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Fix T83196: bad matrix to quaternion precision near 180 degrees rotation. 

Adjust the threshold for switching from the base case to trace > 0,
based on very similar example code from www.euclideanspace.com to
avoid float precision issues when trace is close to -1.

Also, remove conversions to and from double, because using double
here doesn't really have benefit, especially with the new threshold.

Finally, add quaternion-matrix-quaternion round trip tests with
full coverage for all 4 branches.

Differential Revision: https://developer.blender.org/D9675
This commit is contained in:
Alexander Gavrilov 2020-11-30 19:31:21 +03:00
parent 6022103264
commit 814b2787ca
Notes: blender-bot 2024-01-22 19:18:23 +01:00 
Referenced by issue #83196, Matrix multiplications/ to_quat/ to_euler outputs incorrect rotation in some cases
Referenced by issue blender/blender-addons#77811, Animation jitter on FBX export
Referenced by issue #117400, The to_quaternion matrix method produces a result that is different from previous versions of blender
3 changed files with 167 additions and 28 deletions
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1
source/blender/blenlib/CMakeLists.txt
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@ -400,6 +400,7 @@ if(WITH_GTESTS)
tests/BLI_math_color_test.cc
tests/BLI_math_geom_test.cc
tests/BLI_math_matrix_test.cc
tests/BLI_math_rotation_test.cc
tests/BLI_math_solvers_test.cc
tests/BLI_math_vector_test.cc
tests/BLI_memiter_test.cc

66
source/blender/blenlib/intern/math_rotation.c
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@ -320,47 +320,57 @@ void quat_to_mat4(float m[4][4], const float q[4])
void mat3_normalized_to_quat(float q[4], const float mat[3][3])
{
double tr, s;
BLI_ASSERT_UNIT_M3(mat);
tr = 0.25 * (double)(1.0f + mat[0][0] + mat[1][1] + mat[2][2]);
/* Check the trace of the matrix - bad precision if close to -1. */
const float trace = mat[0][0] + mat[1][1] + mat[2][2];
if (tr > (double)1e-4f) {
s = sqrt(tr);
q[0] = (float)s;
s = 1.0 / (4.0 * s);
q[1] = (float)((double)(mat[1][2] - mat[2][1]) * s);
q[2] = (float)((double)(mat[2][0] - mat[0][2]) * s);
q[3] = (float)((double)(mat[0][1] - mat[1][0]) * s);
if (trace > 0) {
float s = 2.0f * sqrtf(1.0f + trace);
q[0] = 0.25f * s;
s = 1.0f / s;
q[1] = (mat[1][2] - mat[2][1]) * s;
q[2] = (mat[2][0] - mat[0][2]) * s;
q[3] = (mat[0][1] - mat[1][0]) * s;
}
else {
/* Find the biggest diagonal element to choose the best formula.
* Here trace should also be always >= 0, avoiding bad precision. */
if (mat[0][0] > mat[1][1] && mat[0][0] > mat[2][2]) {
s = 2.0f * sqrtf(1.0f + mat[0][0] - mat[1][1] - mat[2][2]);
q[1] = (float)(0.25 * s);
float s = 2.0f * sqrtf(1.0f + mat[0][0] - mat[1][1] - mat[2][2]);
s = 1.0 / s;
q[0] = (float)((double)(mat[1][2] - mat[2][1]) * s);
q[2] = (float)((double)(mat[1][0] + mat[0][1]) * s);
q[3] = (float)((double)(mat[2][0] + mat[0][2]) * s);
q[1] = 0.25f * s;
s = 1.0f / s;
q[0] = (mat[1][2] - mat[2][1]) * s;
q[2] = (mat[1][0] + mat[0][1]) * s;
q[3] = (mat[2][0] + mat[0][2]) * s;
}
else if (mat[1][1] > mat[2][2]) {
s = 2.0f * sqrtf(1.0f + mat[1][1] - mat[0][0] - mat[2][2]);
q[2] = (float)(0.25 * s);
float s = 2.0f * sqrtf(1.0f + mat[1][1] - mat[0][0] - mat[2][2]);
s = 1.0 / s;
q[0] = (float)((double)(mat[2][0] - mat[0][2]) * s);
q[1] = (float)((double)(mat[1][0] + mat[0][1]) * s);
q[3] = (float)((double)(mat[2][1] + mat[1][2]) * s);
q[2] = 0.25f * s;
s = 1.0f / s;
q[0] = (mat[2][0] - mat[0][2]) * s;
q[1] = (mat[1][0] + mat[0][1]) * s;
q[3] = (mat[2][1] + mat[1][2]) * s;
}
else {
s = 2.0f * sqrtf(1.0f + mat[2][2] - mat[0][0] - mat[1][1]);
q[3] = (float)(0.25 * s);
float s = 2.0f * sqrtf(1.0f + mat[2][2] - mat[0][0] - mat[1][1]);
s = 1.0 / s;
q[0] = (float)((double)(mat[0][1] - mat[1][0]) * s);
q[1] = (float)((double)(mat[2][0] + mat[0][2]) * s);
q[2] = (float)((double)(mat[2][1] + mat[1][2]) * s);
q[3] = 0.25f * s;
s = 1.0f / s;
q[0] = (mat[0][1] - mat[1][0]) * s;
q[1] = (mat[2][0] + mat[0][2]) * s;
q[2] = (mat[2][1] + mat[1][2]) * s;
}
}

128
source/blender/blenlib/tests/BLI_math_rotation_test.cc Normal file
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@ -0,0 +1,128 @@
/* Apache License, Version 2.0 */
#include "testing/testing.h"
#include "BLI_math_rotation.h"
#include <math.h>
/* Test that quaternion converts to itself via matrix. */
static void test_quat_to_mat_to_quat(float w, float x, float y, float z)
{
float in_quat[4] = {w, x, y, z};
float norm_quat[4], matrix[3][3], out_quat[4];
normalize_qt_qt(norm_quat, in_quat);
quat_to_mat3(matrix, norm_quat);
mat3_normalized_to_quat(out_quat, matrix);
/* The expected result is flipped (each orientation corresponds to 2 quats) */
if (w < 0) {
mul_qt_fl(norm_quat, -1);
}
EXPECT_V4_NEAR(norm_quat, out_quat, FLT_EPSILON);
}
TEST(math_rotation, quat_to_mat_to_quat_rot180)
{
test_quat_to_mat_to_quat(1, 0, 0, 0);
test_quat_to_mat_to_quat(0, 1, 0, 0);
test_quat_to_mat_to_quat(0, 0, 1, 0);
test_quat_to_mat_to_quat(0, 0, 0, 1);
}
TEST(math_rotation, quat_to_mat_to_quat_rot180n)
{
test_quat_to_mat_to_quat(-1.000f, 0, 0, 0);
test_quat_to_mat_to_quat(-1e-20f, -1, 0, 0);
test_quat_to_mat_to_quat(-1e-20f, 0, -1, 0);
test_quat_to_mat_to_quat(-1e-20f, 0, 0, -1);
}
TEST(math_rotation, quat_to_mat_to_quat_rot90)
{
const float s2 = 1 / sqrtf(2);
test_quat_to_mat_to_quat(s2, s2, 0, 0);
test_quat_to_mat_to_quat(s2, -s2, 0, 0);
test_quat_to_mat_to_quat(s2, 0, s2, 0);
test_quat_to_mat_to_quat(s2, 0, -s2, 0);
test_quat_to_mat_to_quat(s2, 0, 0, s2);
test_quat_to_mat_to_quat(s2, 0, 0, -s2);
}
TEST(math_rotation, quat_to_mat_to_quat_rot90n)
{
const float s2 = 1 / sqrtf(2);
test_quat_to_mat_to_quat(-s2, s2, 0, 0);
test_quat_to_mat_to_quat(-s2, -s2, 0, 0);
test_quat_to_mat_to_quat(-s2, 0, s2, 0);
test_quat_to_mat_to_quat(-s2, 0, -s2, 0);
test_quat_to_mat_to_quat(-s2, 0, 0, s2);
test_quat_to_mat_to_quat(-s2, 0, 0, -s2);
}
TEST(math_rotation, quat_to_mat_to_quat_bad_T83196)
{
test_quat_to_mat_to_quat(0.0032f, 0.9999f, -0.0072f, -0.0100f);
test_quat_to_mat_to_quat(0.0058f, 0.9999f, -0.0090f, -0.0101f);
test_quat_to_mat_to_quat(0.0110f, 0.9998f, -0.0140f, -0.0104f);
test_quat_to_mat_to_quat(0.0142f, 0.9997f, -0.0192f, -0.0107f);
test_quat_to_mat_to_quat(0.0149f, 0.9996f, -0.0212f, -0.0107f);
}
TEST(math_rotation, quat_to_mat_to_quat_near_1000)
{
test_quat_to_mat_to_quat(0.9999f, 0.01f, -0.001f, -0.01f);
test_quat_to_mat_to_quat(0.9999f, 0.02f, -0.002f, -0.02f);
test_quat_to_mat_to_quat(0.9999f, 0.03f, -0.003f, -0.03f);
test_quat_to_mat_to_quat(0.9999f, 0.04f, -0.004f, -0.04f);
test_quat_to_mat_to_quat(0.9999f, 0.05f, -0.005f, -0.05f);
test_quat_to_mat_to_quat(0.999f, 0.10f, -0.010f, -0.10f);
test_quat_to_mat_to_quat(0.99f, 0.15f, -0.015f, -0.15f);
test_quat_to_mat_to_quat(0.98f, 0.20f, -0.020f, -0.20f);
test_quat_to_mat_to_quat(0.97f, 0.25f, -0.025f, -0.25f);
test_quat_to_mat_to_quat(0.95f, 0.30f, -0.030f, -0.30f);
}
TEST(math_rotation, quat_to_mat_to_quat_near_0100)
{
test_quat_to_mat_to_quat(0.01f, 0.9999f, -0.001f, -0.01f);
test_quat_to_mat_to_quat(0.02f, 0.9999f, -0.002f, -0.02f);
test_quat_to_mat_to_quat(0.03f, 0.9999f, -0.003f, -0.03f);
test_quat_to_mat_to_quat(0.04f, 0.9999f, -0.004f, -0.04f);
test_quat_to_mat_to_quat(0.05f, 0.9999f, -0.005f, -0.05f);
test_quat_to_mat_to_quat(0.10f, 0.999f, -0.010f, -0.10f);
test_quat_to_mat_to_quat(0.15f, 0.99f, -0.015f, -0.15f);
test_quat_to_mat_to_quat(0.20f, 0.98f, -0.020f, -0.20f);
test_quat_to_mat_to_quat(0.25f, 0.97f, -0.025f, -0.25f);
test_quat_to_mat_to_quat(0.30f, 0.95f, -0.030f, -0.30f);
}
TEST(math_rotation, quat_to_mat_to_quat_near_0010)
{
test_quat_to_mat_to_quat(0.01f, -0.001f, 0.9999f, -0.01f);
test_quat_to_mat_to_quat(0.02f, -0.002f, 0.9999f, -0.02f);
test_quat_to_mat_to_quat(0.03f, -0.003f, 0.9999f, -0.03f);
test_quat_to_mat_to_quat(0.04f, -0.004f, 0.9999f, -0.04f);
test_quat_to_mat_to_quat(0.05f, -0.005f, 0.9999f, -0.05f);
test_quat_to_mat_to_quat(0.10f, -0.010f, 0.999f, -0.10f);
test_quat_to_mat_to_quat(0.15f, -0.015f, 0.99f, -0.15f);
test_quat_to_mat_to_quat(0.20f, -0.020f, 0.98f, -0.20f);
test_quat_to_mat_to_quat(0.25f, -0.025f, 0.97f, -0.25f);
test_quat_to_mat_to_quat(0.30f, -0.030f, 0.95f, -0.30f);
}
TEST(math_rotation, quat_to_mat_to_quat_near_0001)
{
test_quat_to_mat_to_quat(0.01f, -0.001f, -0.01f, 0.9999f);
test_quat_to_mat_to_quat(0.02f, -0.002f, -0.02f, 0.9999f);
test_quat_to_mat_to_quat(0.03f, -0.003f, -0.03f, 0.9999f);
test_quat_to_mat_to_quat(0.04f, -0.004f, -0.04f, 0.9999f);
test_quat_to_mat_to_quat(0.05f, -0.005f, -0.05f, 0.9999f);
test_quat_to_mat_to_quat(0.10f, -0.010f, -0.10f, 0.999f);
test_quat_to_mat_to_quat(0.15f, -0.015f, -0.15f, 0.99f);
test_quat_to_mat_to_quat(0.20f, -0.020f, -0.20f, 0.98f);
test_quat_to_mat_to_quat(0.25f, -0.025f, -0.25f, 0.97f);
test_quat_to_mat_to_quat(0.30f, -0.030f, -0.30f, 0.95f);
}