES specifications. (I know, u,v,w is the way it has been documented since OpenGL V1.0.) Also there is no reason to have conditional application of [eq]#w~base~, h~base~, d~base~# for rectangle textures either, since they do not support implicit derivatives. ==== endif::editing-notes[] The minimum and maximum scale factors [eq]#({rho}~min~,{rho}~max~)# are determined by: {empty}:: [eq]#{rho}~max~ = max({rho}~x~, {rho}~y~)# {empty}:: [eq]#{rho}~min~ = min({rho}~x~, {rho}~y~)# The ratio of anisotropy is determined by: {empty}:: [eq]#{eta} = min({rho}~max~/{rho}~min~, max~Aniso~)# where: {empty}:: [eq]#sampler.max~Aniso~ = pname:maxAnisotropy# (from sampler descriptor) {empty}:: [eq]#limits.max~Aniso~ = pname:maxSamplerAnisotropy# (from physical device limits) {empty}:: [eq]#max~Aniso~ = min(sampler.max~Aniso~, limits.max~Aniso~)# If [eq]#{rho}~max~ = {rho}~min~ = 0#, then all the partial derivatives are zero, the fragment's footprint in texel space is a point, and [eq]#{eta}# should: be treated as 1. If [eq]#{rho}~max~ {neq} 0# and [eq]#{rho}~min~ = 0# then all partial derivatives along one axis are zero, the fragment's footprint in texel space is a line segment, and [eq]#{eta}# should: be treated as [eq]#max~Aniso~#. However, anytime the footprint is small in texel space the implementation may: use a smaller value of [eq]#{eta}#, even when [eq]#{rho}~min~# is zero or close to zero. If either slink:VkPhysicalDeviceFeatures::pname:samplerAnisotropy or slink:VkSamplerCreateInfo::pname:anisotropyEnable are ename:VK_FALSE, [eq]#max~Aniso~# is set to 1. If [eq]#{eta} = 1#, sampling is isotropic. If [eq]#{eta} > 1#, sampling is anisotropic. The sampling rate ([eq]#N#) is derived as: {empty}:: [eq]#N = {lceil}{eta}{rceil}# An implementation may: round [eq]#N# up to the nearest supported sampling rate. An implementation may: use the value of [eq]#N# as an approximation of [eq]#{eta}#. [[textures-level-of-detail-operation]] ==== Level-of-Detail Operation The LOD parameter [eq]#{lambda}# is computed as follows: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \lambda_{base}(x,y) & = \begin{cases} shaderOp.Lod & \text{(from optional SPIR-V operand)} \\ \log_2 \left ( \frac{\rho_{max}}{\eta} \right ) & \text{otherwise} \end{cases} \\ \lambda'(x,y) & = \lambda_{base} + \mathbin{clamp}(sampler.bias + shaderOp.bias,-maxSamplerLodBias,maxSamplerLodBias) \\ \lambda & = \begin{cases} lod_{max}, & \lambda' > lod_{max} \\ \lambda', & lod_{min} \leq \lambda' \leq lod_{max} \\ lod_{min}, & \lambda' < lod_{min} \\ \textit{undefined}, & lod_{min} > lod_{max} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} sampler.bias & = mipLodBias & \text{(from sampler descriptor)} \\ shaderOp.bias & = \begin{cases} Bias & \text{(from optional SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ sampler.lod_{min} & = minLod & \text{(from sampler descriptor)} \\ shaderOp.lod_{min} & = \begin{cases} MinLod & \text{(from optional SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ \\ lod_{min} & = \max(sampler.lod_{min}, shaderOp.lod_{min}) \\ lod_{max} & = maxLod & \text{(from sampler descriptor)} \end{aligned} ++++++++++++++++++++++++ and [eq]#maxSamplerLodBias# is the value of the slink:VkPhysicalDeviceLimits feature <>. [[textures-image-level-selection]] ==== Image Level(s) Selection The image level(s) [eq]#d#, [eq]#d~hi~#, and [eq]#d~lo~# which texels are read from are determined by an image-level parameter [eq]#d~l~#, which is computed based on the LOD parameter, as follows: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d_{l} = \begin{cases} nearest(d'), & \text{mipmapMode is VK\_SAMPLER\_MIPMAP\_MODE\_NEAREST} \\ d', & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} ifdef::VK_EXT_image_view_min_lod[] d' = max(level_{base} + \text{clamp}(\lambda, 0, q), minLod_{imageView}) endif::VK_EXT_image_view_min_lod[] ifndef::VK_EXT_image_view_min_lod[] d' = level_{base} + \text{clamp}(\lambda, 0, q) endif::VK_EXT_image_view_min_lod[] \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} nearest(d') & = \begin{cases} \left \lceil d' + 0.5\right \rceil - 1, & \text{preferred} \\ \left \lfloor d' + 0.5\right \rfloor, & \text{alternative} \end{cases} \end{aligned} ++++++++++++++++++++++++ and: ifdef::VK_EXT_image_view_min_lod[] {empty}:: [eq]#minLod~imageView~ = pname:minLod# endif::VK_EXT_image_view_min_lod[] {empty}:: [eq]#level~base~ = pname:baseMipLevel# {empty}:: [eq]#q = pname:levelCount - 1# pname:baseMipLevel and pname:levelCount are taken from the pname:subresourceRange of the image view. ifdef::VK_EXT_image_view_min_lod[] pname:minLod is taken from the slink:VkImageViewMinLodCreateInfoEXT::pname:minLod of the image view if present and the selection is part of the result of a sampling operation, otherwise it is `0.0`. pname:minLod must: be less or equal to [eq]#level~base~ + q#. endif::VK_EXT_image_view_min_lod[] If the sampler's pname:mipmapMode is ename:VK_SAMPLER_MIPMAP_MODE_NEAREST, then the level selected is [eq]#d = d~l~#. If the sampler's pname:mipmapMode is ename:VK_SAMPLER_MIPMAP_MODE_LINEAR, two neighboring levels are selected: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d_{hi} & = \left\lfloor d_{l} \right\rfloor \\ d_{lo} & = min( d_{hi} + 1, q ) \\ \delta & = d_{l} - d_{hi} \end{aligned} ++++++++++++++++++++++++ [eq]#{delta}# is the fractional value, quantized to the number of <>, used for <> between levels. [[textures-normalized-to-unnormalized]] === (s,t,r,q,a) to (u,v,w,a) Transformation The normalized texel coordinates are scaled by the image level dimensions and the array layer is selected. This transformation is performed once for each level used in <> (either [eq]#d#, or [eq]#d~hi~# and [eq]#d~lo~#). [latexmath] ++++++++++++++++++++++++ \begin{aligned} u(x,y) & = s(x,y) \times width_{scale} + \Delta_i\\ v(x,y) & = \begin{cases} 0 & \text{for 1D images} \\ t(x,y) \times height_{scale} + \Delta_j & \text{otherwise} \end{cases} \\ w(x,y) & = \begin{cases} 0 & \text{for 2D or Cube images} \\ r(x,y) \times depth_{scale} + \Delta_k & \text{otherwise} \end{cases} \\ \\ a(x,y) & = \begin{cases} a(x,y) & \text{for array images} \\ 0 & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: {empty}:: [eq]#width~scale~ = width~level~# {empty}:: [eq]#height~scale~ = height~level~# {empty}:: [eq]#depth~scale~ = depth~level~# ifdef::VK_NV_corner_sampled_image[] for conventional images, and: {empty}:: [eq]#width~scale~ = width~level~ - 1# {empty}:: [eq]#height~scale~ = height~level~ - 1# {empty}:: [eq]#depth~scale~ = depth~level~ - 1# for corner-sampled images. endif::VK_NV_corner_sampled_image[] and where [eq]#({DeltaUpper}~i~, {DeltaUpper}~j~, {DeltaUpper}~k~)# are taken from the image instruction if it includes a code:ConstOffset or code:Offset operand, otherwise they are taken to be zero. Operations then proceed to Unnormalized Texel Coordinate Operations. == Unnormalized Texel Coordinate Operations [[textures-unnormalized-to-integer]] === (u,v,w,a) to (i,j,k,l,n) Transformation And Array Layer Selection The unnormalized texel coordinates are transformed to integer texel coordinates relative to the selected mipmap level. The layer index [eq]#l# is computed as: {empty}:: [eq]#l = clamp(RNE(a), 0, pname:layerCount - 1) {plus} pname:baseArrayLayer# where pname:layerCount is the number of layers in the image subresource range of the image view, pname:baseArrayLayer is the first layer from the subresource range, and where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \mathbin{RNE}(a) & = \begin{cases} \mathbin{roundTiesToEven}(a) & \text{preferred, from IEEE Std 754-2008 Floating-Point Arithmetic} \\ \left \lfloor a + 0.5 \right \rfloor & \text{alternative} \end{cases} \end{aligned} ++++++++++++++++++++++++ The sample index [eq]#n# is assigned the value 0. Nearest filtering (ename:VK_FILTER_NEAREST) computes the integer texel coordinates that the unnormalized coordinates lie within: [latexmath] ++++++++++++++++++++++++ \begin{aligned} i &= \left\lfloor u + shift \right\rfloor \\ j &= \left\lfloor v + shift \right\rfloor \\ k &= \left\lfloor w + shift \right\rfloor \end{aligned} ++++++++++++++++++++++++ where: {empty}:: [eq]#shift = 0.0# ifdef::VK_NV_corner_sampled_image[] for conventional images, and: {empty}:: [eq]#shift = 0.5# for corner-sampled images. endif::VK_NV_corner_sampled_image[] Linear filtering (ename:VK_FILTER_LINEAR) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of [eq]#i~0~# or [eq]#i~1~#, [eq]#j~0~# or [eq]#j~1~#, [eq]#k~0~# or [eq]#k~1~#, as well as weights [eq]#{alpha}, {beta}#, and [eq]#{gamma}#. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_0 &= \left\lfloor u - shift \right\rfloor \\ i_1 &= i_0 + 1 \\ j_0 &= \left\lfloor v - shift \right\rfloor \\ j_1 &= j_0 + 1 \\ k_0 &= \left\lfloor w - shift \right\rfloor \\ k_1 &= k_0 + 1 \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \alpha &= \mathbin{frac}\left(u - shift\right) \\[1em] \beta &= \mathbin{frac}\left(v - shift\right) \\[1em] \gamma &= \mathbin{frac}\left(w - shift\right) \end{aligned} ++++++++++++++++++++++++ where: {empty}:: [eq]#shift = 0.5# ifdef::VK_NV_corner_sampled_image[] for conventional images, and: {empty}:: [eq]#shift = 0.0# for corner-sampled images, endif::VK_NV_corner_sampled_image[] and where: [latexmath] ++++++++++++++++++++++++ \mathbin{frac}(x) = x - \left\lfloor x \right\rfloor ++++++++++++++++++++++++ where the number of fraction bits retained is specified by sname:VkPhysicalDeviceLimits::pname:subTexelPrecisionBits. ifdef::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] Cubic filtering (ename:VK_FILTER_CUBIC_EXT) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of [eq]#i~0~#, [eq]#i~1~#, [eq]#i~2~# or [eq]#i~3~#, [eq]#j~0~#, [eq]#j~1~#, [eq]#j~2~# or [eq]#j~3~#, ifndef::VK_EXT_filter_cubic[] as well as weights [eq]#{alpha}# and [eq]#{beta}#. endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] [eq]#k~0~#, [eq]#k~1~#, [eq]#k~2~# or [eq]#k~3~#, as well as weights [eq]#{alpha}#, [eq]#{beta}#, and [eq]#{gamma}#. endif::VK_EXT_filter_cubic[] ifndef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} & = {\left \lfloor {u - \frac{3}{2}} \right \rfloor} & i_{1} & = i_{0} + 1 & i_{2} & = i_{1} + 1 & i_{3} & = i_{2} + 1 \\[1em] j_{0} & = {\left \lfloor {v - \frac{3}{2}} \right \rfloor} & j_{1} & = j_{0} + 1 & j_{2} & = j_{1} + 1 & j_{3} & = j_{2} + 1 \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} alpha &= \mathbin{frac}\left(u - \frac{1}{2}\right) \\[1em] \beta &= \mathbin{frac}\left(v - \frac{1}{2}\right) \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} & = {\left \lfloor {u - \frac{3}{2}} \right \rfloor} & i_{1} & = i_{0} + 1 & i_{2} & = i_{1} + 1 & i_{3} & = i_{2} + 1 \\[1em] j_{0} & = {\left \lfloor {v - \frac{3}{2}} \right \rfloor} & j_{1} & = j_{0} + 1 & j_{2} & = j_{1} + 1 & j_{3} & = j_{2} + 1 \\[1em] k_{0} & = {\left \lfloor {w - \frac{3}{2}} \right \rfloor} & k_{1} & = k_{0} + 1 & k_{2} & = k_{1} + 1 & k_{3} & = k_{2} + 1 \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \alpha &= \mathbin{frac}\left(u - \frac{1}{2}\right) \\[1em] \beta &= \mathbin{frac}\left(v - \frac{1}{2}\right) \\[1em] \gamma &= \mathbin{frac}\left(w - \frac{1}{2}\right) \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_filter_cubic[] where: [latexmath] ++++++++++++++++++++++++ \mathbin{frac}(x) = x - \left\lfloor x \right\rfloor ++++++++++++++++++++++++ where the number of fraction bits retained is specified by sname:VkPhysicalDeviceLimits::pname:subTexelPrecisionBits. endif::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] [[textures-integer-coordinate-operations]] == Integer Texel Coordinate Operations ifdef::VK_AMD_shader_image_load_store_lod[] Integer texel coordinate operations may: supply a LOD which texels are to be read from or written to using the optional SPIR-V operand code:Lod. endif::VK_AMD_shader_image_load_store_lod[] ifndef::VK_AMD_shader_image_load_store_lod[] The code:OpImageFetch and code:OpImageFetchSparse SPIR-V instructions may: supply a LOD from which texels are to be fetched using the optional SPIR-V operand code:Lod. Other integer-coordinate operations must: not. endif::VK_AMD_shader_image_load_store_lod[] If the code:Lod is provided then it must: be an integer. The image level selected is: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d & = level_{base} + \begin{cases} Lod & \text{(from optional SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ \end{aligned} ++++++++++++++++++++++++ If [eq]#d# does not lie in the range [eq]#[pname:baseMipLevel, pname:baseMipLevel {plus} pname:levelCount)# ifdef::VK_EXT_image_view_min_lod[] or [eq]#d# is less than minLodInteger~imageView~, endif::VK_EXT_image_view_min_lod[] then any values fetched are ifdef::VK_EXT_robustness2[] zero if <> is enabled, otherwise are endif::VK_EXT_robustness2[] undefined:, and any writes (if supported) are discarded. ifdef::VK_EXT_image_view_min_lod[] where: [eq]#minLodInteger~imageView~ = {lfloor}pname:minLod{rfloor}# pname:minLod is taken from the slink:VkImageViewMinLodCreateInfoEXT::pname:minLod of the image view if present and the selection is part of the result of a sampling operation, otherwise it is `0.0`. If the integer texel operation is not a sampling operation, the image view parameter is ignored, and pname:minLod is `0.0`. endif::VK_EXT_image_view_min_lod[] [[textures-sample-operations]] == Image Sample Operations [[textures-wrapping-operation]] === Wrapping Operation code:Cube images ignore the wrap modes specified in the sampler. Instead, if ename:VK_FILTER_NEAREST is used within a mip level then ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE is used, and if ename:VK_FILTER_LINEAR is used within a mip level then sampling at the edges is performed as described earlier in the <> section. The first integer texel coordinate i is transformed based on the pname:addressModeU parameter of the sampler. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i &= \begin{cases} i \bmod size & \text{for repeat} \\ (size - 1) - \mathbin{mirror} ((i \bmod (2 \times size)) - size) & \text{for mirrored repeat} \\ \mathbin{clamp}(i,0,size-1) & \text{for clamp to edge} \\ \mathbin{clamp}(i,-1,size) & \text{for clamp to border} \\ \mathbin{clamp}(\mathbin{mirror}(i),0,size-1) & \text{for mirror clamp to edge} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} & \mathbin{mirror}(n) = \begin{cases} n & \text{for}\ n \geq 0 \\ -(1+n) & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ [eq]#j# (for 2D and Cube image) and [eq]#k# (for 3D image) are similarly transformed based on the pname:addressModeV and pname:addressModeW parameters of the sampler, respectively. [[textures-gather]] === Texel Gathering SPIR-V instructions with code:Gather in the name return a vector derived from 4 texels in the base level of the image view. The rules for the ename:VK_FILTER_LINEAR minification filter are applied to identify the four selected texels. Each texel is then converted to an RGBA value according to <> and then <>. A four-component vector is then assembled by taking the component indicated by the code:Component value in the instruction from the swizzled color value of the four texels. If the operation does not use the code:ConstOffsets image operand then the four texels form the 2 {times} 2 rectangle used for texture filtering: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[R] &= \tau_{i0j1}[level_{base}][comp] \\ \tau[G] &= \tau_{i1j1}[level_{base}][comp] \\ \tau[B] &= \tau_{i1j0}[level_{base}][comp] \\ \tau[A] &= \tau_{i0j0}[level_{base}][comp] \end{aligned} ++++++++++++++++++++++++ If the operation does use the code:ConstOffsets image operand then the offsets allow a custom filter to be defined: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[R] &= \tau_{i0j0 + \Delta_0}[level_{base}][comp] \\ \tau[G] &= \tau_{i0j0 + \Delta_1}[level_{base}][comp] \\ \tau[B] &= \tau_{i0j0 + \Delta_2}[level_{base}][comp] \\ \tau[A] &= \tau_{i0j0 + \Delta_3}[level_{base}][comp] \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level_{base}][comp] &= \begin{cases} \tau[level_{base}][R], & \text{for}\ comp = 0 \\ \tau[level_{base}][G], & \text{for}\ comp = 1 \\ \tau[level_{base}][B], & \text{for}\ comp = 2 \\ \tau[level_{base}][A], & \text{for}\ comp = 3 \end{cases}\\ comp & \,\text{from SPIR-V operand Component} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] code:OpImage*Gather must: not be used on a sampled image with <> enabled. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-texel-filtering]] === Texel Filtering Texel filtering is first performed for each level (either [eq]#d# or [eq]#d~hi~# and [eq]#d~lo~#). If [eq]#{lambda}# is less than or equal to zero, the texture is said to be _magnified_, and the filter mode within a mip level is selected by the pname:magFilter in the sampler. If [eq]#{lambda}# is greater than zero, the texture is said to be _minified_, and the filter mode within a mip level is selected by the pname:minFilter in the sampler. [[textures-texel-nearest-filtering]] ==== Texel Nearest Filtering Within a mip level, ename:VK_FILTER_NEAREST filtering selects a single value using the [eq]#(i, j, k)# texel coordinates, with all texels taken from layer l. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level] &= \begin{cases} \tau_{ijk}[level], & \text{for 3D image} \\ \tau_{ij}[level], & \text{for 2D or Cube image} \\ \tau_{i}[level], & \text{for 1D image} \end{cases} \end{aligned} ++++++++++++++++++++++++ [[textures-texel-linear-filtering]] ==== Texel Linear Filtering Within a mip level, ename:VK_FILTER_LINEAR filtering combines 8 (for 3D), 4 (for 2D or Cube), or 2 (for 1D) texel values, together with their linear weights. The linear weights are derived from the fractions computed earlier: [latexmath] ++++++++++++++++++++++++ \begin{aligned} w_{i_0} &= (1-\alpha) \\ w_{i_1} &= (\alpha) \\ w_{j_0} &= (1-\beta) \\ w_{j_1} &= (\beta) \\ w_{k_0} &= (1-\gamma) \\ w_{k_1} &= (\gamma) \end{aligned} ++++++++++++++++++++++++ ifndef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple texels, together with their weights, are combined using a weighted average to produce a filtered value: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple texels, together with their weights, are combined to produce a filtered value. The slink:VkSamplerReductionModeCreateInfo::pname:reductionMode can: control the process by which multiple texels, together with their weights, are combined to produce a filtered texture value. When the pname:reductionMode is set (explicitly or implicitly) to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, a weighted average is computed: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{3D} &= \sum_{k=k_0}^{k_1}\sum_{j=j_0}^{j_1}\sum_{i=i_0}^{i_1}(w_{i})(w_{j})(w_{k})\tau_{ijk} \\ \tau_{2D} &= \sum_{j=j_0}^{j_1}\sum_{i=i_0}^{i_1}(w_{i})(w_{j})\tau_{ij} \\ \tau_{1D} &= \sum_{i=i_0}^{i_1}(w_{i})\tau_{i} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above set of multiple texels, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the set of texels with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] [[textures-texel-cubic-filtering]] ==== Texel Cubic Filtering Within a mip level, ename:VK_FILTER_CUBIC_EXT, filtering computes a weighted average of ifdef::VK_EXT_filter_cubic[] 64 (for 3D), endif::VK_EXT_filter_cubic[] 16 (for 2D), or 4 (for 1D) texel values, together with their Catmull-Rom weights. Catmull-Rom weights are derived from the fractions computed earlier. ifndef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ The values of multiple texels, together with their weights, are combined using a weighted average to produce a filtered value: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{2D} &= \sum_{j=j_0}^{j_3}\sum_{i=i_0}^{i_3}(w_{i})(w_{j})\tau_{ij} \\ \tau_{1D} &= \sum_{i=i_0}^{i_3}(w_{i})\tau_{i} \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{k_0}\phantom{,} w_{k_1}\phantom{,} w_{k_2}\phantom{,} w_{k_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \gamma & \gamma^2 & \gamma^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ The values of multiple texels, together with their weights, are combined to produce a filtered value. The slink:VkSamplerReductionModeCreateInfo::pname:reductionMode can: control the process by which multiple texels, together with their weights, are combined to produce a filtered texture value. When the pname:reductionMode is set (explicitly or implicitly) to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, a weighted average is computed: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{3D} &= \sum_{k=j_0}^{k_3}\sum_{j=j_0}^{j_3}\sum_{i=i_0}^{i_3}(w_{i})(w_{j})(w_{k})\tau_{ijk} \\ \tau_{2D} &= \sum_{j=j_0}^{j_3}\sum_{i=i_0}^{i_3}(w_{i})(w_{j})\tau_{ij} \\ \tau_{1D} &= \sum_{i=i_0}^{i_3}(w_{i})\tau_{i} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above set of multiple texels, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the set of texels with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] endif::VK_EXT_filter_cubic[] endif::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] [[textures-texel-mipmap-filtering]] ==== Texel Mipmap Filtering ename:VK_SAMPLER_MIPMAP_MODE_NEAREST filtering returns the value of a single mipmap level, [eq]#{tau} = {tau}[d]#. ename:VK_SAMPLER_MIPMAP_MODE_LINEAR filtering combines the values of multiple mipmap levels ({tau}[hi] and {tau}[lo]), together with their linear weights. The linear weights are derived from the fraction computed earlier: [latexmath] ++++++++++++++++++++++++ \begin{aligned} w_{hi} &= (1-\delta) \\ w_{lo} &= (\delta) \\ \end{aligned} ++++++++++++++++++++++++ ifndef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple mipmap levels together with their linear weights, are combined using a weighted average to produce a final filtered value: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple mipmap levels, together with their weights, are combined to produce a final filtered value. The slink:VkSamplerReductionModeCreateInfo::pname:reductionMode can: control the process by which multiple texels, together with their weights, are combined to produce a filtered texture value. When the pname:reductionMode is set (explicitly or implicitly) to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, a weighted average is computed: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau &= (w_{hi})\tau[hi]+(w_{lo})\tau[lo] \end{aligned} ++++++++++++++++++++++++ [[textures-texel-anisotropic-filtering]] ==== Texel Anisotropic Filtering Anisotropic filtering is enabled by the pname:anisotropyEnable in the sampler. When enabled, the image filtering scheme accounts for a degree of anisotropy. The particular scheme for anisotropic texture filtering is implementation-dependent. Implementations should: consider the pname:magFilter, pname:minFilter and pname:mipmapMode of the sampler to control the specifics of the anisotropic filtering scheme used. In addition, implementations should: consider pname:minLod and pname:maxLod of the sampler. The following describes one particular approach to implementing anisotropic filtering for the 2D Image case, implementations may: choose other methods: Given a pname:magFilter, pname:minFilter of ename:VK_FILTER_LINEAR and a pname:mipmapMode of ename:VK_SAMPLER_MIPMAP_MODE_NEAREST: Instead of a single isotropic sample, N isotropic samples are sampled within the image footprint of the image level [eq]#d# to approximate an anisotropic filter. The sum [eq]#{tau}~2Daniso~# is defined using the single isotropic [eq]#{tau}~2D~(u,v)# at level [eq]#d#. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{2Daniso} & = \frac{1}{N}\sum_{i=1}^{N} {\tau_{2D}\left ( u \left ( x - \frac{1}{2} + \frac{i}{N+1} , y \right ), \left ( v \left (x-\frac{1}{2}+\frac{i}{N+1}, y \right ), \right ) \right )}, & \text{when}\ \rho_{x} > \rho_{y} \\ \tau_{2Daniso} &= \frac{1}{N}\sum_{i=1}^{N} {\tau_{2D}\left ( u \left ( x, y - \frac{1}{2} + \frac{i}{N+1} \right ), \left ( v \left (x,y-\frac{1}{2}+\frac{i}{N+1} \right ) \right ) \right )}, & \text{when}\ \rho_{y} \geq \rho_{x} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] When slink:VkSamplerReductionModeCreateInfo::pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, the above summation is used. However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above values, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the values with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_NV_shader_image_footprint[] [[textures-footprint]] == Texel Footprint Evaluation The SPIR-V instruction code:OpImageSampleFootprintNV evaluates the set of texels from a single mip level that would be accessed during a <> operation. In addition to the inputs that would be accepted by an equivalent code:OpImageSample* instruction, code:OpImageSampleFootprintNV accepts two additional inputs. The code:Granularity input is an integer identifying the size of texel groups used to evaluate the footprint. Each bit in the returned footprint mask corresponds to an aligned block of texels whose size is given by the following table: .Texel footprint granularity values [width="50%",options="header"] |===== | code:Granularity | code:Dim = 2D | code:Dim = 3D | 0 | unsupported | unsupported | 1 | 2x2 | 2x2x2 | 2 | 4x2 | unsupported | 3 | 4x4 | 4x4x2 | 4 | 8x4 | unsupported | 5 | 8x8 | unsupported | 6 | 16x8 | unsupported | 7 | 16x16 | unsupported | 8 | unsupported | unsupported | 9 | unsupported | unsupported | 10 | unsupported | 16x16x16 | 11 | 64x64 | 32x16x16 | 12 | 128x64 | 32x32x16 | 13 | 128x128 | 32x32x32 | 14 | 256x128 | 64x32x32 | 15 | 256x256 | unsupported |===== The code:Coarse input is used to select between the two mip levels that may: be accessed during texel filtering when using a pname:mipmapMode of ename:VK_SAMPLER_MIPMAP_MODE_LINEAR. When filtering between two mip levels, a code:Coarse value of code:true requests the footprint in the lower-resolution mip level (higher level number), while code:false requests the footprint in the higher-resolution mip level. If texel filtering would access only a single mip level, the footprint in that level would be returned when code:Coarse is set to code:false; an empty footprint would be returned when code:Coarse is set to code:true. The footprint for code:OpImageSampleFootprintNV is returned in a structure with six members: * The first member is a boolean value that is true if the texel filtering operation would access only a single mip level. * The second member is a two- or three-component integer vector holding the footprint anchor location. For two-dimensional images, the returned components are in units of eight texel groups. For three-dimensional images, the returned components are in units of four texel groups. * The third member is a two- or three-component integer vector holding a footprint offset relative to the anchor. All returned components are in units of texel groups. * The fourth member is a two-component integer vector mask, which holds a bitfield identifying the set of texel groups in an 8x8 or 4x4x4 neighborhood relative to the anchor and offset. * The fifth member is an integer identifying the mip level containing the footprint identified by the anchor, offset, and mask. * The sixth member is an integer identifying the granularity of the returned footprint. For footprints in two-dimensional images (code:Dim2D), the mask returned by code:OpImageSampleFootprintNV indicates whether each texel group in a 8x8 local neighborhood of texel groups would have one or more texels accessed during texel filtering. In the mask, the texel group with local group coordinates latexmath:[(lgx,lgy)] is considered covered if and only if [latexmath] +++++++++++++++++++ \begin{aligned} 0 \neq ((mask.x + (mask.y << 32)) \text{ \& } (1 << (lgy \times 8 + lgx))) \end{aligned} +++++++++++++++++++ where: * latexmath:[0 \leq lgx < 8] and latexmath:[0 \leq lgy < 8]; and * latexmath:[mask] is the returned two-component mask. The local group with coordinates latexmath:[(lgx,lgy)] in the mask is considered covered if and only if the texel filtering operation would access one or more texels latexmath:[\tau_{ij}] in the returned miplevel where: [latexmath] +++++++++++++++++++ \begin{aligned} i0 & = \begin{cases} gran.x \times (8 \times anchor.x + lgx), & \text{if } lgx + offset.x < 8 \\ gran.x \times (8 \times (anchor.x - 1) + lgx), & \text{otherwise} \end{cases} \\ i1 & = i0 + gran.x - 1 \\ j0 & = \begin{cases} gran.y \times (8 \times anchor.y + lgy), & \text{if } lgy + offset.y < 8 \\ gran.y \times (8 \times (anchor.y - 1) + lgy), & otherwise \end{cases} \\ j1 & = j0 + gran.y - 1 \end{aligned} +++++++++++++++++++ and * latexmath:[i0 \leq i \leq i1] and latexmath:[j0 \leq j \leq j1]; * latexmath:[gran] is a two-component vector holding the width and height of the texel group identified by the granularity; * latexmath:[anchor] is the returned two-component anchor vector; and * latexmath:[offset] is the returned two-component offset vector. For footprints in three-dimensional images (code:Dim3D), the mask returned by code:OpImageSampleFootprintNV indicates whether each texel group in a 4x4x4 local neighborhood of texel groups would have one or more texels accessed during texel filtering. In the mask, the texel group with local group coordinates latexmath:[(lgx,lgy,lgz)], is considered covered if and only if: [latexmath] +++++++++++++++++++ \begin{aligned} 0 \neq ((mask.x + (mask.y << 32)) \text{ \& } (1 << (lgz \times 16 + lgy \times 4 + lgx))) \end{aligned} +++++++++++++++++++ where: * latexmath:[0 \leq lgx < 4], latexmath:[0 \leq lgy < 4], and latexmath:[0 \leq lgz < 4]; and * latexmath:[mask] is the returned two-component mask. The local group with coordinates latexmath:[(lgx,lgy,lgz)] in the mask is considered covered if and only if the texel filtering operation would access one or more texels latexmath:[\tau_{ijk}] in the returned miplevel where: [latexmath] +++++++++++++++++++ \begin{aligned} i0 & = \begin{cases} gran.x \times (4 \times anchor.x + lgx), & \text{if } lgx + offset.x < 4 \\ gran.x \times (4 \times (anchor.x - 1) + lgx), & \text{otherwise} \end{cases} \\ i1 & = i0 + gran.x - 1 \\ j0 & = \begin{cases} gran.y \times (4 \times anchor.y + lgy), & \text{if } lgy + offset.y < 4 \\ gran.y \times (4 \times (anchor.y - 1) + lgy), & otherwise \end{cases} \\ j1 & = j0 + gran.y - 1 \\ k0 & = \begin{cases} gran.z \times (4 \times anchor.z + lgz), & \text{if } lgz + offset.z < 4 \\ gran.z \times (4 \times (anchor.z - 1) + lgz), & otherwise \end{cases} \\ k1 & = k0 + gran.z - 1 \end{aligned} +++++++++++++++++++ and * latexmath:[i0 \leq i \leq i1], latexmath:[j0 \leq j \leq j1], latexmath:[k0 \leq k \leq k1]; * latexmath:[gran] is a three-component vector holding the width, height, and depth of the texel group identified by the granularity; * latexmath:[anchor] is the returned three-component anchor vector; and * latexmath:[offset] is the returned three-component offset vector. If the sampler used by code:OpImageSampleFootprintNV enables anisotropic texel filtering via pname:anisotropyEnable, it is possible that the set of texel groups accessed in a mip level may be too large to be expressed using an 8x8 or 4x4x4 mask using the granularity requested in the instruction. In this case, the implementation uses a texel group larger than the requested granularity. When a larger texel group size is used, code:OpImageSampleFootprintNV returns an integer granularity value that can: be interpreted in the same manner as the granularity value provided to the instruction to determine the texel group size used. If anisotropic texel filtering is disabled in the sampler, or if an anisotropic footprint can be represented as an 8x8 or 4x4x4 mask with the requested granularity, code:OpImageSampleFootprintNV will use the requested granularity as-is and return a granularity value of zero. code:OpImageSampleFootprintNV supports only two- and three-dimensional image accesses (code:Dim2D and code:Dim3D), and the footprint returned is undefined: if a sampler uses an addressing mode other than ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. endif::VK_NV_shader_image_footprint[] [[textures-instructions]] == Image Operation Steps Each step described in this chapter is performed by a subset of the image instructions: * Texel Input Validation Operations, Format Conversion, Texel Replacement, Conversion to RGBA, and Component Swizzle: Performed by all instructions except code:OpImageWrite. * Depth Comparison: Performed by code:OpImage*Dref instructions. * All Texel output operations: Performed by code:OpImageWrite. * Projection: Performed by all code:OpImage*Proj instructions. * Derivative Image Operations, Cube Map Operations, Scale Factor Operation, Level-of-Detail Operation and Image Level(s) Selection, and Texel Anisotropic Filtering: Performed by all code:OpImageSample* and code:OpImageSparseSample* instructions. * (s,t,r,q,a) to (u,v,w,a) Transformation, Wrapping, and (u,v,w,a) to (i,j,k,l,n) Transformation And Array Layer Selection: Performed by all code:OpImageSample, code:OpImageSparseSample, and code:OpImage*Gather instructions. * Texel Gathering: Performed by code:OpImage*Gather instructions. ifdef::VK_NV_shader_image_footprint[] * Texel Footprint Evaluation: Performed by code:OpImageSampleFootprint instructions. endif::VK_NV_shader_image_footprint[] * Texel Filtering: Performed by all code:OpImageSample* and code:OpImageSparseSample* instructions. * Sparse Residency: Performed by all code:OpImageSparse* instructions. [[textures-queries]] == Image Query Instructions === Image Property Queries code:OpImageQuerySize, code:OpImageQuerySizeLod, code:OpImageQueryLevels, and code:OpImageQuerySamples query properties of the image descriptor that would be accessed by a shader image operation. ifdef::VK_EXT_robustness2[] They return 0 if the bound descriptor is a null descriptor. endif::VK_EXT_robustness2[] code:OpImageQuerySizeLod returns the size of the image level identified by the code:Level code:of code:Detail operand. If that level does not exist in the image, ifdef::VK_EXT_robustness2[and the descriptor is not null,] then the value returned is undefined:. === Lod Query code:OpImageQueryLod returns the Lod parameters that would be used in an image operation with the given image and coordinates. ifdef::VK_EXT_robustness2[] If the descriptor that would be accessed is a null descriptor then (0, 0) is returned. endif::VK_EXT_robustness2[] ifdef::VK_EXT_robustness2[Otherwise, the] ifndef::VK_EXT_robustness2[The] steps described in this chapter are performed as if for code:OpImageSampleImplicitLod, up to <>. The return value is the vector [eq]#({lambda}', d~l~)#. These values may: be subject to implementation-specific maxima and minima for very large, out-of-range values.