BlackMATov/vmath.hpp
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qua: lerp, nlerp, slerp

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BlackMATov
2021-01-31 01:44:55 +07:00
parent 89f9872d96
commit 7e62c77436
2 changed files with 107 additions and 3 deletions
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37
headers/vmath.hpp/vmath_qua_fun.hpp
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@@ -161,6 +161,43 @@ namespace vmath_hpp
namespace vmath_hpp
{
template < typename T >
[[nodiscard]] qua<T> lerp(const qua<T>& xs, const qua<T>& ys, T a) {
return qua(lerp(vec{xs}, vec{ys}, a));
}
template < typename T >
[[nodiscard]] qua<T> lerp(const qua<T>& xs, const qua<T>& ys, T xs_a, T ys_a) {
return qua(lerp(vec{xs}, vec{ys}, xs_a, ys_a));
}
template < typename T >
[[nodiscard]] qua<T> nlerp(const qua<T>& unit_xs, const qua<T>& unit_ys, T a) {
const T xs_scale = T(1) - a;
const T ys_scale = a * sign(dot(unit_xs, unit_ys));
return normalize(lerp(unit_xs, unit_ys, xs_scale, ys_scale));
}
template < typename T >
[[nodiscard]] qua<T> slerp(const qua<T>& unit_xs, const qua<T>& unit_ys, T a) {
const T raw_cos_theta = dot(unit_xs, unit_ys);
const T raw_cos_theta_sign = sign(raw_cos_theta);
// half degree linear threshold: cos((pi / 180) * 0.25)
if ( const T cos_theta = raw_cos_theta * raw_cos_theta_sign; cos_theta < T(0.99999) ) {
const T theta = acos(cos_theta);
const T rsin_theta = rsqrt(T(1) - sqr(cos_theta));
const T xs_scale = sin((T(1) - a) * theta) * rsin_theta;
const T ys_scale = sin(a * theta) * raw_cos_theta_sign * rsin_theta;
return lerp(unit_xs, unit_ys, xs_scale, ys_scale);
} else {
// use linear interpolation for small angles
const T xs_scale = T(1) - a;
const T ys_scale = a * raw_cos_theta_sign;
return normalize(lerp(unit_xs, unit_ys, xs_scale, ys_scale));
}
}
template < typename T >
[[nodiscard]] vec<bool, 4> isnan(const qua<T>& xs) {
return isnan(vec{xs});

73
untests/vmath_qua_fun_tests.cpp
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@@ -73,9 +73,76 @@ TEST_CASE("vmath/qua_fun") {
}
SECTION("Common Functions") {
REQUIRE_FALSE(any(isnan(fqua(1,1,1,1))));
REQUIRE_FALSE(any(isinf(fqua(1,1,1,1))));
REQUIRE(all(isfinite(fqua(1,1,1,1))));
{
REQUIRE(all(approx(
qrotate_z(radians(5.f)),
nlerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 0.f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(6.f)),
nlerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 0.1f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(10.f)),
nlerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 0.5f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(15.f)),
nlerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 1.f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(315.f)),
nlerp(qrotate_z(radians(270.f)), qrotate_z(radians(0.f)), 0.5f))));
REQUIRE(all(approx(
qrotate_z(radians(290.f)),
nlerp(qrotate_z(radians(220.f)), qrotate_z(radians(0.f)), 0.5f))));
}
{
REQUIRE(all(approx(
qrotate_z(radians(5.f)),
slerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 0.f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(6.f)),
slerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 0.1f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(10.f)),
slerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 0.5f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(15.f)),
slerp(qrotate_z(radians(5.f)), qrotate_z(radians(15.f)), 1.f),
0.00001f)));
REQUIRE(all(approx(
qrotate_z(radians(0.f)),
slerp(qrotate_z(radians(0.f)), qrotate_z(radians(0.f)), 0.5f))));
REQUIRE(all(approx(
qrotate_z(radians(0.25f)),
slerp(qrotate_z(radians(0.f)), qrotate_z(radians(0.5f)), 0.5f))));
REQUIRE(all(approx(
qrotate_z(radians(-45.f)),
slerp(qrotate_z(radians(0.f)), qrotate_z(radians(270.f)), 0.5f))));
REQUIRE(all(approx(
qrotate_z(radians(-70.f)),
slerp(qrotate_z(radians(0.f)), qrotate_z(radians(220.f)), 0.5f))));
REQUIRE(all(approx(
qrotate_z(radians(315.f)),
slerp(qrotate_z(radians(270.f)), qrotate_z(radians(0.f)), 0.5f))));
REQUIRE(all(approx(
qrotate_z(radians(290.f)),
slerp(qrotate_z(radians(220.f)), qrotate_z(radians(0.f)), 0.5f))));
}
{
REQUIRE_FALSE(any(isnan(fqua(1,1,1,1))));
REQUIRE_FALSE(any(isinf(fqua(1,1,1,1))));
REQUIRE(all(isfinite(fqua(1,1,1,1))));
}
}
SECTION("Geometric Functions") {