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12 …qvm"><img style="margin-left:8px; margin-top:21px; float:right; vertical-align: top" src="https://…
21 https://github.com/boostorg/qvm[GitHub] | link:./qvm.pdf[PDF]
68 namespace boost { namespace qvm {
103 namespace boost { namespace qvm {
141 …qvm/quat_traits_array.hpp,`boost/qvm/quat_traits_array.hpp`>>, <<boost/qvm/vec_traits_array.hpp,`b…
265 …ad the same {CPP} operators as QVM, it is safe to bring the entire `boost::qvm` namespace in scope…
269 using namespace boost::qvm;
274 - Most `boost::qvm` function overloads and all operator overloads use SFINAE/`enable_if`, which mak…
278 …qvm namespace in scope may introduce ambiguities when accessing types (as opposed to functions) de…
282 Bringing the `boost::qvm` namespace in scope lets you mix vector and matrix types that come from di…
302 namespace boost { namespace qvm {
354 The header `boost/qvm/all.hpp` is provided for convenience. It includes all other QVM headers.
359 | Quaternion traits |#include <boost/qvm/quat_traits.hpp>
360 #include <boost/qvm/quat_traits_array.hpp>
361 #include <boost/qvm/deduce_quat.hpp>
362 | Quaternion element access |#include <boost/qvm/quat_access.hpp>
363 | Quaternion operations |#include <boost/qvm/quat_operations.hpp>
364 | <<quat,`quat`>> class template |#include <boost/qvm/quat.hpp>
370 | Vector traits |#include <boost/qvm/vec_traits.hpp>
371 #include <boost/qvm/vec_traits_array.hpp>
372 #include <boost/qvm/deduce_vec.hpp>
373 | Vector element access |#include <boost/qvm/vec_access.hpp>
374 | Vector <<swizzling,swizzling>> |#include <boost/qvm/swizzle.hpp>
375 #include <boost/qvm/swizzle2.hpp>
376 #include <boost/qvm/swizzle3.hpp>
377 #include <boost/qvm/swizzle4.hpp>
378 | Vector operations |#include <boost/qvm/vec_operations.hpp>
379 #include <boost/qvm/vec_operations2.hpp>
380 #include <boost/qvm/vec_operations3.hpp>
381 #include <boost/qvm/vec_operations4.hpp>
382 | Quaternion-vector operations |#include <boost/qvm/quat_vec_operations.hpp>
383 | Vector-matrix operations |#include <boost/qvm/vec_mat_operations.hpp>
384 | Vector-matrix <<view_proxy,view proxies>> |#include <boost/qvm/map_vec_mat.hpp>
385 | <<vec,`vec`>> class template |#include <boost/qvm/vec.hpp>
391 | Matrix traits |#include <boost/qvm/mat_traits.hpp>
392 #include <boost/qvm/mat_traits_array.hpp>
393 #include <boost/qvm/deduce_mat.hpp>
394 | Matrix element access |#include <boost/qvm/mat_access.hpp>
395 | Matrix operations |#include <boost/qvm/mat_operations.hpp>
396 #include <boost/qvm/mat_operations2.hpp>
397 #include <boost/qvm/mat_operations3.hpp>
398 #include <boost/qvm/mat_operations4.hpp>
399 | Matrix-matrix <<view_proxy,view proxies>> |#include <boost/qvm/map_mat_mat.hpp>
400 | Matrix-vector <<view_proxy,view proxies>> |#include <boost/qvm/map_mat_vec.hpp>
401 | <<mat,`mat`>> class template |#include <boost/qvm/mat.hpp>
439 .#include <boost/qvm/scalar_traits.hpp>
442 namespace boost { namespace qvm {
472 .#include <boost/qvm/scalar_traits.hpp>
475 namespace boost { namespace qvm {
497 .#include <boost/qvm/deduce_scalar.hpp>
500 namespace boost { namespace qvm {
528 .#include <boost/qvm/scalar_traits.hpp>
531 namespace boost { namespace qvm {
554 .#include <boost/qvm/quat_traits.hpp>
557 namespace boost { namespace qvm {
576 .#include <boost/qvm/quat_traits.hpp>
579 namespace boost { namespace qvm {
630 #include <boost/qvm/quat_traits.hpp>
634 namespace boost { namespace qvm {
660 namespace boost { namespace qvm {
680 .#include <boost/qvm/quat_traits_defaults.hpp>
683 namespace boost { namespace qvm {
711 .#include <boost/qvm/deduce_quat.hpp>
714 namespace boost { namespace qvm {
741 .#include <boost/qvm/deduce_quat.hpp>
744 namespace boost { namespace qvm {
772 .#include <boost/qvm/vec_traits.hpp>
775 namespace boost { namespace qvm {
794 .#include <boost/qvm/vec_traits.hpp>
797 namespace boost { namespace qvm {
861 #include <boost/qvm/vec_traits.hpp>
865 namespace boost { namespace qvm {
901 namespace boost { namespace qvm {
926 .#include <boost/qvm/vec_traits_defaults.hpp>
929 namespace boost { namespace qvm {
969 .#include <boost/qvm/deduce_vec.hpp>
972 namespace boost { namespace qvm {
1002 .#include <boost/qvm/deduce_vec.hpp>
1005 namespace boost { namespace qvm {
1034 .#include <boost/qvm/mat_traits.hpp>
1037 namespace boost { namespace qvm {
1056 .#include <boost/qvm/mat_traits.hpp>
1059 namespace boost { namespace qvm {
1120 #include <boost/qvm/mat_traits.hpp>
1124 namespace boost { namespace qvm {
1160 namespace boost { namespace qvm {
1181 .#include <boost/qvm/mat_traits_defaults.hpp>
1184 namespace boost { namespace qvm {
1225 .#include <boost/qvm/deduce_mat.hpp>
1228 namespace boost { namespace qvm {
1262 .#include <boost/qvm/deduce_mat.hpp>
1265 namespace boost { namespace qvm {
1301 .#include <boost/qvm/quat.hpp>
1304 namespace boost { namespace qvm {
1352 .#include <boost/qvm/vec.hpp>
1355 namespace boost { namespace qvm {
1411 .#include <boost/qvm/mat.hpp>
1414 namespace boost { namespace qvm {
1474 .#include <boost/qvm/quat_access.hpp>
1477 namespace boost { namespace qvm {
1516 .#include <boost/qvm/vec_access.hpp>
1519 namespace boost { namespace qvm {
1566 .#include <boost/qvm/swizzle.hpp>
1569 namespace boost { namespace qvm {
1686 .#include <boost/qvm/mat_access.hpp>
1689 namespace boost { namespace qvm {
1732 .#include <boost/qvm/quat_operations.hpp>
1735 namespace boost { namespace qvm {
1754 .#include <boost/qvm/quat_operations.hpp>
1757 namespace boost { namespace qvm {
1786 .#include <boost/qvm/quat_operations.hpp>
1789 namespace boost { namespace qvm {
1808 .#include <boost/qvm/quat_operations.hpp>
1811 namespace boost { namespace qvm {
1831 .#include <boost/qvm/quat_operations.hpp>
1834 namespace boost { namespace qvm {
1855 .#include <boost/qvm/quat_operations.hpp>
1858 namespace boost { namespace qvm {
1877 .#include <boost/qvm/quat_operations.hpp>
1880 namespace boost { namespace qvm {
1900 .#include <boost/qvm/quat_operations.hpp>
1903 namespace boost { namespace qvm {
1921 .#include <boost/qvm/quat_operations.hpp>
1924 namespace boost { namespace qvm {
1943 .#include <boost/qvm/quat_operations.hpp>
1946 namespace boost { namespace qvm {
1964 .#include <boost/qvm/quat_operations.hpp>
1967 namespace boost { namespace qvm {
1991 .#include <boost/qvm/quat_operations.hpp>
1994 namespace boost { namespace qvm {
2013 .#include <boost/qvm/quat_operations.hpp>
2016 namespace boost { namespace qvm {
2036 .#include <boost/qvm/quat_operations.hpp>
2039 namespace boost { namespace qvm {
2056 .#include <boost/qvm/quat_operations.hpp>
2059 namespace boost { namespace qvm {
2076 .#include <boost/qvm/quat_operations.hpp>
2079 namespace boost { namespace qvm {
2096 .#include <boost/qvm/quat_operations.hpp>
2099 namespace boost { namespace qvm {
2116 .#include <boost/qvm/quat_operations.hpp>
2119 namespace boost { namespace qvm {
2136 .#include <boost/qvm/quat_operations.hpp>
2139 namespace boost { namespace qvm {
2166 .#include <boost/qvm/quat_operations.hpp>
2169 namespace boost { namespace qvm {
2189 .#include <boost/qvm/quat_operations.hpp>
2192 namespace boost { namespace qvm {
2212 .#include <boost/qvm/quat_operations.hpp>
2215 namespace boost { namespace qvm {
2234 .#include <boost/qvm/quat_operations.hpp>
2237 namespace boost { namespace qvm {
2260 .#include <boost/qvm/quat_operations.hpp>
2263 namespace boost { namespace qvm {
2285 .#include <boost/qvm/quat_operations.hpp>
2288 namespace boost { namespace qvm {
2303 .#include <boost/qvm/quat_operations.hpp>
2306 namespace boost { namespace qvm {
2328 .#include <boost/qvm/quat_operations.hpp>
2331 namespace boost { namespace qvm {
2345 .#include <boost/qvm/quat_operations.hpp>
2348 namespace boost { namespace qvm {
2371 .#include <boost/qvm/quat_operations.hpp>
2374 namespace boost { namespace qvm {
2395 .#include <boost/qvm/quat_operations.hpp>
2398 namespace boost { namespace qvm {
2423 .#include <boost/qvm/quat_operations.hpp>
2426 namespace boost { namespace qvm {
2444 .#include <boost/qvm/quat_operations.hpp>
2447 namespace boost { namespace qvm {
2462 .#include <boost/qvm/quat_operations.hpp>
2465 namespace boost { namespace qvm {
2488 .#include <boost/qvm/quat_operations.hpp>
2491 namespace boost { namespace qvm {
2507 .#include <boost/qvm/quat_operations.hpp>
2510 namespace boost { namespace qvm {
2525 .#include <boost/qvm/quat_operations.hpp>
2528 namespace boost { namespace qvm {
2551 .#include <boost/qvm/quat_operations.hpp>
2554 namespace boost { namespace qvm {
2570 .#include <boost/qvm/quat_operations.hpp>
2573 namespace boost { namespace qvm {
2588 .#include <boost/qvm/quat_operations.hpp>
2591 namespace boost { namespace qvm {
2614 .#include <boost/qvm/quat_operations.hpp>
2617 namespace boost { namespace qvm {
2633 .#include <boost/qvm/quat_operations.hpp>
2636 namespace boost { namespace qvm {
2652 .#include <boost/qvm/quat_operations.hpp>
2655 namespace boost { namespace qvm {
2675 .#include <boost/qvm/vec_operations.hpp>
2678 namespace boost { namespace qvm {
2698 .#include <boost/qvm/vec_operations.hpp>
2701 namespace boost { namespace qvm {
2721 .#include <boost/qvm/vec_operations.hpp>
2724 namespace boost { namespace qvm {
2746 .#include <boost/qvm/vec_operations.hpp>
2749 namespace boost { namespace qvm {
2768 .#include <boost/qvm/vec_operations.hpp>
2771 namespace boost { namespace qvm {
2792 .#include <boost/qvm/vec_operations.hpp>
2795 namespace boost { namespace qvm {
2815 .#include <boost/qvm/vec_operations.hpp>
2818 namespace boost { namespace qvm {
2839 .#include <boost/qvm/vec_operations.hpp>
2842 namespace boost { namespace qvm {
2860 .#include <boost/qvm/vec_operations.hpp>
2863 namespace boost { namespace qvm {
2882 .#include <boost/qvm/vec_operations.hpp>
2885 namespace boost { namespace qvm {
2903 .#include <boost/qvm/vec_operations.hpp>
2906 namespace boost { namespace qvm {
2925 .#include <boost/qvm/vec_operations.hpp>
2928 namespace boost { namespace qvm {
2946 .#include <boost/qvm/vec_operations.hpp>
2949 namespace boost { namespace qvm {
2968 .#include <boost/qvm/mat_operations.hpp>
2972   namespace qvm
2991 .#include <boost/qvm/vec_operations.hpp>
2994 namespace boost { namespace qvm {
3012 .#include <boost/qvm/vec_operations.hpp>
3015 namespace boost { namespace qvm {
3033 .#include <boost/qvm/vec_operations.hpp>
3036 namespace boost { namespace qvm {
3064 .#include <boost/qvm/vec_operations.hpp>
3067 namespace boost { namespace qvm {
3090 .#include <boost/qvm/vec_operations.hpp>
3093 namespace boost { namespace qvm {
3114 .#include <boost/qvm/vec_operations.hpp>
3117 namespace boost { namespace qvm {
3138 .#include <boost/qvm/vec_operations.hpp>
3141 namespace boost { namespace qvm {
3156 .#include <boost/qvm/vec_operations.hpp>
3159 namespace boost { namespace qvm {
3184 .#include <boost/qvm/vec_operations.hpp>
3187 namespace boost { namespace qvm {
3203 .#include <boost/qvm/vec_operations.hpp>
3206 namespace boost { namespace qvm {
3226 .#include <boost/qvm/mat_operations.hpp>
3229 namespace boost { namespace qvm {
3250 .#include <boost/qvm/mat_operations.hpp>
3253 namespace boost { namespace qvm {
3276 .#include <boost/qvm/mat_operations.hpp>
3279 namespace boost { namespace qvm {
3300 .#include <boost/qvm/mat_operations.hpp>
3303 namespace boost { namespace qvm {
3322 .#include <boost/qvm/mat_operations.hpp>
3325 namespace boost { namespace qvm {
3347 .#include <boost/qvm/mat_operations.hpp>
3350 namespace boost { namespace qvm {
3371 .#include <boost/qvm/mat_operations.hpp>
3374 namespace boost { namespace qvm {
3396 .#include <boost/qvm/mat_operations.hpp>
3399 namespace boost { namespace qvm {
3417 .#include <boost/qvm/mat_operations.hpp>
3420 namespace boost { namespace qvm {
3439 .#include <boost/qvm/mat_operations.hpp>
3442 namespace boost { namespace qvm {
3469 .#include <boost/qvm/mat_operations.hpp>
3472 namespace boost { namespace qvm {
3490 .#include <boost/qvm/mat_operations.hpp>
3493 namespace boost { namespace qvm {
3514 .#include <boost/qvm/mat_operations.hpp>
3517 namespace boost { namespace qvm {
3541 .#include <boost/qvm/mat_operations.hpp>
3544 namespace boost { namespace qvm {
3563 .#include <boost/qvm/mat_operations.hpp>
3566 namespace boost { namespace qvm {
3585 .#include <boost/qvm/mat_operations.hpp>
3588 namespace boost { namespace qvm {
3607 .#include <boost/qvm/mat_operations.hpp>
3610 namespace boost { namespace qvm {
3640 .#include <boost/qvm/mat_operations.hpp>
3643 namespace boost { namespace qvm {
3661 .#include <boost/qvm/mat_operations.hpp>
3664 namespace boost { namespace qvm {
3690 .#include <boost/qvm/mat_operations.hpp>
3692 namespace boost { namespace qvm {
3707 .#include <boost/qvm/mat_operations.hpp>
3710 namespace boost { namespace qvm {
3738 .#include <boost/qvm/mat_operations.hpp>
3741 namespace boost { namespace qvm {
3811 .#include <boost/qvm/mat_operations.hpp>
3814 namespace boost { namespace qvm {
3911 .#include <boost/qvm/mat_operations.hpp>
3914 namespace boost { namespace qvm {
4005 .#include <boost/qvm/mat_operations.hpp>
4008 namespace boost { namespace qvm {
4023 .#include <boost/qvm/mat_operations.hpp>
4026 namespace boost { namespace qvm {
4051 .#include <boost/qvm/mat_operations.hpp>
4054 namespace boost { namespace qvm {
4073 .#include <boost/qvm/mat_operations.hpp>
4076 namespace boost { namespace qvm {
4091 .#include <boost/qvm/mat_operations.hpp>
4094 namespace boost { namespace qvm {
4119 .#include <boost/qvm/mat_operations.hpp>
4122 namespace boost { namespace qvm {
4140 .#include <boost/qvm/mat_operations.hpp>
4143 namespace boost { namespace qvm {
4158 .#include <boost/qvm/mat_operations.hpp>
4161 namespace boost { namespace qvm {
4186 .#include <boost/qvm/mat_operations.hpp>
4189 namespace boost { namespace qvm {
4207 .#include <boost/qvm/mat_operations.hpp>
4210 namespace boost { namespace qvm {
4228 .#include <boost/qvm/mat_operations.hpp>
4231 namespace boost { namespace qvm {
4257 .#include <boost/qvm/mat_operations.hpp>
4260 namespace boost { namespace qvm {
4286 .#include <boost/qvm/mat_operations.hpp>
4289 namespace boost { namespace qvm {
4305 .#include <boost/qvm/mat_operations.hpp>
4308 namespace boost { namespace qvm {
4328 .#include <boost/qvm/quat_vec_operations.hpp>
4331 namespace boost { namespace qvm {
4354 .#include <boost/qvm/vec_mat_operations.hpp>
4357 namespace boost { namespace qvm {
4378 .#include <boost/qvm/vec_mat_operations.hpp>
4381 namespace boost { namespace qvm {
4401 .#include <boost/qvm/vec_mat_operations.hpp>
4404 namespace boost { namespace qvm {
4426 .#include <boost/qvm/map_mat_mat.hpp>
4429 namespace boost { namespace qvm {
4444 .#include <boost/qvm/map_mat_mat.hpp>
4447 namespace boost { namespace qvm {
4462 .#include <boost/qvm/map_mat_mat.hpp>
4465 namespace boost { namespace qvm {
4480 .#include <boost/qvm/map_mat_mat.hpp>
4483 namespace boost { namespace qvm {
4498 .#include <boost/qvm/map_mat_mat.hpp>
4501 namespace boost { namespace qvm {
4516 .#include <boost/qvm/map_mat_mat.hpp>
4519 namespace boost { namespace qvm {
4534 .#include <boost/qvm/map_mat_mat.hpp>
4537 namespace boost { namespace qvm {
4552 .#include <boost/qvm/map_mat_mat.hpp>
4555 namespace boost { namespace qvm {
4571 .#include <boost/qvm/map_vec_mat.hpp>
4574 namespace boost { namespace qvm {
4590 .#include <boost/qvm/map_vec_mat.hpp>
4593 namespace boost { namespace qvm {
4609 .#include <boost/qvm/map_vec_mat.hpp>
4612 namespace boost { namespace qvm {
4628 .#include <boost/qvm/map_vec_mat.hpp>
4631 namespace boost { namespace qvm {
4651 .#include <boost/qvm/map_mat_vec.hpp>
4654 namespace boost { namespace qvm {
4670 .#include <boost/qvm/map_mat_vec.hpp>
4673 namespace boost { namespace qvm {
4689 .#include <boost/qvm/map_mat_vec.hpp>
4692 namespace boost { namespace qvm {
4708 .#include <boost/qvm/map_mat_vec.hpp>
4711 namespace boost { namespace qvm {
4731 .#include <boost/qvm/error.hpp>
4734 namespace boost { namespace qvm {
4748 .#include <boost/qvm/error.hpp>
4751 namespace boost { namespace qvm {
4765 .#include <boost/qvm/error.hpp>
4768 namespace boost { namespace qvm {
4785 .#include <boost/qvm/inline.hpp>
4788 namespace boost { namespace qvm {
4797 … directly by QVM, except as the default value of other macros from `<boost/qvm/inline.hpp>`. A use…
4805 .#include <boost/qvm/inline.hpp>
4808 namespace boost { namespace qvm {
4817 … directly by QVM, except as the default value of other macros from `<boost/qvm/inline.hpp>`. A use…
4825 .#include <boost/qvm/inline.hpp>
4828 namespace boost { namespace qvm {
4845 .#include <boost/qvm/inline.hpp>
4848 namespace boost { namespace qvm {
4865 .#include <boost/qvm/inline.hpp>
4868 namespace boost { namespace qvm {
4885 .#include <boost/qvm/inline.hpp>
4888 namespace boost { namespace qvm {
4905 .#include <boost/qvm/assert.hpp>
4908 namespace boost { namespace qvm {
4926 .#include <boost/qvm/static_assert.hpp>
4929 namespace boost { namespace qvm {
4947 .#include <boost/qvm/throw_exception.hpp>
4950 namespace boost { namespace qvm {
4991 …mand-line utility program. Its source code can be found in the `boost/libs/qvm/gen` directory. It …
4994 ** `boost/qvm/gen/mat_operations2.hpp` (matrices of size 2x2, 2x1 and 1x2, included by `boost/qvm/m…
4995 ** `boost/qvm/gen/mat_operations3.hpp` (matrices of size 3x3, 3x1 and 1x3, included by `boost/qvm/m…
4996 ** `boost/qvm/gen/mat_operations4.hpp` (matrices of size 4x4, 4x1 and 1x4, included by `boost/qvm/m…
4998 ** `boost/qvm/gen/v2.hpp` (included by `boost/qvm/vec_operations2.hpp`)
4999 ** `boost/qvm/gen/v3.hpp` (included by `boost/qvm/vec_operations3.hpp`)
5000 ** `boost/qvm/gen/v4.hpp` (included by `boost/qvm/vec_operations4.hpp`)
5002 ** `boost/qvm/gen/vm2.hpp` (included by `boost/qvm/vec_mat_operations2.hpp`)
5003 ** `boost/qvm/gen/vm3.hpp` (included by `boost/qvm/vec_mat_operations3.hpp`)
5004 ** `boost/qvm/gen/vm4.hpp` (included by `boost/qvm/vec_mat_operations4.hpp`)
5006 ** `boost/qvm/gen/sw2.hpp` (included by `boost/qvm/swizzle2.hpp`)
5007 ** `boost/qvm/gen/sw3.hpp` (included by `boost/qvm/swizzle3.hpp`)
5008 ** `boost/qvm/gen/sw4.hpp` (included by `boost/qvm/swizzle4.hpp`)
5010 …qvm/gen/m5.hpp`, it must be included before `boost/qvm/mat_operations.hpp` in included. However, t…
5012 …qvm/gen` are not part of the public interface of QVM. For example, `boost/qvm/gen/mat_operations2.…
5038 …qvm` are designed to work with user-defined types. Typically it is sufficient to make these operat…
5050   using namespace boost::qvm;
5062 …qvm::operator==` is made visible in namespace `ns2` by `using namespace boost::qvm`, the call orig…
5068   using boost::qvm::operator==;
5077 … Instead, it calls function templates declared in `boost/qvm/math.hpp` in namespace `boost::qvm`. …
5081 …)` will compile successfully but fail to link, since it calls e.g. `boost::qvm::sin<int>`, which i…
5087 The source code is available in https://github.com/boostorg/qvm[QVM GitHub repository].
5093 See the link:https://travis-ci.org/boostorg/qvm[QVM Travis CI Builds].
5104 …qvm::<<vec,vec>>` (or `qvm::<<mat,mat>>`, or `qvm::<<quat,quat>>`) template compare to vector type…