chore: Update tutorial.cpp with TinySO(3) examples #9

README.md

@@ -66,7 +66,80 @@ See the test directory for detailed examples.
 
 [tutorial.cpp](tutorial.cpp)
 
-(Work in Progress)
+```cpp
+/**
+ * @file tutorial.cpp
+ * 
+ * A simple tutorial for TinySO(3).
+ */
+#include <tinyso3/tinyso3.hpp>
+
+using namespace tinyso3;
+
+int main(int argc, char const* argv[]) {
+    /**
+     * Basic Matrix and Vector operations
+     */
+    float matrix_43_data[4][3] = {
+      {01.f, 02.f, 03.f},
+      {04.f, 05.f, 06.f},
+      {07.f, 08.f, 09.f},
+      {10.f, 11.f, 12.f}};
+
+    float matrix_34_data[3][4] = {
+      {01.f, 02.f, 03.f, 04.f},
+      {05.f, 06.f, 07.f, 08.f},
+      {09.f, 10.f, 11.f, 12.f}};
+
+    Matrix<4, 3, float> matrix_43(matrix_43_data);
+    Matrix<3, 4, float> matrix_34(matrix_34_data);
+
+    SquareMatrix<4, float> matrix_44 = matrix_43 * matrix_34;
+    Vector<4, float> vector_4 = matrix_44.slice<4, 1>(0, 2);
+    Vector3<float> vector3 = vector_4.slice<3, 1>(1, 0);
+    vector3 -= SquareMatrix<3, float>::Identity().diag() * 2.f;
+    vector3.normalize();
+    vector3 = vector3.hat().vee();
+
+    /**
+     * 3D Rotation Representations
+     */
+    Euler<INTRINSIC, ZYX, float> euler{0.1f, 0.2f, 0.3f};
+    Quaternion<HAMILTON, float> quaternion = euler;
+    AxisAngle<float> axis_angle = quaternion;
+    RotationMatrix<ACTIVE, float> rotation_matrix = axis_angle;
+
+    /**
+     * Rotate vectors
+     */
+    vector3 = rotation_matrix * vector3;
+    vector3 = quaternion * vector3;
+
+    /**
+     * Normalize quaternion or rotation matrix
+     */
+    quaternion.normalize();
+    rotation_matrix.normalize();
+
+    /**
+     * Interpolation between two rotations
+     */
+    Euler<INTRINSIC, ZYX, float> euler_compare{0.2f, 0.3f, 0.4f};
+    Quaternion<HAMILTON, float> quaternion_compare = euler_compare;
+    Quaternion<HAMILTON, float> quaternion_interpolated = quaternion.slerp(quaternion_compare, 0.5f);
+    RotationMatrix<ACTIVE, float> rotation_matrix_compare = euler_compare;
+    RotationMatrix<ACTIVE, float> rotation_matrix_interpolated = rotation_matrix.interpolate(rotation_matrix_compare, 0.5f);
+
+    /**
+     * Conversion between angular velocity and Euler rate
+     */
+    AngularVelocity<float> angular_velocity(Vector3<float>{0.1f, 0.2f, 0.3f});
+    EulerRate<INTRINSIC, ZYX, float> euler_rate = angular_velocity;
+    angular_velocity = euler_rate;
+
+    return 0;
+}
+```
 
 # Development
 ## Running the tests

tutorial.cpp

@@ -1,5 +1,72 @@
-int main(int argc, char const *argv[])
-{
-    /* code */
+/**
+ * @file tutorial.cpp
+ * 
+ * A simple tutorial for TinySO(3).
+ */
+#include <tinyso3/tinyso3.hpp>
+
+using namespace tinyso3;
+
+int main(int argc, char const* argv[]) {
+    /**
+     * Basic Matrix and Vector operations
+     */
+    float matrix_43_data[4][3] = {
+      {01.f, 02.f, 03.f},
+      {04.f, 05.f, 06.f},
+      {07.f, 08.f, 09.f},
+      {10.f, 11.f, 12.f}};
+
+    float matrix_34_data[3][4] = {
+      {01.f, 02.f, 03.f, 04.f},
+      {05.f, 06.f, 07.f, 08.f},
+      {09.f, 10.f, 11.f, 12.f}};
+
+    Matrix<4, 3, float> matrix_43(matrix_43_data);
+    Matrix<3, 4, float> matrix_34(matrix_34_data);
+
+    SquareMatrix<4, float> matrix_44 = matrix_43 * matrix_34;
+    Vector<4, float> vector_4 = matrix_44.slice<4, 1>(0, 2);
+    Vector3<float> vector3 = vector_4.slice<3, 1>(1, 0);
+    vector3 -= SquareMatrix<3, float>::Identity().diag() * 2.f;
+    vector3.normalize();
+    vector3 = vector3.hat().vee();
+
+    /**
+     * 3D Rotation Representations
+     */
+    Euler<INTRINSIC, ZYX, float> euler{0.1f, 0.2f, 0.3f};
+    Quaternion<HAMILTON, float> quaternion = euler;
+    AxisAngle<float> axis_angle = quaternion;
+    RotationMatrix<ACTIVE, float> rotation_matrix = axis_angle;
+
+    /**
+     * Rotate vectors
+     */
+    vector3 = rotation_matrix * vector3;
+    vector3 = quaternion * vector3;
+
+    /**
+     * Normalize quaternion or rotation matrix
+     */
+    quaternion.normalize();
+    rotation_matrix.normalize();
+
+    /**
+     * Interpolation between two rotations
+     */
+    Euler<INTRINSIC, ZYX, float> euler_compare{0.2f, 0.3f, 0.4f};
+    Quaternion<HAMILTON, float> quaternion_compare = euler_compare;
+    Quaternion<HAMILTON, float> quaternion_interpolated = quaternion.slerp(quaternion_compare, 0.5f);
+    RotationMatrix<ACTIVE, float> rotation_matrix_compare = euler_compare;
+    RotationMatrix<ACTIVE, float> rotation_matrix_interpolated = rotation_matrix.interpolate(rotation_matrix_compare, 0.5f);
+
+    /**
+     * Conversion between angular velocity and Euler rate
+     */
+    AngularVelocity<float> angular_velocity(Vector3<float>{0.1f, 0.2f, 0.3f});
+    EulerRate<INTRINSIC, ZYX, float> euler_rate = angular_velocity;
+    angular_velocity = euler_rate;
+
     return 0;
 }