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qua: qrotate(from, to)

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BlackMATov
2021-02-10 17:52:53 +07:00
parent 7c79e05c89
commit 914ef69521
2 changed files with 80 additions and 16 deletions
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27
headers/vmath.hpp/vmath_ext.hpp
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@@ -942,6 +942,33 @@ namespace vmath_hpp
}
}
template < typename T >
[[nodiscard]] qua<T> qrotate(const qua<T>& q, const mat<T, 3>& m) {
return q * qrotate(m);
}
template < typename T >
[[nodiscard]] qua<T> qrotate(const vec<T, 3>& from, const vec<T, 3>& to) {
/// REFERENCE:
/// http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final
const T n = sqrt(length2(from) * length2(to));
const T s = dot(from, to) + n;
if ( s < T(0.000001) * n ) {
return abs(from.x) > abs(from.z)
? normalize(qua{vec{-from.y, from.x, T(0)}, T(0)})
: normalize(qua{vec{T(0), -from.z, from.y}, T(0)});
}
return normalize(qua{cross(from, to), s});
}
template < typename T >
[[nodiscard]] qua<T> qrotate(const qua<T>& q, const vec<T, 3>& from, const vec<T, 3>& to) {
return q * qrotate(from, to);
}
template < typename T >
[[nodiscard]] qua<T> qrotate(T angle, const vec<T, 3>& axis) {
/// REFERENCE:

69
untests/vmath_ext_tests.cpp
View File

@@ -16,6 +16,10 @@ namespace
{
using namespace vmath_hpp;
using namespace vmath_tests;
constexpr float pi = radians(180.f);
constexpr float pi_2 = radians(90.f);
constexpr float pi_4 = radians(45.f);
}
TEST_CASE("vmath/ext") {
@@ -220,10 +224,6 @@ TEST_CASE("vmath/ext") {
}
SECTION("matrix rotate") {
constexpr float pi = radians(180.f);
constexpr float pi_2 = radians(90.f);
constexpr float pi_4 = radians(45.f);
REQUIRE(float4(0.f,1.f,0.f,1.f) * rotate_x(pi_2) == uapprox4(0.f,0.f,1.f,1.f));
REQUIRE(float4(0.f,0.f,1.f,1.f) * rotate_y(pi_2) == uapprox4(1.f,0.f,0.f,1.f));
REQUIRE(float4(1.f,0.f,0.f,1.f) * rotate_z(pi_2) == uapprox4(0.f,1.f,0.f,1.f));
@@ -339,11 +339,46 @@ TEST_CASE("vmath/ext") {
STATIC_REQUIRE(perpendicular(float3(2.f, 2.f, 2.f), float3(0.f, 0.f, 1.f)) == uapprox3(2.f, 2.f, 0.f));
}
SECTION("quaternion qrotate") {
constexpr float pi = radians(180.f);
constexpr float pi_2 = radians(90.f);
constexpr float pi_4 = radians(45.f);
SECTION("quaternion/qrotate(m)") {
REQUIRE(all(approx(
vec{4.f,3.f,2.f,1.f} * rotate(qrotate(float3x3(rotate(0.f, vec{1.f,2.f,3.f})))),
vec{4.f,3.f,2.f,1.f} * rotate(0.f, vec{1.f,2.f,3.f}), 0.001f)));
REQUIRE(all(approx(
vec{4.f,3.f,2.f,1.f} * rotate(qrotate(float3x3(rotate(radians(12.5f), vec{1.f,2.f,3.f})))),
vec{4.f,3.f,2.f,1.f} * rotate(radians(12.5f), vec{1.f,2.f,3.f}), 0.001f)));
REQUIRE(all(approx(
vec{4.f,3.f,2.f,1.f} * rotate(qrotate(float3x3(rotate(radians(-190.5f), vec{1.f,2.f,3.f})))),
vec{4.f,3.f,2.f,1.f} * rotate(radians(-190.5f), vec{1.f,2.f,3.f}), 0.001f)));
}
SECTION("quaternion/qrotate(q, m)") {
REQUIRE(all(approx(
vec{4.f,3.f,2.f} * qrotate(
qrotate(float3x3(rotate(0.f, vec{1.f,2.f,3.f}))),
float3x3(rotate(0.f, vec{3.f,2.f,1.f}))),
vec{4.f,3.f,2.f} *
float3x3(rotate(0.f, vec{1.f,2.f,3.f})) *
float3x3(rotate(0.f, vec{3.f,2.f,1.f})))));
}
SECTION("quaternion/qrotate(from, to)") {
REQUIRE(+unit3_x<float> * qrotate(-unit3_x<float>, +unit3_x<float>) == uapprox3(-unit3_x<float>));
REQUIRE(-unit3_y<float> * qrotate(+unit3_y<float>, -unit3_y<float>) == uapprox3(+unit3_y<float>));
REQUIRE(+unit3_z<float> * qrotate(-unit3_z<float>, +unit3_z<float>) == uapprox3(-unit3_z<float>));
REQUIRE(vec{1.f,2.f,3.f} * qrotate(vec{1.f,2.f,3.f}, vec{-2.f,1.f,3.f}) == uapprox3(-2.f,1.f,3.f));
REQUIRE(vec{-2.f,1.f,3.f} * qrotate(vec{-2.f,1.f,3.f}, vec{1.f,2.f,3.f}) == uapprox3(1.f,2.f,3.f));
}
SECTION("quaternion/qrotate(q, from, to)") {
REQUIRE(vec{1.f,2.f,3.f} *
inverse(qrotate(float3x3(rotate(radians(12.f), {2.f,2.f,2.f})))) *
qrotate(
qrotate(float3x3(rotate(radians(12.f), {2.f,2.f,2.f}))),
vec{1.f,2.f,3.f},
vec{-2.f,1.f,3.f}) == uapprox3(vec{-2.f,1.f,3.f}));
}
SECTION("quaternion/qrotate(angle, axis)") {
REQUIRE(all(approx(
rotate(12.3f, float3(1.f,2.f,3.f)),
rotate(qrotate(12.3f, float3(1.f,2.f,3.f)) * 2.f))));
@@ -352,22 +387,24 @@ TEST_CASE("vmath/ext") {
REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(pi_2) == uapprox3(1.f,0.f,0.f));
REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(pi_2) == uapprox3(0.f,1.f,0.f));
REQUIRE(float3(0.f,1.f,0.f) * qrotate_x(qrotate_x(pi_4),pi_4) == uapprox3(0.f,0.f,1.f));
REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(qrotate_y(pi_4),pi_4) == uapprox3(1.f,0.f,0.f));
REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(qrotate_z(pi_4),pi_4) == uapprox3(0.f,1.f,0.f));
REQUIRE(float3(2.f,3.f,4.f) * qrotate(pi,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
REQUIRE(float3(2.f,3.f,4.f) * qrotate(pi,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,{0.f,0.f,1.f}),pi_2,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,float3{0.f,0.f,1.f}),pi_2,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
REQUIRE(qrotate_x(12.3f) == qrotate(12.3f, unit3_x<float> * 2.f));
REQUIRE(qrotate_y(12.3f) == qrotate(12.3f, unit3_y<float> * 2.f));
REQUIRE(qrotate_z(12.3f) == qrotate(12.3f, unit3_z<float> * 2.f));
}
SECTION("quaternion look_at") {
SECTION("quaternion/qrotate(q, angle, axis)") {
REQUIRE(float3(0.f,1.f,0.f) * qrotate_x(qrotate_x(pi_4),pi_4) == uapprox3(0.f,0.f,1.f));
REQUIRE(float3(0.f,0.f,1.f) * qrotate_y(qrotate_y(pi_4),pi_4) == uapprox3(1.f,0.f,0.f));
REQUIRE(float3(1.f,0.f,0.f) * qrotate_z(qrotate_z(pi_4),pi_4) == uapprox3(0.f,1.f,0.f));
REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,{0.f,0.f,1.f}),pi_2,{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
REQUIRE(float3(2.f,3.f,4.f) * qrotate(qrotate(pi_2,float3{0.f,0.f,1.f}),pi_2,float3{0.f,0.f,1.f}) == uapprox3(-2.f,-3.f,4.f));
}
SECTION("quaternion/qlook_at") {
REQUIRE(all(approx(
qlook_at_lh(float3(1.f,2.f,3.f), float3(0,1,0)),
qrotate(float3x3(look_at_lh(float3(), float3(1.f,2.f,3.f), float3(0,1,0)))))));