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Tests: added simple unittests for matrix interpolation

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The interpolation of 4x4 and 3x3 matrices will fail when the rotation
component has a singularity, i.e. when there is one axis mirrored. Two
mirrored axes are just a rotation of 180 degrees around the third, and
three mirrored axes are such a rotation + a single axis mirror. To
prepare for a fix, I first wanted to cover the basic functionality with
a few unit tests.

These tests check that `interpolate(A, B, alpha)` always returns `A` for
`alpha=0`, always return `B` for `alpha=1`, and something in between for
`alpha=0.5`.
This commit is contained in:
Sybren A. Stüvel
2020-06-16 15:36:08 +02:00
parent 099d47f8a3
commit 46e4cdf788
2 changed files with 78 additions and 0 deletions
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77
tests/gtests/blenlib/BLI_math_matrix_test.cc Normal file
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@@ -0,0 +1,77 @@
/* Apache License, Version 2.0 */
#include "testing/testing.h"
#include "BLI_math_matrix.h"
TEST(math_matrix, interp_m4_m4m4_regular)
{
/* Test 4x4 matrix interpolation without singularity, i.e. without axis flip. */
/* Transposed matrix, so that the code here is written in the same way as print_m4() outputs. */
/* This matrix represents T=(0.1, 0.2, 0.3), R=(40, 50, 60) degrees, S=(0.7, 0.8, 0.9) */
float matrix_a[4][4] = {
{0.224976f, -0.333770f, 0.765074f, 0.100000f},
{0.389669f, 0.647565f, 0.168130f, 0.200000f},
{-0.536231f, 0.330541f, 0.443163f, 0.300000f},
{0.000000f, 0.000000f, 0.000000f, 1.000000f},
};
transpose_m4(matrix_a);
float matrix_i[4][4];
unit_m4(matrix_i);
float result[4][4];
const float epsilon = 1e-6;
interp_m4_m4m4(result, matrix_i, matrix_a, 0.0f);
EXPECT_M4_NEAR(result, matrix_i, epsilon);
interp_m4_m4m4(result, matrix_i, matrix_a, 1.0f);
EXPECT_M4_NEAR(result, matrix_a, epsilon);
/* This matrix is based on the current implementation of the code, and isn't guaranteed to be
* correct. It's just consistent with the current implementation. */
float matrix_halfway[4][4] = {
{0.690643f, -0.253244f, 0.484996f, 0.050000f},
{0.271924f, 0.852623f, 0.012348f, 0.100000f},
{-0.414209f, 0.137484f, 0.816778f, 0.150000f},
{0.000000f, 0.000000f, 0.000000f, 1.000000f},
};
transpose_m4(matrix_halfway);
interp_m4_m4m4(result, matrix_i, matrix_a, 0.5f);
EXPECT_M4_NEAR(result, matrix_halfway, epsilon);
}
TEST(math_matrix, interp_m3_m3m3_singularity)
{
/* A singluarity means that there is an axis mirror in the rotation component of the matrix. This
* is reflected in its negative determinant.
*
* The interpolation of 4x4 matrices performs linear interpolation on the translation component,
* and then uses the 3x3 interpolation function to handle rotation and scale. As a result, this
* test for a singularity in the rotation matrix only needs to test the 3x3 case. */
/* Transposed matrix, so that the code here is written in the same way as print_m4() outputs. */
/* This matrix represents R=(4, 5, 6) degrees, S=(-1, 1, 1) */
float matrix_a[3][3] = {
{-0.990737f, -0.098227f, 0.093759f},
{-0.104131f, 0.992735f, -0.060286f},
{0.087156f, 0.069491f, 0.993768f},
};
transpose_m3(matrix_a);
EXPECT_NEAR(-1.0f, determinant_m3_array(matrix_a), 1e-6);
float matrix_i[3][3];
unit_m3(matrix_i);
float result[3][3];
const float epsilon = 1e-6;
interp_m3_m3m3(result, matrix_i, matrix_a, 0.0f);
EXPECT_M3_NEAR(result, matrix_i, epsilon);
/* This fails for matrices with a negative determinant, i.e. with an axis mirror in the rotation
* component. See T77154. */
// interp_m3_m3m3(result, matrix_i, matrix_a, 1.0f);
// EXPECT_M3_NEAR(result, matrix_a, epsilon);
}

1
tests/gtests/blenlib/CMakeLists.txt
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@@ -60,6 +60,7 @@ BLENDER_TEST(BLI_math_base "bf_blenlib")
BLENDER_TEST(BLI_math_bits "bf_blenlib")
BLENDER_TEST(BLI_math_color "bf_blenlib")
BLENDER_TEST(BLI_math_geom "bf_blenlib")
BLENDER_TEST(BLI_math_matrix "bf_blenlib")
BLENDER_TEST(BLI_math_vector "bf_blenlib")
BLENDER_TEST(BLI_memiter "bf_blenlib")
BLENDER_TEST(BLI_optional "bf_blenlib")