BLI: Add float3x3

This patch adds a float3x3 class that represents a 3x3 matrix. The class
can be used to represent a 2D affine transformation stored in a 3x3
matrix in column major order. The class provides various constructors
and processing methods, which utilizes the existing mat3 utilities in
BLI. Corresponding tests were also added.

This is needed by the upcoming viewport compositor to represent domain
transformations.

Reviewed By: fclem

Differential Revision: https://developer.blender.org/D14687

1 files changed, 119 insertions, 0 deletions

diff --git a/source/blender/blenlib/tests/BLI_float3x3_test.cc b/source/blender/blenlib/tests/BLI_float3x3_test.cc
new file mode 100644
index 00000000000..d22993ee69e
--- /dev/null
+++ b/source/blender/blenlib/tests/BLI_float3x3_test.cc
@@ -0,0 +1,119 @@
+/* SPDX-License-Identifier: Apache-2.0 */
+
+#include "testing/testing.h"
+
+#include "BLI_float3x3.hh"
+#include "BLI_math_base.h"
+#include "BLI_math_vec_types.hh"
+
+namespace blender::tests {
+
+TEST(float3x3, Identity)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 transformation = float3x3::identity();
+  float2 result = transformation * point;
+  EXPECT_EQ(result, point);
+}
+
+TEST(float3x3, Translation)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 transformation = float3x3::from_translation(float2(5.0f, 3.0f));
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], 6.0f);
+  EXPECT_FLOAT_EQ(result[1], 5.0f);
+}
+
+TEST(float3x3, Rotation)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 transformation = float3x3::from_rotation(M_PI_2);
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], -2.0f);
+  EXPECT_FLOAT_EQ(result[1], 1.0f);
+}
+
+TEST(float3x3, TranslationRotationScale)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 transformation = float3x3::from_translation_rotation_scale(
+      float2(1.0f, 3.0f), M_PI_2, float2(2.0f, 3.0f));
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], -5.0f);
+  EXPECT_FLOAT_EQ(result[1], 5.0f);
+}
+
+TEST(float3x3, NormalizedAxes)
+{
+  float2 point(1.0f, 2.0f);
+
+  /* The horizontal is aligned with (1, 1) and vertical is aligned with (-1, 1), in other words, a
+   * Pi / 4 rotation. */
+  float value = std::sqrt(2.0f) / 2.0f;
+  float3x3 transformation = float3x3::from_normalized_axes(
+      float2(1.0f, 3.0f), float2(value), float2(-value, value));
+  float2 result = transformation * point;
+
+  float3x3 expected_transformation = float3x3::from_translation_rotation_scale(
+      float2(1.0f, 3.0f), M_PI_4, float2(1.0f));
+  float2 expected = expected_transformation * point;
+
+  EXPECT_FLOAT_EQ(result[0], expected[0]);
+  EXPECT_FLOAT_EQ(result[1], expected[1]);
+}
+
+TEST(float3x3, PostTransformationMultiplication)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 translation = float3x3::from_translation(float2(5.0f, 3.0f));
+  float3x3 rotation = float3x3::from_rotation(M_PI_2);
+  float3x3 transformation = translation * rotation;
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], 3.0f);
+  EXPECT_FLOAT_EQ(result[1], 4.0f);
+}
+
+TEST(float3x3, PreTransformationMultiplication)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 translation = float3x3::from_translation(float2(5.0f, 3.0f));
+  float3x3 rotation = float3x3::from_rotation(M_PI_2);
+  float3x3 transformation = rotation * translation;
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], -5.0f);
+  EXPECT_FLOAT_EQ(result[1], 6.0f);
+}
+
+TEST(float3x3, TransformationMultiplicationAssignment)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 transformation = float3x3::from_translation(float2(5.0f, 3.0f));
+  transformation *= float3x3::from_rotation(M_PI_2);
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], 3.0f);
+  EXPECT_FLOAT_EQ(result[1], 4.0f);
+}
+
+TEST(float3x3, Inverted)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 transformation = float3x3::from_translation_rotation_scale(
+      float2(1.0f, 3.0f), M_PI_4, float2(1.0f));
+  transformation *= transformation.inverted();
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], 1.0f);
+  EXPECT_FLOAT_EQ(result[1], 2.0f);
+}
+
+TEST(float3x3, Origin)
+{
+  float2 point(1.0f, 2.0f);
+  float3x3 rotation = float3x3::from_rotation(M_PI_2);
+  float3x3 transformation = float3x3::from_origin_transformation(rotation, float2(0.0f, 2.0f));
+  float2 result = transformation * point;
+  EXPECT_FLOAT_EQ(result[0], 0.0f);
+  EXPECT_FLOAT_EQ(result[1], 3.0f);
+}
+
+}  // namespace blender::tests