Tests: added simple unittests for matrix interpolation

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`.

2 files changed, 78 insertions, 0 deletions

diff --git a/tests/gtests/blenlib/BLI_math_matrix_test.cc b/tests/gtests/blenlib/BLI_math_matrix_test.cc
new file mode 100644
index 00000000000..0baccf9ee60
--- /dev/null
+++ b/tests/gtests/blenlib/BLI_math_matrix_test.cc
@@ -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);
+}
diff --git a/tests/gtests/blenlib/CMakeLists.txt b/tests/gtests/blenlib/CMakeLists.txt
index 8ddb2702b83..31c8e983292 100644
--- a/tests/gtests/blenlib/CMakeLists.txt
+++ b/tests/gtests/blenlib/CMakeLists.txt
@@ -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")