From fc175dbb72f80764431c1fe82ab8996b114831da Mon Sep 17 00:00:00 2001 From: 3gg <3gg@shellblade.net> Date: Sat, 4 Feb 2023 11:07:21 -0800 Subject: Add slerp and qslerp. --- test/quat_test.c | 85 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ test/vec3_test.c | 68 +++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 153 insertions(+) create mode 100644 test/quat_test.c create mode 100644 test/vec3_test.c (limited to 'test') diff --git a/test/quat_test.c b/test/quat_test.c new file mode 100644 index 0000000..83519c3 --- /dev/null +++ b/test/quat_test.c @@ -0,0 +1,85 @@ +#include + +#include + +#include "test.h" + +#include + +static const float eps = 1e-7; + +static inline void print_quat(quat q) { + printf("{ %f, %f, %f, %f }\n", q.x, q.y, q.z, q.w); +} + +static inline void print_vec3(vec3 v) { + printf("{ %f, %f, %f }\n", v.x, v.y, v.z); +} + +/// Slerp between two vectors forming an acute angle. +TEST_CASE(quat_slerp_acute_angle) { + const R angle1 = 0; + const R angle2 = PI / 4; + const R t = 0.5; + + const quat a = qmake_rot(angle1, 0, 0, 1); + const quat b = qmake_rot(angle2, 0, 0, 1); + + const quat c = qslerp(a, b, t); + const vec3 result = qrot(c, vec3_make(1, 0, 0)); + + const R angle3 = lerp(angle1, angle2, t); + const vec3 expected = vec3_make(cos(angle3), sin(angle3), 0.0); + TEST_TRUE(vec3_eq(result, expected, eps)); +} + +/// Slerp between two vectors forming an obtuse angle (negative dot product). +/// +/// The interpolation must follow the shortest path between both vectors. +TEST_CASE(quat_slerp_obtuse_angle) { + const R angle1 = 0; + const R angle2 = 3 * PI / 4; + const R t = 0.5; + + const quat a = qmake_rot(angle1, 0, 0, 1); + const quat b = qmake_rot(angle2, 0, 0, 1); + + const quat c = qslerp(a, b, t); + const vec3 result = qrot(c, vec3_make(1, 0, 0)); + + const R angle3 = lerp(angle1, angle2, t); + const vec3 expected = vec3_make(cos(angle3), sin(angle3), 0.0); + TEST_TRUE(vec3_eq(result, expected, eps)); +} + +/// Slerp between two vectors forming a reflex angle. +/// +/// The interpolation must follow the shortest path between both vectors. +TEST_CASE(quat_slerp_reflex_angle) { + const R angle1 = 0; + const R angle2 = 5 * PI / 4; + const R t = 0.5; + + const quat a = qmake_rot(angle1, 0, 0, 1); + const quat b = qmake_rot(angle2, 0, 0, 1); + + const quat c = qslerp(a, b, t); + const vec3 result = qrot(c, vec3_make(1, 0, 0)); + + // Because it's a reflex angle, we expect the rotation to follow the short + // path from 'a' down clockwise to 'b'. Could add +PI to the result of lerp(), + // but that adds more error than negating cos and sin. + const R angle3 = lerp(angle1, angle2, t); + const vec3 expected = vec3_make(-cos(angle3), -sin(angle3), 0.0); + TEST_TRUE(vec3_eq(result, expected, eps)); +} + +TEST_CASE(quat_mat4_from_quat) { + const R angle = PI / 8; + const quat q = qmake_rot(angle, 0, 0, 1); + + const mat4 m = mat4_from_quat(q); + const vec3 p = mat4_mul_vec3(m, vec3_make(1, 0, 0), /*w=*/1); + + TEST_TRUE(vec3_eq(p, vec3_make(cos(angle), sin(angle), 0), eps)); +} diff --git a/test/vec3_test.c b/test/vec3_test.c new file mode 100644 index 0000000..886fee3 --- /dev/null +++ b/test/vec3_test.c @@ -0,0 +1,68 @@ +#include + +#include + +#include "test.h" + +#include + +static const float eps = 1e-7; + +static inline void print_vec3(vec3 v) { + printf("{ %f, %f, %f }\n", v.x, v.y, v.z); +} + +/// Slerp between two vectors forming an acute angle. +TEST_CASE(vec3_slerp_acute_angle) { + const R angle1 = 0; + const R angle2 = PI / 4; + const R t = 0.5; + + const vec3 a = vec3_make(cos(angle1), sin(angle1), 0); + const vec3 b = vec3_make(cos(angle2), sin(angle2), 0); + + const vec3 result = vec3_slerp(a, b, t); + + const R angle3 = lerp(angle1, angle2, t); + const vec3 expected = vec3_make(cos(angle3), sin(angle3), 0.0); + TEST_TRUE(vec3_eq(result, expected, eps)); +} + +/// Slerp between two vectors forming an obtuse angle (negative dot product). +/// +/// The interpolation must follow the shortest path between both vectors. +TEST_CASE(vec3_slerp_obtuse_angle) { + const R angle1 = 0; + const R angle2 = 3 * PI / 4; + const R t = 0.5; + + const vec3 a = vec3_make(cos(angle1), sin(angle1), 0); + const vec3 b = vec3_make(cos(angle2), sin(angle2), 0); + + const vec3 result = vec3_slerp(a, b, t); + + const R angle3 = lerp(angle1, angle2, t); + const vec3 expected = vec3_make(cos(angle3), sin(angle3), 0.0); + TEST_TRUE(vec3_eq(result, expected, eps)); +} + +/// Slerp between two vectors forming a reflex angle. +/// +/// The interpolation must follow the shortest path between both vectors. +TEST_CASE(vec3_slerp_reflex_angle) { + const R angle1 = 0; + const R angle2 = 5 * PI / 4; + const R t = 0.5; + + const vec3 a = vec3_make(cos(angle1), sin(angle1), 0); + const vec3 b = vec3_make(cos(angle2), sin(angle2), 0); + + const vec3 result = vec3_slerp(a, b, t); + + // slerp goes from a to b following the shortest path, which is down from a + // towards b. The resulting angle is therefore +PI of the angle we get from + // lerping the two input angles. + const R angle3 = lerp(angle1, angle2, t) + PI; + const vec3 expected = vec3_make(cos(angle3), sin(angle3), 0.0); + TEST_TRUE(vec3_eq(result, expected, 1e-5)); +} -- cgit v1.2.3