matrix: add 2d rotation matrix

src/lib/matrix/matrix/Dcm2.hpp

@@ -0,0 +1,127 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2023 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file Dcm2.hpp
+ *
+ * A givens rotation matrix 2x2.
+ * All rotations and axis systems follow the right-hand rule.
+ *
+ * This library uses the convention that premultiplying a two dimensional
+ * vector represented in coordinate system 1 will apply a rotation from coordinate system
+ * 1 to coordinate system 2 to the vector.
+ * Likewise, a matrix instance of this class also represents a coordinate transformation
+ * from frame 2 to frame 1.
+ *
+ * @author Matthias Grob <maetugr@gmail.com>
+ */
+
+#pragma once
+
+#include "math.hpp"
+
+namespace matrix
+{
+
+template<typename Type>
+class Dcm2 : public SquareMatrix<Type, 2>
+{
+public:
+	/**
+	 * Standard constructor
+	 *
+	 * Initializes to identity
+	 */
+	Dcm2() : SquareMatrix<Type, 2>(eye<Type, 2>()) {}
+
+	/**
+	 * Constructor from array
+	 *
+	 * @param _data pointer to array
+	 */
+	explicit Dcm2(const Type data_[2][2]) : SquareMatrix<Type, 2>(data_)
+	{
+	}
+
+	/**
+	 * Constructor from array
+	 *
+	 * @param _data pointer to array
+	 */
+	explicit Dcm2(const Type data_[4]) : SquareMatrix<Type, 2>(data_)
+	{
+	}
+
+	/**
+	 * Copy constructor
+	 *
+	 * @param other Matrix22 to set dcm to
+	 */
+	Dcm2(const Matrix<Type, 2, 2> &other) : SquareMatrix<Type, 2>(other)
+	{
+	}
+
+	/**
+	 * Constructor from an angle
+	 *
+	 * This sets the transformation matrix from frame 2 to frame 1 where the rotation
+	 * from frame 1 to frame 2 is described by an angle in radians.
+	 *
+	 * @param angle from frame 1 to frame 2 in radians
+	 */
+	Dcm2(const Type angle)
+	{
+		Dcm2 &dcm = *this;
+		Type sin_angle = sin(angle);
+		Type cos_angle = cos(angle);
+
+		dcm(0, 0) = cos_angle;
+		dcm(0, 1) = -sin_angle;
+		dcm(1, 0) = sin_angle;
+		dcm(1, 1) = cos_angle;
+	}
+
+	void renormalize()
+	{
+		/* renormalize rows */
+		for (size_t r = 0; r < 2; r++) {
+			matrix::Vector2<Type> rvec(Matrix<Type, 1, 2>(this->Matrix<Type, 2, 2>::row(r)).transpose());
+			this->Matrix<Type, 2, 2>::row(r) = rvec.normalized();
+		}
+	}
+};
+
+using Dcm2f = Dcm2<float>;
+using Dcm2d = Dcm2<double>;
+
+} // namespace matrix

src/lib/matrix/matrix/math.hpp

@@ -14,6 +14,7 @@
 #include "Vector4.hpp"
 #include "Euler.hpp"
 #include "Dcm.hpp"
+#include "Dcm2.hpp"
 #include "Scalar.hpp"
 #include "Quaternion.hpp"
 #include "AxisAngle.hpp"

src/lib/matrix/test/CMakeLists.txt

@@ -6,6 +6,7 @@ add_compile_options(
 px4_add_unit_gtest(SRC MatrixAssignmentTest.cpp)
 px4_add_unit_gtest(SRC MatrixAttitudeTest.cpp)
 px4_add_unit_gtest(SRC MatrixCopyToTest.cpp)
+px4_add_unit_gtest(SRC MatrixDcm2Test.cpp)
 px4_add_unit_gtest(SRC MatrixDualTest.cpp)
 px4_add_unit_gtest(SRC MatrixFilterTest.cpp)
 px4_add_unit_gtest(SRC MatrixHatveeTest.cpp)

src/lib/matrix/test/MatrixDcm2Test.cpp

@@ -0,0 +1,75 @@
+/****************************************************************************
+ *
+ *   Copyright (C) 2023 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in
+ *    the documentation and/or other materials provided with the
+ *    distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ *    used to endorse or promote products derived from this software
+ *    without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+#include <gtest/gtest.h>
+#include <matrix/Dcm.hpp>
+#include <matrix/Dcm2.hpp>
+
+using namespace matrix;
+
+TEST(MatrixDcm2Test, CompareToDcm)
+{
+	// 2D matrix and 3D matrix rotating around yaw are equivalent
+	Dcm2f R2(1.f);
+	Dcmf R3(Eulerf(0.f, 0.f, 1.f));
+	EXPECT_EQ(Dcm2f(R3.slice<2, 2>(0, 0)), R2);
+
+	// Rotating a 2D and a 3D vector respectively is equivalent
+	Vector2f v2(1.f, 2.f);
+	Vector3f v3(v2(0), v2(1), 0.f);
+	Vector2f result2 = R2 * v2;
+	Vector3f result3 = R3 * v3;
+	EXPECT_EQ(Vector2f(result2), result2);
+	EXPECT_EQ(result2, result3.xy());
+}
+
+TEST(MatrixDcm2Test, 45DegreeRotation)
+{
+	Vector2f v(1.0f, 0.0f);
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(1.f, 1.f) * (sqrt(2) / 2));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(0.f, 1.f));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(-1.f, 1.f) * (sqrt(2) / 2));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(-1.f, 0.f));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(-1.f, -1.f) * (sqrt(2) / 2));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(0.f, -1.f));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(1.f, -1.f) * (sqrt(2) / 2));
+	v = Dcm2f(M_PI / 4.f) * v;
+	EXPECT_EQ(v, Vector2f(1.f, 0.f));
+}