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Use FX to:</p> 100 101<ul> 102 <li>create canvases, gradients, mathematical colormaps</li> 103 <li>move color values between images and channels</li> 104 <li>translate, flip, mirror, rotate, scale, shear and generally distort images</li> 105 <li>merge or composite multiple images together</li> 106 <li>convolve or merge neighboring pixels together</li> 107 <li>generate image metrics or 'fingerprints'</li> 108</ul> 109 110<p>The expression can be simple:</p> 111 112<pre class="highlight"><code>magick -size 64x64 canvas:black -channel blue -fx "1/2" fx_navy.png 113</code></pre> 114 115<p>Here, we convert a black to a navy blue image:</p> 116 117<ul> 118 <a href="../images/black.png"><img src="../images/black.png" width="64" height="64" alt="black" /></a> 119 <img style="margin-top:22px; margin-bottom:22px;" src="../images/right.gif" width="20" height="20" alt="==>" /> 120 <a href="../images/navy.png"><img src="../images/navy.png" width="64" height="64" alt="navy" /></a> 121</ul> 122 123<p>Or the expression can be complex:</p> 124 125<pre class="highlight"><code>magick rose: \ 126 -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" \ 127 rose-sigmoidal.png 128</code></pre> 129 130<p>This expression results in a high contrast version of the source image:</p> 131 132<ul> 133 <a href="../images/rose.jpg"><img src="../images/rose.jpg" width="70" height="46" alt="rose" /></a> 134 <img style="margin-top:13px; margin-bottom:13px;" src="../images/right.gif" width="20" height="20" alt="==>" /> 135 <a href="../images/rose-sigmoidal.png"><img src="../images/rose-sigmoidal.png" width="70" height="46" alt="rose-sigmoidal" /></a> 136</ul> 137 138<p>The expression can include variable assignments. Assignments, in most cases, reduce the complexity of an expression and permit some operations that might not be possible any other way. For example, lets create a radial gradient:</p> 139 140<pre class="highlight"><code>magick -size 70x70 canvas: \ 141 -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" \ 142 radial-gradient.png 143</code></pre> 144 145<p>The command above returns this image:</p> 146 147<ul> 148 <a href="../images/radial-gradient.png"><img src="../images/radial-gradient.png" width="70" height="70" alt="radial-gradient" /></a> 149</ul> 150 151<p>This FX expression adds random noise to an image:</p> 152 153<pre class="highlight"><code>magick photo.jpg -fx 'iso=32; rone=rand(); rtwo=rand(); \ 154 myn=sqrt(-2*ln(rone))*cos(2*Pi*rtwo); myntwo=sqrt(-2*ln(rtwo))* \ 155 cos(2*Pi*rone); pnoise=sqrt(p)*myn*sqrt(iso)* \ 156 channel(4.28,3.86,6.68,0)/255; max(0,p+pnoise)' noisy.png 157</code></pre> 158 159<p>This FX script utilizes a loop to create a <a href="https://en.wikipedia.org/wiki/Julia_set">Julia set</a>:</p> 160 161<pre class="highlight"><code>magick -size 400x400 xc:black -colorspace gray -fx " \ 162 Xi=2.4*i/w-1.2; \ 163 Yj=2.4*j/h-1.2; \ 164 for (pixel=0.0, (hypot(Xi,Yj) < 2.0) && (pixel < 1.0), \ 165 delta=Xi^2-Yj^2; \ 166 Yj=2.0*Xi*Yj+0.2; \ 167 Xi=delta+0.4; \ 168 pixel+=0.00390625 \ 169 ); \ 170 pixel == 1.0 ? 0.0 : pixel" \ 171 \( -size 1x1 xc:white xc:red xc:orange xc:yellow xc:green1 xc:cyan xc:blue \ 172 xc:blueviolet xc:white -reverse +append -filter Cubic -resize 1024x1! \) \ 173 -clut -rotate -90 julia-set.png</code></pre> 174 175<ul> 176 <a href="../images/julia-set.png"><img src="../images/julia-set.png" width="160" height="160" alt="Julia Fractals" /></a> 177</ul> 178 179<p>This FX script prints the first 10 prime numbers:</p> 180<pre class="highlight"><code>magick xc: -channel gray -fx " \ 181 for (prime=2, prime < 30, composite=0; \ 182 for (nn=2, nn < (prime/2+1), if ((prime % nn) == 0, composite++, ); nn++); \ 183 if (composite <= 0, debug(prime), ); prime++)" null:</code></pre> 184 185<p>See <a href="https://legacy.imagemagick.org/Usage/transform/index.html#fx">Using FX, The Special Effects Image Operator</a> for more examples.</p> 186 187<p>The next section discusses the FX expression language.</p> 188 189<h2><a class="anchor" id="anatomy"></a>The Anatomy of an FX Expression</h2> 190 191<h5>The FX Expression Language</h5> 192 193<p>The formal FX expression language is defined here:</p> 194 195<dl class="row"> 196 <dt class="col-md-4"> numbers:</dt> 197 <dd class="col-md-8"> integer, floating point, scientific notation (+/- required, e.g. 3.81469e-06), International System number postfixes (.e.g KB, Mib, GB, etc.)</dd> 198 <dt class="col-md-4"> constants: </dt> 199 <dd class="col-md-8"> E (Euler's number), Epsilon, QuantumRange, QuantumScale, Opaque, Phi (golden ratio), Pi, Transparent</dd> 200 <dt class="col-md-4"> FX operators (in order of precedence): </dt> 201 <dd class="col-md-8"> ^ (power), unary -, *, /, % (modulo), +, -, 202 <<, >>, <, <=, >, >=, +=, -=, *=, /=, %=, <<= 203, >>=, 204 &=, |=, ++, --, ==, !=, & (bitwise AND), | (bitwise OR), 205 && (logical AND), || (logical OR), 206 ~ (logical NOT), ?: (ternary conditional)</dd> 207 <dt class="col-md-4"> array: </dt> 208 <dd class="col-md-8">an image offers array storage (e.g. p[-1,-1].r) bounded by its width and height. An image sequence represents multiple arrays (e.g. u.p[0,0].r, v.p[0,0].r). Storage is limited to Quantum values, e.g. [0..65535] for Q16 builds and floating point for HDRI-enabled builds.</dd> 209 <dt class="col-md-4"> math functions: </dt> 210 <dd class="col-md-8"> abs(), acos(), acosh(), airy(), alt(), asin(), asinh(), atan(), atanh(), atan2(), ceil(), clamp(), cos(), cosh(), debug(), drc(), erf(), exp(), floor(), gauss(), gcd(), hypot(), int(), isnan(), j0(), j1(), jinc(), ln(), log(), logtwo(), max(), min(), mod(), not(), pow(), rand(), round(), sign(), sin(), sinc(), sinh(), sqrt(), squish(), tan(), tanh(), trunc()</dd> 211 <dt class="col-md-4"> channel functions: </dt> 212 <dd class="col-md-8"> channel(r,g,b,a), channel(c,m,y,k,a)</dd> 213 <dt class="col-md-4"> color names:</dt> 214 <dd class="col-md-8"> red, cyan, black, etc.</dd> 215 <dt class="col-md-4"> color functions:</dt> 216 <dd class="col-md-8"> srgb(), srgba(), rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla(), etc.</dd> 217 <dt class="col-md-4"> color hex values:</dt> 218 <dd class="col-md-8"> #ccc, #cbfed0, #b9e1cc00, etc.</dd> 219 <dt class="col-md-4"> symbols:</dt><dd class="col-md-8"><dl> 220 <dd><code>u</code>: first image in list</dd> 221 <dd><code>v</code>: second image in list</dd> 222 <dd><code>s</code>: current image in list (for %[fx:] otherwise = u)</dd> 223 <dd><code>t</code>: index of current image (s) in list</dd> 224 <dd><code>n</code>: number of images in list</dd> 225 226 <dd><code>i</code>: column offset</dd> 227 <dd><code>j</code>: row offset</dd> 228 <dd><code>p</code>: pixel to use (absolute or relative to current pixel)</dd> 229 230 <dd><code>w</code>: width of this image</dd> 231 <dd><code>h</code>: height of this image</dd> 232 <dd><code>z</code>: channel depth</dd> 233 234 <dd><code>r</code>: red value (from RGBA), of a specific or current pixel</dd> 235 <dd><code>g</code>: green</dd> 236 <dd><code>b</code>: blue</dd> 237 <dd><code>a</code>: alpha</dd> 238 <dd><code>o</code>: opacity</dd> 239 240 <dd><code>c</code>: cyan value of CMYK color of pixel</dd> 241 <dd><code>y</code>: yellow</dd> 242 <dd><code>m</code>: magenta</dd> 243 <dd><code>k</code>: black</dd> 244 245 <dd><code>intensity</code>: pixel intensity</dd> 246 247 <dd><code>hue</code>: pixel hue</dd> 248 <dd><code>saturation</code>: pixel saturation</dd> 249 <dd><code>lightness</code>: pixel lightness</dd> 250 <dd><code>luma</code>: pixel luma</dd> 251 252 <dd><code>page.width</code>: page width</dd> 253 <dd><code>page.height</code>: page height</dd> 254 <dd><code>page.x</code>: page x offset</dd> 255 <dd><code>page.y</code>: page y offset</dd> 256 257 <dd><code>printsize.x</code>: x printsize</dd> 258 <dd><code>printsize.y</code>: y printsize</dd> 259 260 <dd><code>resolution.x</code>: x resolution</dd> 261 <dd><code>resolution.y</code>: y resolution</dd> 262 263 <dd><code>depth</code>: image depth</dd> 264 <dd><code>extent</code>: image extent</dd> 265 <dd><code>minima</code>: image minima</dd> 266 <dd><code>maxima</code>: image maxima</dd> 267 <dd><code>mean</code>: image mean</dd> 268 <dd><code>median</code>: image median</dd> 269 <dd><code>standard_deviation</code>: image standard deviation</dd> 270 <dd><code>kurtosis</code>: image kurtosis</dd> 271 <dd><code>skewness</code>: image skewness (add a channel specifier to compute a statistic for that channel, e.g. depth.r)</dd></dl></dd> 272 <dt class="col-md-4"> iterators:</dt> 273 <dd class="col-md-8"> do(), for(), while()</dd> 274 <dt class="col-md-4"> image attributes:</dt> 275 <dd class="col-md-8"> image.depth, image.kurtosis, image.maxima, image.minima, image.resolution.x, image.resolution.y, image.skewness, image.standard_deviation</dd> 276 <dt class="col-md-4"> image settings:</dt> 277 <dd class="col-md-8"> .e.g. <code>magick ... -set option:wd1 "%[fx:w/2]" -resize "%[fx:wd1-5]" ...</code><dd> 278</dl> 279 280<h5>The FX Expression</h5> 281 282<p>An FX expression may include any combination of the following:</p> 283<dl class="row"> 284<dt class="col-md-4"> <var>x</var> <code>^</code> <var>y</var></dt><dd class="col-md-8"> exponentiation (<var>x<sup>y</sup></var>)</dd> 285<dt class="col-md-4"> <code>(</code> ... <code>)</code></dt><dd class="col-md-8"> grouping</dd> 286<dt class="col-md-4"> <var>x</var> <code>*</code> <var>y</var></dt><dd class="col-md-8"> multiplication (the asterisk <code>*</code> is optional, for example, <code>2u</code> or <code>2(x+y)</code> are acceptable)</dd> 287<dt class="col-md-4"> <var>x</var> <code>/</code> <var>y</var></dt><dd class="col-md-8"> division</dd> 288<dt class="col-md-4"> <var>x</var> <code>%</code> <var>y</var></dt><dd class="col-md-8"> modulo</dd> 289<dt class="col-md-4"> <var>x</var> <code>+</code> <var>y</var></dt><dd class="col-md-8"> addition</dd> 290<dt class="col-md-4"> <var>x</var> <code>-</code> <var>y</var></dt><dd class="col-md-8"> subtraction</dd> 291<dt class="col-md-4"> <var>x</var> <code><<</code> <var>y</var></dt><dd class="col-md-8"> left shift</dd> 292<dt class="col-md-4"> <var>x</var> <code>>></code> <var>y</var></dt><dd class="col-md-8"> right shift</dd> 293<dt class="col-md-4"> <var>x</var> <code><</code> <var>y</var></dt><dd class="col-md-8"> boolean relation, return value 1.0 if <var>x</var> < <var>y</var>, otherwise 0.0</dd> 294<dt class="col-md-4"> <var>x</var> <code><=</code> <var>y</var></dt><dd class="col-md-8"> boolean relation, return value 1.0 if <var>x</var> <= <var>y</var>, otherwise 0.0</dd> 295<dt class="col-md-4"> <var>x</var> <code>></code> <var>y</var></dt><dd class="col-md-8"> boolean relation, return value 1.0 if <var>x</var> > <var>y</var>, otherwise 0.0</dd> 296<dt class="col-md-4"> <var>x</var> <code>>=</code> <var>y</var></dt><dd class="col-md-8"> boolean relation, return value 1.0 if <var>x</var> >= <var>y</var>, otherwise 0.0</dd> 297<dt class="col-md-4"> <var>x</var> <code>==</code> <var>y</var></dt><dd class="col-md-8"> boolean relation, return value 1.0 if <var>x </var>==<var> y</var>, otherwise 0.0</dd> 298<dt class="col-md-4"> <var>x</var> <code>!=</code> <var>y</var></dt><dd class="col-md-8"> boolean relation, return value 1.0 if <var>x </var>!=<var> y</var>, otherwise 0.0</dd> 299<dt class="col-md-4"> <var>x</var> <code>&</code> <var>y</var></dt><dd class="col-md-8"> binary AND</dd> 300<dt class="col-md-4"> <var>x</var> <code>|</code> <var>y</var></dt><dd class="col-md-8"> binary OR</dd> 301<dt class="col-md-4"> <var>x</var> <code>&&</code> <var>y</var></dt><dd class="col-md-8"> logical AND connective, return value 1.0 if <var>x</var> > 0 and <var>y</var> > 0, otherwise 0.0</dd> 302<dt class="col-md-4"> <var>x</var> <code>||</code> <var>y</var></dt><dd class="col-md-8"> logical OR connective (inclusive), return value 1.0 if <var>x</var> > 0 or <var>y</var> > 0 (or both), otherwise 0.0</dd> 303<dt class="col-md-4"> <code>~</code><var>x</var></dt><dd class="col-md-8"> logical NOT operator, return value 1.0 if <var>not</var> <var>x</var> > 0, otherwise 0.0</dd> 304<dt class="col-md-4"> <code>+</code><var>x</var></dt><dd class="col-md-8"> unary plus, return 1.0*value</dd> 305<dt class="col-md-4"> <code>-</code><var>x</var></dt><dd class="col-md-8"> unary minus, return -1.0*value</dd> 306<dt class="col-md-4"> <var>x</var> <code>?</code> <var>y</var> <code>:</code> <var>z</var> </dt><dd class="col-md-8">ternary conditional expression, return value <var>y</var> if <var>x</var> != 0, otherwise <var>z</var>; only one ternary conditional permitted per statement</dd> 307<dt class="col-md-4"> <var>x</var> <code>=</code> <var>y</var></dt><dd class="col-md-8">assignment; single character variables are reserved, instead use 2 or more characters, letter combinations only (e.g. Xi not X1)</dd> 308<dt class="col-md-4"> <var>x</var> <code>;</code> <var>y</var></dt><dd class="col-md-8">statement separator </dd> 309<dt class="col-md-4"> <code>phi</code></dt><dd class="col-md-8"> constant (1.618034...)</dd> 310<dt class="col-md-4"> <code>pi</code></dt><dd class="col-md-8"> constant (3.14159265359...)</dd> 311<dt class="col-md-4"> <code>e</code></dt><dd class="col-md-8"> constant (2.71828...)</dd> 312<dt class="col-md-4"> <code>QuantumRange</code></dt><dd class="col-md-8"> constant maximum pixel value (255 for Q8, 65535 for Q16)</dd> 313<dt class="col-md-4"> <code>QuantumScale</code></dt><dd class="col-md-8"> constant 1.0/<code>QuantumRange</code></dd> 314<dt class="col-md-4"> <code>intensity</code></dt><dd class="col-md-8"> pixel intensity whose value respects the <a href="../www/command-line-options.html#intensity">-intensity</a> option.</dd> 315<dt class="col-md-4"> <code>hue</code></dt><dd class="col-md-8"> pixel hue</dd> 316<dt class="col-md-4"> <code>saturation</code></dt><dd class="col-md-8"> pixel saturation</dd> 317<dt class="col-md-4"> <code>lightness</code></dt><dd class="col-md-8"> pixel lightness; equivalent to 0.5*max(red,green,blue) + 0.5*min(red,green,blue)</dd> 318<dt class="col-md-4"> <code>luminance</code></dt><dd class="col-md-8"> pixel luminance; equivalent to <code>0.212656*red + 0.715158*green + 0.072186*blue</code></dd> 319<dt class="col-md-4"> <code>red, green, blue</code>, etc.</dt><dd class="col-md-8"> color names</dd> 320<dt class="col-md-4"> <code>#ccc, #cbfed0, #b9e1cc00</code>, etc.</dt><dd class="col-md-8"> color hex values</dd> 321<dt class="col-md-4"> <code>rgb(), rgba(), cmyk(), cmyka(), hsl(), hsla()</code></dt><dd class="col-md-8"> color functions</dd> 322<dt class="col-md-4"> <code>s, t, u, v, n, i, j, w, h, z, r, g, b, a, o, c, y, m, k</code></dt><dd class="col-md-8"> symbols</dd> 323<dt class="col-md-4"> <code>abs(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> absolute value function</dd> 324<dt class="col-md-4"> <code>acos(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> arc cosine function</dd> 325<dt class="col-md-4"> <code>acosh(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> inverse hyperbolic cosine function</dd> 326<dt class="col-md-4"> <code>airy(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> Airy function (max=1, min=0); airy(<var>x</var>)=[jinc(<var>x</var>)]<sup>2</sup>=[2*j1(<var>pi*x</var>)/(<var>pi*x</var>)]<sup>2</sup></dd> 327<dt class="col-md-4"> <code>alt(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> sign alternation function (return 1.0 if int(<var>x</var>) is even, -1.0 if int(<var>x</var>) is odd)</dd> 328<dt class="col-md-4"> <code>asin(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> arc sine function</dd> 329<dt class="col-md-4"> <code>asinh(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> inverse hyperbolic sine function</dd> 330<dt class="col-md-4"> <code>atan(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> arc tangent function</dd> 331<dt class="col-md-4"> <code>atanh(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> inverse hyperbolic tangent function</dd> 332<dt class="col-md-4"> <code>atan2(</code><var>y</var>,<var>x</var><code>)</code></dt><dd class="col-md-8"> arc tangent function of two variables</dd> 333<dt class="col-md-4"> <code>ceil(</code><var>x</var><code>)</code></dt><dd class="col-md-8">smallest integral value not less than argument</dd> 334<dt class="col-md-4"> <code>channel(</code><var>r</var>,<var>g</var>,<var>b</var>,<var>a</var><code>)</code></dt><dd class="col-md-8">select numeric argument based on current channel</dd> 335<dt class="col-md-4"> <code>channel(</code><var>c</var>,<var>m</var>,<var>y</var>,<var>k</var>,<var>a</var><code>)</code></dt><dd class="col-md-8">select numeric argument based on current channel</dd> 336<dt class="col-md-4"> <code>clamp(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> clamp value</dd> 337<dt class="col-md-4"> <code>cos(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> cosine function</dd> 338<dt class="col-md-4"> <code>cosh(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> hyperbolic cosine function</dd> 339<dt class="col-md-4"> <code>debug(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> print <var>x</var> (useful for debugging your expression)</dd> 340<dt class="col-md-4"> <code>do(</code><var>expression</var>, <var>condition test</var><code>)</code></dt><dd class="col-md-8"> iterate while the condition is not equal to 0</dd> 341<dt class="col-md-4"> <code>drc(</code><var>x</var>,<var>y</var><code>)</code></dt><dd class="col-md-8"> dynamic range compression (knee curve); drc(<var>x</var>,<var>y</var>)=(<var>x</var>)/(<var>y</var>*(<var>x</var>-1)+1); -1<<var>y</var><1 </dd> 342<dt class="col-md-4"> <code>erf(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> error function</dd> 343<dt class="col-md-4"> <code>exp(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> natural exponential function (<var>e<sup>x</sup></var>)</dd> 344<dt class="col-md-4"> <code>floor(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> largest integral value not greater than argument</dd> 345<dt class="col-md-4"> <code>for(</code><var>initialization</var>, <var>condition test</var>, <var>expression</var><code>)</code></dt><dd class="col-md-8"> iterate while the condition is not equal to 0</dd> 346<dt class="col-md-4"> <code>gauss(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> gaussian function; gauss(<var>x</var>)=exp(<var>-x*x/2</var>)/sqrt(2*pi)</dd> 347<dt class="col-md-4"> <code>gcd(</code><var>x</var>,<var>y</var><code>)</code></dt><dd class="col-md-8"> greatest common denominator</dd> 348<dt class="col-md-4"> <code>hypot(</code><var>x</var>,<var>y</var><code>)</code></dt><dd class="col-md-8"> the square root of x<sup>2</sup>+y<sup>2</sup></dd> 349<dt class="col-md-4"> <code>if(</code><var>condition test</var>, <var>nonzero-expression</var>, <var>zero-expression</var><code>)</code></dt><dd class="col-md-8"> interpret expression depending on condition</dd> 350<dt class="col-md-4"> <code>int(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> greatest integer function (return greatest integer less than or equal to <var>x</var>)</dd> 351<dt class="col-md-4"> <code>isnan(</code><var>x</var><code>)</code></dt><dd class="col-md-8">return 1.0 if <var>x</var> is NAN, 0.0 otherwise</dd> 352<dt class="col-md-4"> <code>j0(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> Bessel functions of <var>x</var> of the first kind of order 0</dd> 353<dt class="col-md-4"> <code>j1(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> Bessel functions of <var>x</var> of the first kind of order 1</dd> 354<dt class="col-md-4"> <code>jinc(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> jinc function (max=1, min=-0.1323); jinc(<var>x</var>)=2*j1(pi*<var>x</var>)/(pi*<var>*x</var>)</dd> 355<dt class="col-md-4"> <code>ln(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> natural logarithm function</dd> 356<dt class="col-md-4"> <code>log(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> logarithm base 10</dd> 357<dt class="col-md-4"> <code>logtwo(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> logarithm base 2</dd> 358<dt class="col-md-4"> <code>ln(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> natural logarithm</dd> 359<dt class="col-md-4"> <code>max(</code><var>x</var>, <var>y</var><code>)</code></dt><dd class="col-md-8"> maximum of <var>x</var> and <var>y</var></dd> 360<dt class="col-md-4"> <code>min(</code><var>x</var>, <var>y</var><code>)</code></dt><dd class="col-md-8"> minimum of <var>x</var> and <var>y</var></dd> 361<dt class="col-md-4"> <code>mod(</code><var>x</var>, <var>y</var><code>)</code></dt><dd class="col-md-8"> floating-point remainder function</dd> 362<dt class="col-md-4"> <code>not(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> return 1.0 if <var>x</var> is zero, 0.0 otherwise</dd> 363<dt class="col-md-4"> <code>pow(</code><var>x</var>,<var>y</var><code>)</code></dt><dd class="col-md-8"> power function (<var>x<sup>y</sup></var>)</dd> 364<dt class="col-md-4"> <code>rand()</code></dt><dd class="col-md-8"> value uniformly distributed over the interval [0.0, 1.0) with a 2 to the 128th-1 period</dd> 365<dt class="col-md-4"> <code>round()</code></dt><dd class="col-md-8"> round to integral value, regardless of rounding direction</dd> 366<dt class="col-md-4"> <code>sign(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> return -1.0 if <var>x</var> is less than 0.0 otherwise 1.0</dd> 367<dt class="col-md-4"> <code>sin(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> sine function</dd> 368<dt class="col-md-4"> <code>sinc(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> sinc function (max=1, min=-0.21); sinc(<var>x</var>)=sin(<var>pi*x</var>)/(<var>pi*x</var>)</dd> 369<dt class="col-md-4"> <code>squish(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> squish function; squish(<var>x</var>)=1.0/(1.0+exp(<var>-x</var>))</dd> 370<dt class="col-md-4"> <code>sinh(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> hyperbolic sine function</dd> 371<dt class="col-md-4"> <code>sqrt(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> square root function</dd> 372<dt class="col-md-4"> <code>tan(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> tangent function</dd> 373<dt class="col-md-4"> <code>tanh(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> hyperbolic tangent function</dd> 374<dt class="col-md-4"> <code>trunc(</code><var>x</var><code>)</code></dt><dd class="col-md-8"> round to integer, towards zero</dd> 375<dt class="col-md-4"> <code>while(</code><var>condition test</var>, <var>expression</var><code>)</code></dt><dd class="col-md-8"> iterate while the condition is not equal to 0</dd> 376<dt class="col-md-4"> <code>image.depth, image.kurtosis, image.maxima, image.minima, image.resolution.x, image.resolution.y, image.skewness, image.standard_deviation</code></dt><dd class="col-md-8"> image attributes</dd> 377</dl> 378<p>The expression semantics include these rules:</p> 379 380<ul> 381<li>symbols are case insensitive</li> 382<li>only one ternary conditional (e.g. x ? y : z) per statement</li> 383<li>statements are assignments or the final expression to return</li> 384<li>an assignment starts a statement, it is not an operator</li> 385<li>single character variables are reserved. Assignments to reserved built-ins do not throw an exception and have no effect; e.g. <code>r=3.0; r</code> returns the pixel red color value, not 3.0</li> 386<li>unary operators have a lower priority than binary operators, that is, the unary minus (negation) has lower precedence than exponentiation, so -3^2 is interpreted as -(3^2) = -9. Use parentheses to clarify your intent (e.g. (-3)^2 = 9).</li> 387<li>care must be exercised when using the slash ('/') symbol. The string of characters <var>1/2x</var> is interpreted as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of parentheses helps clarify the meaning and should be used whenever there is any chance of misinterpretation.</li> 388</ul> 389<br/> 390 391 392<h5>Source Images</h5> 393 394<p>The symbols <code>u</code> and <code>v</code> refer to the first and second images, respectively, in the current image sequence. Refer to a particular image in a sequence by appending its index to any image reference (usually <code>u</code>), with a zero index for the beginning of the sequence. A negative index counts from the end. For example, <code>u[0]</code> is the first image in the sequence, <code>u[2]</code> is the third, <code>u[-1]</code> is the last image, and <code>u[t]</code> is the current image. The current image can also be referenced by <code>s</code>. If the sequence number exceeds the length of the sequence, the count is wrapped. Thus in a 3-image sequence, <code>u[-1]</code>, <code>u[2]</code>, and <code>u[5]</code> all refer to the same (third) image.</p> 395 396<p>As an example, we form an image by averaging the first image and third images (the second (index 1) image is ignored and just junked):</p> 397 398<pre class="highlight"><code>magick image1.jpg image2.jpg image3.jpg -fx "(u+u[2])/2.0" image.jpg 399</code></pre> 400 401<p>By default, the image to which <code>p</code>, <code>r</code>, <code>g</code>, <code>b</code>, <code>a</code>, etc., are applied is the current image <code>s</code> in the image list. This is equivalent to <code>u</code> except when used in an escape sequence <code>%[fx:...]</code>. </p> 402 403<p>It is important to note the special role played by the first image. This is the only image in the image sequence that is modified, other images are used only for their data. As an illustrative example, consider the following, and note that the setting <a href="../www/command-line-options.html#channel">-channel red</a> instructs <a href="../www/command-line-options.html#fx">-fx</a> to modify only the red channel; nothing in the green or blue channels will change. It is instructive to ponder why the result is not symmetric.</p> 404 405<pre class="highlight"><code>magick -channel red logo: -flop logo: -resize "20%" -fx "(u+v)/2" image.jpg 406</code></pre> 407 408<ul> 409 <a href="../images/logo-sm-flop.png"><img src="../images/logo-sm-flop.png" width="128" height="96" alt="logo-sm-flop.png" /></a> 410 <a href="../images/logo-sm.png"><img src="../images/logo-sm.png" width="128" height="96" alt="logo-sm.png" /></a> 411<img style="margin-top:38px; margin-bottom:38px;" src="../images/right.gif" width="20" height="20" alt="==>" /> 412 <a href="../images/logo-sm-fx.png"><img src="../images/logo-sm-fx.png" width="128" height="96" alt="logo-sm-fx.png" /></a> 413</ul> 414 415<br/> 416<h5>Accessing Pixels</h5> 417 418<p>All color values are normalized to the range of 0.0 to 1.0. The alpha channel ranges from 0.0 (fully transparent) to 1.0 (fully opaque).</p> 419 420<p>The pixels are processed one at a time, but a different pixel of an image can be specified using a pixel index represented by <code>p</code>. For example,</p> 421 422<pre class="highlight"><code>p[-1].g green value of pixel to the immediate left of the current pixel 423p[-1,-1].r red value of the pixel diagonally left and up from current pixel 424</code></pre> 425 426<p>To specify an absolute position, use braces, rather than brackets.</p> 427 428<pre class="highlight"><code>p{0,0}.r red value of the pixel in the upper left corner of the image 429p{12,34}.b blue pixel value at column number 12, row 34 of the image 430</code></pre> 431 432<p>Integer values of the position retrieve the color of the pixel referenced, while non-integer position values return a blended color according to the current <a href="../www/command-line-options.html#interpolate">-interpolate</a> setting.</p> 433 434<p>A position outside the boundary of the image retrieves a value dictated by the <a href="../www/command-line-options.html#virtual-pixel">-virtual-pixel</a> option setting.</p> 435 436<h5>Apply an Expression to Select Image Channels</h5> 437 438<p>Use the <a href="../www/command-line-options.html#channel">-channel</a> setting to specify the output channel of the result. If no output channel is given, the result is set over all channels except the opacity channel. For example, to replace the red channel of <code>alpha.png</code> with the average of the green channels from the images <code>alpha.png</code> and <code>beta.png</code>, use:</p> 439 440<pre class="highlight"><code>magick alpha.png beta.png -channel red -fx "(u.g+v.g)/2" gamma.png 441</code></pre> 442 443 444<h5>Results</h5> 445 446<p>The <a href="../www/command-line-options.html#fx">-fx</a> operator evaluates the given expression for each channel (set by <a href="../www/command-line-options.html#channel">-channel</a>) of each pixel in the first image (<code>u</code>) in the sequence. The computed values are temporarily stored in a copy (clone) of that first image until all the pixels have been processed, after which this single new image replaces the list of images in the current image sequence. As such, in the previous example the updated version of <code>alpha.png</code> replaces both of the original images, <code>alpha.png</code> and <code>beta.png</code>, before being saved as <code>gamma.png</code>.</p> 447 448<p>The current image <code>s</code> is set to the first image in the sequence (<code>u</code>), and <code>t</code> to its index, 0. The symbols <code>i</code> and <code>j</code> reference the current pixel being processed.</p> 449 450 451<p>For use with <a href="../www/command-line-options.html#format_identify_">-format</a>, the value-escape <code>%[fx:]</code> is evaluated just once for each image in the current image sequence. As each image in the sequence is being evaluated, <code>s</code> and <code>t</code> successively refer to the current image and its index, while <code>i</code> and <code>j</code> are set to zero, and the current channel set to red (<a href="../www/command-line-options.html#channel">-channel</a> is ignored). An example:</p> 452 453<pre class="highlight"><code>$ magick canvas:'rgb(25%,50%,75%)' rose: -colorspace rgb \ 454 -format 'Red channel of NW corner of image #%[fx:t] is %[fx:s]\n' info: 455Red channel of NW corner of image #0 is 0.464883 456Red channel of NW corner of image #1 is 0.184582 457</code></pre> 458 459<p>Here we use the image indexes to <var>rotate</var> each image differently, and use <code>-set</code> with the image index to set a different <var>pause delay</var> on the first image in the animation:</p> 460 461<pre class="highlight"><code>magick rose: -duplicate 29 -virtual-pixel Gray -distort SRT '%[fx:360.0*t/n]' \ 462 -set delay '%[fx:t == 0 ? 240 : 10]' -loop 0 rose.gif" 463</code></pre> 464 465<p>The color-escape <code>%[pixel:]</code> or <code>%[hex:]</code> is evaluated once per image and per color channel in that image (<a href="../www/command-line-options.html#channel">-channel</a> is ignored), The values generated are then converted into a color string (a named color or hex color value). The symbols <code>i</code> and <code>j</code> are set to zero, and <code>s</code> and <code>t</code> refer to each successively current image and index.</p> 466 467</div> 468 </div> 469 </main><!-- /.container --> 470 <footer class="magick-footer"> 471 <div class="container-fluid"> 472 <a href="../www/security-policy.html">Security</a> • 473 <a href="../www/news.html">News</a> 474 475 <a href="fx.html#"><img class="d-inline" id="wand" alt="And Now a Touch of Magick" width="16" height="16" src="../images/wand.ico"/></a> 476 477 <a href="../www/links.html">Related</a> • 478 <a href="../www/sitemap.html">Sitemap</a> 479 <br/> 480 <a href="../www/support.html">Sponsor</a> • 481 <a href="../www/cite.html">Cite</a> • 482 <a href="http://pgp.mit.edu/pks/lookup?op=get&search=0x89AB63D48277377A">Public Key</a> • 483 <a href="../www/https://imagemagick.org/script/contact.php">Contact Us</a> 484 <br/> 485 <a href="https://github.com/imagemagick/imagemagick" target="_blank" rel="noopener" aria-label="GitHub"><svg xmlns="http://www.w3.org/2000/svg" class="navbar-nav-svg" viewBox="0 0 512 499.36" width="2%" height="2%" role="img" focusable="false"><title>GitHub</title><path fill="currentColor" fill-rule="evenodd" d="M256 0C114.64 0 0 114.61 0 256c0 113.09 73.34 209 175.08 242.9 12.8 2.35 17.47-5.56 17.47-12.34 0-6.08-.22-22.18-.35-43.54-71.2 15.49-86.2-34.34-86.2-34.34-11.64-29.57-28.42-37.45-28.42-37.45-23.27-15.84 1.73-15.55 1.73-15.55 25.69 1.81 39.21 26.38 39.21 26.38 22.84 39.12 59.92 27.82 74.5 21.27 2.33-16.54 8.94-27.82 16.25-34.22-56.84-6.43-116.6-28.43-116.6-126.49 0-27.95 10-50.8 26.35-68.69-2.63-6.48-11.42-32.5 2.51-67.75 0 0 21.49-6.88 70.4 26.24a242.65 242.65 0 0 1 128.18 0c48.87-33.13 70.33-26.24 70.33-26.24 14 35.25 5.18 61.27 2.55 67.75 16.41 17.9 26.31 40.75 26.31 68.69 0 98.35-59.85 120-116.88 126.32 9.19 7.9 17.38 23.53 17.38 47.41 0 34.22-.31 61.83-.31 70.23 0 6.85 4.61 14.81 17.6 12.31C438.72 464.97 512 369.08 512 256.02 512 114.62 397.37 0 256 0z"/></svg></a> • 486 <a href="https://twitter.com/imagemagick" target="_blank" rel="noopener" aria-label="Twitter"><svg xmlns="http://www.w3.org/2000/svg" class="navbar-nav-svg" viewBox="0 0 512 416.32" width="2%" height="2%" role="img" focusable="false"><title>Twitter</title><path fill="currentColor" d="M160.83 416.32c193.2 0 298.92-160.22 298.92-298.92 0-4.51 0-9-.2-13.52A214 214 0 0 0 512 49.38a212.93 212.93 0 0 1-60.44 16.6 105.7 105.7 0 0 0 46.3-58.19 209 209 0 0 1-66.79 25.37 105.09 105.09 0 0 0-181.73 71.91 116.12 116.12 0 0 0 2.66 24c-87.28-4.3-164.73-46.3-216.56-109.82A105.48 105.48 0 0 0 68 159.6a106.27 106.27 0 0 1-47.53-13.11v1.43a105.28 105.28 0 0 0 84.21 103.06 105.67 105.67 0 0 1-47.33 1.84 105.06 105.06 0 0 0 98.14 72.94A210.72 210.72 0 0 1 25 370.84a202.17 202.17 0 0 1-25-1.43 298.85 298.85 0 0 0 160.83 46.92"/></svg></a> 487 <br/> 488 <small>© 1999-2021 ImageMagick Studio LLC</small> 489 </div> 490 </footer> 491 492 <!-- Javascript assets --> 493 <script src="assets/magick.js" ></script> 494 </body> 495</html> 496<!-- Magick Cache 13th February 2021 12:27 -->
