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/* SPDX-License-Identifier: Apache-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 singularity 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);
/* This matrix represents R=(0, 0, 0), S=(-1, 0, 0) */
float matrix_b[3][3] = {
{-1.0f, 0.0f, 0.0f},
{0.0f, 1.0f, 0.0f},
{0.0f, 0.0f, 1.0f},
};
transpose_m3(matrix_b);
float result[3][3];
interp_m3_m3m3(result, matrix_a, matrix_b, 0.0f);
EXPECT_M3_NEAR(result, matrix_a, 1e-5);
interp_m3_m3m3(result, matrix_a, matrix_b, 1.0f);
EXPECT_M3_NEAR(result, matrix_b, 1e-5);
interp_m3_m3m3(result, matrix_a, matrix_b, 0.5f);
float expect[3][3] = {
{-0.997681f, -0.049995f, 0.046186f},
{-0.051473f, 0.998181f, -0.031385f},
{0.044533f, 0.033689f, 0.998440f},
};
transpose_m3(expect);
EXPECT_M3_NEAR(result, expect, 1e-5);
/* Interpolating between a matrix with and without axis flip can cause it to go through a zero
* point. The determinant det(A) of a matrix represents the change in volume; interpolating
* between matrices with det(A)=-1 and det(B)=1 will have to go through a point where
* det(result)=0, so where the volume becomes zero. */
float matrix_i[3][3];
unit_m3(matrix_i);
zero_m3(expect);
interp_m3_m3m3(result, matrix_a, matrix_i, 0.5f);
EXPECT_NEAR(0.0f, determinant_m3_array(result), 1e-5);
EXPECT_M3_NEAR(result, expect, 1e-5);
}
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