Add methods in the mathematics classes

src/mathematics/Matrix3x3.cpp

@@ -56,9 +56,9 @@ Matrix3x3::~Matrix3x3() {
 
 // Copy-constructor
 Matrix3x3::Matrix3x3(const Matrix3x3& matrix) {
-    setAllValues(matrix.mArray[0][0], matrix.mArray[0][1], matrix.mArray[0][2],
+    setAllValues(matrix.mRows[0][0], matrix.mRows[0][1], matrix.mRows[0][2],
-                 matrix.mArray[1][0], matrix.mArray[1][1], matrix.mArray[1][2],
+                 matrix.mRows[1][0], matrix.mRows[1][1], matrix.mRows[1][2],
-                 matrix.mArray[2][0], matrix.mArray[2][1], matrix.mArray[2][2]);
+                 matrix.mRows[2][0], matrix.mRows[2][1], matrix.mRows[2][2]);
 }
 
 // Assignment operator
@@ -66,9 +66,9 @@ Matrix3x3& Matrix3x3::operator=(const Matrix3x3& matrix) {
 
     // Check for self-assignment
     if (&matrix != this) {
-        setAllValues(matrix.mArray[0][0], matrix.mArray[0][1], matrix.mArray[0][2],
+        setAllValues(matrix.mRows[0][0], matrix.mRows[0][1], matrix.mRows[0][2],
-                     matrix.mArray[1][0], matrix.mArray[1][1], matrix.mArray[1][2],
+                     matrix.mRows[1][0], matrix.mRows[1][1], matrix.mRows[1][2],
-                     matrix.mArray[2][0], matrix.mArray[2][1], matrix.mArray[2][2]);
+                     matrix.mRows[2][0], matrix.mRows[2][1], matrix.mRows[2][2]);
     }
     return *this;
 }
@@ -84,15 +84,15 @@ Matrix3x3 Matrix3x3::getInverse() const {
 
     decimal invDeterminant = decimal(1.0) / determinant;
 
-    Matrix3x3 tempMatrix((mArray[1][1]*mArray[2][2]-mArray[2][1]*mArray[1][2]),
+    Matrix3x3 tempMatrix((mRows[1][1]*mRows[2][2]-mRows[2][1]*mRows[1][2]),
-                         -(mArray[0][1]*mArray[2][2]-mArray[2][1]*mArray[0][2]),
+                         -(mRows[0][1]*mRows[2][2]-mRows[2][1]*mRows[0][2]),
-                         (mArray[0][1]*mArray[1][2]-mArray[0][2]*mArray[1][1]),
+                         (mRows[0][1]*mRows[1][2]-mRows[0][2]*mRows[1][1]),
-                            -(mArray[1][0]*mArray[2][2]-mArray[2][0]*mArray[1][2]),
+                            -(mRows[1][0]*mRows[2][2]-mRows[2][0]*mRows[1][2]),
-                         (mArray[0][0]*mArray[2][2]-mArray[2][0]*mArray[0][2]),
+                         (mRows[0][0]*mRows[2][2]-mRows[2][0]*mRows[0][2]),
-                         -(mArray[0][0]*mArray[1][2]-mArray[1][0]*mArray[0][2]),
+                         -(mRows[0][0]*mRows[1][2]-mRows[1][0]*mRows[0][2]),
-                            (mArray[1][0]*mArray[2][1]-mArray[2][0]*mArray[1][1]),
+                            (mRows[1][0]*mRows[2][1]-mRows[2][0]*mRows[1][1]),
-                         -(mArray[0][0]*mArray[2][1]-mArray[2][0]*mArray[0][1]),
+                         -(mRows[0][0]*mRows[2][1]-mRows[2][0]*mRows[0][1]),
-                         (mArray[0][0]*mArray[1][1]-mArray[0][1]*mArray[1][0]));
+                         (mRows[0][0]*mRows[1][1]-mRows[0][1]*mRows[1][0]));
 
     // Return the inverse matrix
     return (invDeterminant * tempMatrix);

src/mathematics/Matrix3x3.h

@@ -46,8 +46,8 @@ class Matrix3x3 {
 
         // -------------------- Attributes -------------------- //
 
-        // Array with the values of the matrix
+        /// Rows of the matrix;
-        decimal mArray[3][3];
+        Vector3 mRows[3];
 
     public :
 
@@ -72,19 +72,19 @@ class Matrix3x3 {
         // Assignment operator
         Matrix3x3& operator=(const Matrix3x3& matrix);
 
-        // Get a value in the matrix
-        decimal getValue(int i, int j) const;
-
-        // Set a value in the matrix
-        void setValue(int i, int j, decimal value);
-
         // Set all the values in the matrix
         void setAllValues(decimal a1, decimal a2, decimal a3, decimal b1, decimal b2, decimal b3,
                   decimal c1, decimal c2, decimal c3);
 
+        /// Set the matrix to zero
+        void setToZero();
+
         // Return a column
         Vector3 getColumn(int i) const;
 
+        /// Return a row
+        Vector3 getRow(int i) const;
+
         // Return the transpose matrix
         Matrix3x3 getTranspose() const;
 
@@ -141,110 +141,120 @@ class Matrix3x3 {
 
         // Overloaded operator for multiplication with a number with assignment
         Matrix3x3& operator*=(decimal nb);
+
+        /// Overloaded operator to read element of the matrix.
+        const Vector3& operator[](int row) const;
+
+        /// Overloaded operator to read/write element of the matrix.
+        Vector3& operator[](int row);
 };
 
-
-// Method to get a value in the matrix (inline)
-inline decimal Matrix3x3::getValue(int i, int j) const {
-    assert(i>=0 && i<3 && j>=0 && j<3);
-    return mArray[i][j];
-}
-
-// Method to set a value in the matrix (inline)
-inline void Matrix3x3::setValue(int i, int j, decimal value) {
-    assert(i>=0 && i<3 && j>=0 && j<3);
-    mArray[i][j] = value;
-}
-
 // Method to set all the values in the matrix
 inline void Matrix3x3::setAllValues(decimal a1, decimal a2, decimal a3,
                                     decimal b1, decimal b2, decimal b3,
                                     decimal c1, decimal c2, decimal c3) {
-    mArray[0][0] = a1; mArray[0][1] = a2; mArray[0][2] = a3;
+    mRows[0][0] = a1; mRows[0][1] = a2; mRows[0][2] = a3;
-    mArray[1][0] = b1; mArray[1][1] = b2; mArray[1][2] = b3;
+    mRows[1][0] = b1; mRows[1][1] = b2; mRows[1][2] = b3;
-    mArray[2][0] = c1; mArray[2][1] = c2; mArray[2][2] = c3;
+    mRows[2][0] = c1; mRows[2][1] = c2; mRows[2][2] = c3;
+}
+
+/// Set the matrix to zero
+inline void Matrix3x3::setToZero() {
+    mRows[0].setToZero();
+    mRows[1].setToZero();
+    mRows[2].setToZero();
 }
 
 // Return a column
 inline Vector3 Matrix3x3::getColumn(int i) const {
     assert(i>= 0 && i<3);
-    return Vector3(mArray[0][i], mArray[1][i], mArray[2][i]);
+    return Vector3(mRows[0][i], mRows[1][i], mRows[2][i]);
+}
+
+/// Return a row
+inline Vector3 Matrix3x3::getRow(int i) const {
+    assert(i>= 0 && i<3);
+    return mRows[i];
 }
 
 // Return the transpose matrix
 inline Matrix3x3 Matrix3x3::getTranspose() const {
+
     // Return the transpose matrix
-    return Matrix3x3(mArray[0][0], mArray[1][0], mArray[2][0],
+    return Matrix3x3(mRows[0][0], mRows[1][0], mRows[2][0],
-                     mArray[0][1], mArray[1][1], mArray[2][1],
+                     mRows[0][1], mRows[1][1], mRows[2][1],
-                     mArray[0][2], mArray[1][2], mArray[2][2]);
+                     mRows[0][2], mRows[1][2], mRows[2][2]);
 }
 
 // Return the determinant of the matrix
 inline decimal Matrix3x3::getDeterminant() const {
+
     // Compute and return the determinant of the matrix
-    return (mArray[0][0]*(mArray[1][1]*mArray[2][2]-mArray[2][1]*mArray[1][2]) -
+    return (mRows[0][0]*(mRows[1][1]*mRows[2][2]-mRows[2][1]*mRows[1][2]) -
-            mArray[0][1]*(mArray[1][0]*mArray[2][2]-mArray[2][0]*mArray[1][2]) +
+            mRows[0][1]*(mRows[1][0]*mRows[2][2]-mRows[2][0]*mRows[1][2]) +
-            mArray[0][2]*(mArray[1][0]*mArray[2][1]-mArray[2][0]*mArray[1][1]));
+            mRows[0][2]*(mRows[1][0]*mRows[2][1]-mRows[2][0]*mRows[1][1]));
 }
 
 // Return the trace of the matrix
 inline decimal Matrix3x3::getTrace() const {
+
     // Compute and return the trace
-    return (mArray[0][0] + mArray[1][1] + mArray[2][2]);
+    return (mRows[0][0] + mRows[1][1] + mRows[2][2]);
 }
 
 // Set the matrix to the identity matrix
 inline void Matrix3x3::setToIdentity() {
-    mArray[0][0] = 1.0; mArray[0][1] = 0.0; mArray[0][2] = 0.0;
+    mRows[0][0] = 1.0; mRows[0][1] = 0.0; mRows[0][2] = 0.0;
-    mArray[1][0] = 0.0; mArray[1][1] = 1.0; mArray[1][2] = 0.0;
+    mRows[1][0] = 0.0; mRows[1][1] = 1.0; mRows[1][2] = 0.0;
-    mArray[2][0] = 0.0; mArray[2][1] = 0.0; mArray[2][2] = 1.0;
+    mRows[2][0] = 0.0; mRows[2][1] = 0.0; mRows[2][2] = 1.0;
 }
 
 // Return the 3x3 identity matrix
 inline Matrix3x3 Matrix3x3::identity() {
+
     // Return the isdentity matrix
     return Matrix3x3(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0);
 }
 
 // Return the matrix with absolute values
 inline Matrix3x3 Matrix3x3::getAbsoluteMatrix() const {
-    return Matrix3x3(fabs(mArray[0][0]), fabs(mArray[0][1]), fabs(mArray[0][2]),
+    return Matrix3x3(fabs(mRows[0][0]), fabs(mRows[0][1]), fabs(mRows[0][2]),
-                     fabs(mArray[1][0]), fabs(mArray[1][1]), fabs(mArray[1][2]),
+                     fabs(mRows[1][0]), fabs(mRows[1][1]), fabs(mRows[1][2]),
-                     fabs(mArray[2][0]), fabs(mArray[2][1]), fabs(mArray[2][2]));
+                     fabs(mRows[2][0]), fabs(mRows[2][1]), fabs(mRows[2][2]));
 }
 
 // Overloaded operator for addition
 inline Matrix3x3 operator+(const Matrix3x3& matrix1, const Matrix3x3& matrix2) {
-    return Matrix3x3(matrix1.mArray[0][0] + matrix2.mArray[0][0], matrix1.mArray[0][1] +
+    return Matrix3x3(matrix1.mRows[0][0] + matrix2.mRows[0][0], matrix1.mRows[0][1] +
-                     matrix2.mArray[0][1], matrix1.mArray[0][2] + matrix2.mArray[0][2],
+                     matrix2.mRows[0][1], matrix1.mRows[0][2] + matrix2.mRows[0][2],
-                     matrix1.mArray[1][0] + matrix2.mArray[1][0], matrix1.mArray[1][1] +
+                     matrix1.mRows[1][0] + matrix2.mRows[1][0], matrix1.mRows[1][1] +
-                     matrix2.mArray[1][1], matrix1.mArray[1][2] + matrix2.mArray[1][2],
+                     matrix2.mRows[1][1], matrix1.mRows[1][2] + matrix2.mRows[1][2],
-                     matrix1.mArray[2][0] + matrix2.mArray[2][0], matrix1.mArray[2][1] +
+                     matrix1.mRows[2][0] + matrix2.mRows[2][0], matrix1.mRows[2][1] +
-                     matrix2.mArray[2][1], matrix1.mArray[2][2] + matrix2.mArray[2][2]);
+                     matrix2.mRows[2][1], matrix1.mRows[2][2] + matrix2.mRows[2][2]);
 }
 
 // Overloaded operator for substraction
 inline Matrix3x3 operator-(const Matrix3x3& matrix1, const Matrix3x3& matrix2) {
-    return Matrix3x3(matrix1.mArray[0][0] - matrix2.mArray[0][0], matrix1.mArray[0][1] -
+    return Matrix3x3(matrix1.mRows[0][0] - matrix2.mRows[0][0], matrix1.mRows[0][1] -
-                     matrix2.mArray[0][1], matrix1.mArray[0][2] - matrix2.mArray[0][2],
+                     matrix2.mRows[0][1], matrix1.mRows[0][2] - matrix2.mRows[0][2],
-                     matrix1.mArray[1][0] - matrix2.mArray[1][0], matrix1.mArray[1][1] -
+                     matrix1.mRows[1][0] - matrix2.mRows[1][0], matrix1.mRows[1][1] -
-                     matrix2.mArray[1][1], matrix1.mArray[1][2] - matrix2.mArray[1][2],
+                     matrix2.mRows[1][1], matrix1.mRows[1][2] - matrix2.mRows[1][2],
-                     matrix1.mArray[2][0] - matrix2.mArray[2][0], matrix1.mArray[2][1] -
+                     matrix1.mRows[2][0] - matrix2.mRows[2][0], matrix1.mRows[2][1] -
-                     matrix2.mArray[2][1], matrix1.mArray[2][2] - matrix2.mArray[2][2]);
+                     matrix2.mRows[2][1], matrix1.mRows[2][2] - matrix2.mRows[2][2]);
 }
 
 // Overloaded operator for the negative of the matrix
 inline Matrix3x3 operator-(const Matrix3x3& matrix) {
-    return Matrix3x3(-matrix.mArray[0][0], -matrix.mArray[0][1], -matrix.mArray[0][2],
+    return Matrix3x3(-matrix.mRows[0][0], -matrix.mRows[0][1], -matrix.mRows[0][2],
-                     -matrix.mArray[1][0], -matrix.mArray[1][1], -matrix.mArray[1][2],
+                     -matrix.mRows[1][0], -matrix.mRows[1][1], -matrix.mRows[1][2],
-                     -matrix.mArray[2][0], -matrix.mArray[2][1], -matrix.mArray[2][2]);
+                     -matrix.mRows[2][0], -matrix.mRows[2][1], -matrix.mRows[2][2]);
 }
 
 // Overloaded operator for multiplication with a number
 inline Matrix3x3 operator*(decimal nb, const Matrix3x3& matrix) {
-    return Matrix3x3(matrix.mArray[0][0] * nb, matrix.mArray[0][1] * nb, matrix.mArray[0][2] * nb,
+    return Matrix3x3(matrix.mRows[0][0] * nb, matrix.mRows[0][1] * nb, matrix.mRows[0][2] * nb,
-                     matrix.mArray[1][0] * nb, matrix.mArray[1][1] * nb, matrix.mArray[1][2] * nb,
+                     matrix.mRows[1][0] * nb, matrix.mRows[1][1] * nb, matrix.mRows[1][2] * nb,
-                     matrix.mArray[2][0] * nb, matrix.mArray[2][1] * nb, matrix.mArray[2][2] * nb);
+                     matrix.mRows[2][0] * nb, matrix.mRows[2][1] * nb, matrix.mRows[2][2] * nb);
 }
 
 // Overloaded operator for multiplication with a matrix
@@ -254,44 +264,44 @@ inline Matrix3x3 operator*(const Matrix3x3& matrix, decimal nb) {
 
 // Overloaded operator for matrix multiplication
 inline Matrix3x3 operator*(const Matrix3x3& matrix1, const Matrix3x3& matrix2) {
-    return Matrix3x3(matrix1.mArray[0][0]*matrix2.mArray[0][0] + matrix1.mArray[0][1] *
+    return Matrix3x3(matrix1.mRows[0][0]*matrix2.mRows[0][0] + matrix1.mRows[0][1] *
-                     matrix2.mArray[1][0] + matrix1.mArray[0][2]*matrix2.mArray[2][0],
+                     matrix2.mRows[1][0] + matrix1.mRows[0][2]*matrix2.mRows[2][0],
-                     matrix1.mArray[0][0]*matrix2.mArray[0][1] + matrix1.mArray[0][1] *
+                     matrix1.mRows[0][0]*matrix2.mRows[0][1] + matrix1.mRows[0][1] *
-                     matrix2.mArray[1][1] + matrix1.mArray[0][2]*matrix2.mArray[2][1],
+                     matrix2.mRows[1][1] + matrix1.mRows[0][2]*matrix2.mRows[2][1],
-                     matrix1.mArray[0][0]*matrix2.mArray[0][2] + matrix1.mArray[0][1] *
+                     matrix1.mRows[0][0]*matrix2.mRows[0][2] + matrix1.mRows[0][1] *
-                     matrix2.mArray[1][2] + matrix1.mArray[0][2]*matrix2.mArray[2][2],
+                     matrix2.mRows[1][2] + matrix1.mRows[0][2]*matrix2.mRows[2][2],
-                     matrix1.mArray[1][0]*matrix2.mArray[0][0] + matrix1.mArray[1][1] *
+                     matrix1.mRows[1][0]*matrix2.mRows[0][0] + matrix1.mRows[1][1] *
-                     matrix2.mArray[1][0] + matrix1.mArray[1][2]*matrix2.mArray[2][0],
+                     matrix2.mRows[1][0] + matrix1.mRows[1][2]*matrix2.mRows[2][0],
-                     matrix1.mArray[1][0]*matrix2.mArray[0][1] + matrix1.mArray[1][1] *
+                     matrix1.mRows[1][0]*matrix2.mRows[0][1] + matrix1.mRows[1][1] *
-                     matrix2.mArray[1][1] + matrix1.mArray[1][2]*matrix2.mArray[2][1],
+                     matrix2.mRows[1][1] + matrix1.mRows[1][2]*matrix2.mRows[2][1],
-                     matrix1.mArray[1][0]*matrix2.mArray[0][2] + matrix1.mArray[1][1] *
+                     matrix1.mRows[1][0]*matrix2.mRows[0][2] + matrix1.mRows[1][1] *
-                     matrix2.mArray[1][2] + matrix1.mArray[1][2]*matrix2.mArray[2][2],
+                     matrix2.mRows[1][2] + matrix1.mRows[1][2]*matrix2.mRows[2][2],
-                     matrix1.mArray[2][0]*matrix2.mArray[0][0] + matrix1.mArray[2][1] *
+                     matrix1.mRows[2][0]*matrix2.mRows[0][0] + matrix1.mRows[2][1] *
-                     matrix2.mArray[1][0] + matrix1.mArray[2][2]*matrix2.mArray[2][0],
+                     matrix2.mRows[1][0] + matrix1.mRows[2][2]*matrix2.mRows[2][0],
-                     matrix1.mArray[2][0]*matrix2.mArray[0][1] + matrix1.mArray[2][1] *
+                     matrix1.mRows[2][0]*matrix2.mRows[0][1] + matrix1.mRows[2][1] *
-                     matrix2.mArray[1][1] + matrix1.mArray[2][2]*matrix2.mArray[2][1],
+                     matrix2.mRows[1][1] + matrix1.mRows[2][2]*matrix2.mRows[2][1],
-                     matrix1.mArray[2][0]*matrix2.mArray[0][2] + matrix1.mArray[2][1] *
+                     matrix1.mRows[2][0]*matrix2.mRows[0][2] + matrix1.mRows[2][1] *
-                     matrix2.mArray[1][2] + matrix1.mArray[2][2]*matrix2.mArray[2][2]);
+                     matrix2.mRows[1][2] + matrix1.mRows[2][2]*matrix2.mRows[2][2]);
 }
 
 // Overloaded operator for multiplication with a vector
 inline Vector3 operator*(const Matrix3x3& matrix, const Vector3& vector) {
-    return Vector3(matrix.mArray[0][0]*vector.x + matrix.mArray[0][1]*vector.y +
+    return Vector3(matrix.mRows[0][0]*vector.x + matrix.mRows[0][1]*vector.y +
-                   matrix.mArray[0][2]*vector.z,
+                   matrix.mRows[0][2]*vector.z,
-                   matrix.mArray[1][0]*vector.x + matrix.mArray[1][1]*vector.y +
+                   matrix.mRows[1][0]*vector.x + matrix.mRows[1][1]*vector.y +
-                   matrix.mArray[1][2]*vector.z,
+                   matrix.mRows[1][2]*vector.z,
-                   matrix.mArray[2][0]*vector.x + matrix.mArray[2][1]*vector.y +
+                   matrix.mRows[2][0]*vector.x + matrix.mRows[2][1]*vector.y +
-                   matrix.mArray[2][2]*vector.z);
+                   matrix.mRows[2][2]*vector.z);
 }
 
 // Overloaded operator for equality condition
 inline bool Matrix3x3::operator==(const Matrix3x3& matrix) const {
-    return (mArray[0][0] == matrix.mArray[0][0] && mArray[0][1] == matrix.mArray[0][1] &&
+    return (mRows[0][0] == matrix.mRows[0][0] && mRows[0][1] == matrix.mRows[0][1] &&
-            mArray[0][2] == matrix.mArray[0][2] &&
+            mRows[0][2] == matrix.mRows[0][2] &&
-            mArray[1][0] == matrix.mArray[1][0] && mArray[1][1] == matrix.mArray[1][1] &&
+            mRows[1][0] == matrix.mRows[1][0] && mRows[1][1] == matrix.mRows[1][1] &&
-            mArray[1][2] == matrix.mArray[1][2] &&
+            mRows[1][2] == matrix.mRows[1][2] &&
-            mArray[2][0] == matrix.mArray[2][0] && mArray[2][1] == matrix.mArray[2][1] &&
+            mRows[2][0] == matrix.mRows[2][0] && mRows[2][1] == matrix.mRows[2][1] &&
-            mArray[2][2] == matrix.mArray[2][2]);
+            mRows[2][2] == matrix.mRows[2][2]);
 }
 
 // Overloaded operator for the is different condition
@@ -301,32 +311,46 @@ inline bool Matrix3x3::operator!= (const Matrix3x3& matrix) const {
 
 // Overloaded operator for addition with assignment
 inline Matrix3x3& Matrix3x3::operator+=(const Matrix3x3& matrix) {
-   mArray[0][0] += matrix.mArray[0][0]; mArray[0][1] += matrix.mArray[0][1];
+   mRows[0][0] += matrix.mRows[0][0]; mRows[0][1] += matrix.mRows[0][1];
-   mArray[0][2] += matrix.mArray[0][2]; mArray[1][0] += matrix.mArray[1][0];
+   mRows[0][2] += matrix.mRows[0][2]; mRows[1][0] += matrix.mRows[1][0];
-   mArray[1][1] += matrix.mArray[1][1]; mArray[1][2] += matrix.mArray[1][2];
+   mRows[1][1] += matrix.mRows[1][1]; mRows[1][2] += matrix.mRows[1][2];
-   mArray[2][0] += matrix.mArray[2][0]; mArray[2][1] += matrix.mArray[2][1];
+   mRows[2][0] += matrix.mRows[2][0]; mRows[2][1] += matrix.mRows[2][1];
-   mArray[2][2] += matrix.mArray[2][2];
+   mRows[2][2] += matrix.mRows[2][2];
    return *this;
 }
 
 // Overloaded operator for substraction with assignment
 inline Matrix3x3& Matrix3x3::operator-=(const Matrix3x3& matrix) {
-   mArray[0][0] -= matrix.mArray[0][0]; mArray[0][1] -= matrix.mArray[0][1];
+   mRows[0][0] -= matrix.mRows[0][0]; mRows[0][1] -= matrix.mRows[0][1];
-   mArray[0][2] -= matrix.mArray[0][2]; mArray[1][0] -= matrix.mArray[1][0];
+   mRows[0][2] -= matrix.mRows[0][2]; mRows[1][0] -= matrix.mRows[1][0];
-   mArray[1][1] -= matrix.mArray[1][1]; mArray[1][2] -= matrix.mArray[1][2];
+   mRows[1][1] -= matrix.mRows[1][1]; mRows[1][2] -= matrix.mRows[1][2];
-   mArray[2][0] -= matrix.mArray[2][0]; mArray[2][1] -= matrix.mArray[2][1];
+   mRows[2][0] -= matrix.mRows[2][0]; mRows[2][1] -= matrix.mRows[2][1];
-   mArray[2][2] -= matrix.mArray[2][2];
+   mRows[2][2] -= matrix.mRows[2][2];
    return *this;
 }
 
 // Overloaded operator for multiplication with a number with assignment
 inline Matrix3x3& Matrix3x3::operator*=(decimal nb) {
-   mArray[0][0] *= nb; mArray[0][1] *= nb; mArray[0][2] *= nb;
+   mRows[0][0] *= nb; mRows[0][1] *= nb; mRows[0][2] *= nb;
-   mArray[1][0] *= nb; mArray[1][1] *= nb; mArray[1][2] *= nb;
+   mRows[1][0] *= nb; mRows[1][1] *= nb; mRows[1][2] *= nb;
-   mArray[2][0] *= nb; mArray[2][1] *= nb; mArray[2][2] *= nb;
+   mRows[2][0] *= nb; mRows[2][1] *= nb; mRows[2][2] *= nb;
    return *this;
 }
 
+// Overloaded operator to return a row of the matrix.
+/// This operator is also used to access a matrix value using the syntax
+/// matrix[row][col].
+inline const Vector3& Matrix3x3::operator[](int row) const {
+    return mRows[row];
+}
+
+// Overloaded operator to return a row of the matrix.
+/// This operator is also used to access a matrix value using the syntax
+/// matrix[row][col].
+inline Vector3& Matrix3x3::operator[](int row) {
+    return mRows[row];
+}
+
 }
 
 #endif

src/mathematics/Quaternion.cpp

@@ -59,58 +59,51 @@ Quaternion::Quaternion(const Matrix3x3& matrix) {
     // Get the trace of the matrix
     decimal trace = matrix.getTrace();
 
-    decimal array[3][3];
-    for (int i=0; i<3; i++) {
-        for (int j=0; j<3; j++) {
-            array[i][j] = matrix.getValue(i, j);
-        }
-    }
-
     decimal r;
     decimal s;
 
     if (trace < 0.0) {
-        if (array[1][1] > array[0][0]) {
+        if (matrix[1][1] > matrix[0][0]) {
-            if(array[2][2] > array[1][1]) {
+            if(matrix[2][2] > matrix[1][1]) {
-                r = sqrt(array[2][2] - array[0][0] - array[1][1] + 1.0);
+                r = sqrt(matrix[2][2] - matrix[0][0] - matrix[1][1] + 1.0);
                 s = 0.5 / r;
                 
                 // Compute the quaternion
-                x = (array[2][0] + array[0][2])*s;
+                x = (matrix[2][0] + matrix[0][2])*s;
-                y = (array[1][2] + array[2][1])*s;
+                y = (matrix[1][2] + matrix[2][1])*s;
                 z = 0.5*r;
-                w = (array[1][0] - array[0][1])*s;
+                w = (matrix[1][0] - matrix[0][1])*s;
             }
             else {
-                r = sqrt(array[1][1] - array[2][2] - array[0][0] + 1.0);
+                r = sqrt(matrix[1][1] - matrix[2][2] - matrix[0][0] + 1.0);
                 s = 0.5 / r;
 
                 // Compute the quaternion
-                x = (array[0][1] + array[1][0])*s;
+                x = (matrix[0][1] + matrix[1][0])*s;
                 y = 0.5 * r;
-                z = (array[1][2] + array[2][1])*s;
+                z = (matrix[1][2] + matrix[2][1])*s;
-                w = (array[0][2] - array[2][0])*s;
+                w = (matrix[0][2] - matrix[2][0])*s;
             }
         }
-        else if (array[2][2] > array[0][0]) {
+        else if (matrix[2][2] > matrix[0][0]) {
-            r = sqrt(array[2][2] - array[0][0] - array[1][1] + 1.0);
+            r = sqrt(matrix[2][2] - matrix[0][0] - matrix[1][1] + 1.0);
             s = 0.5 / r;
 
             // Compute the quaternion
-            x = (array[2][0] + array[0][2])*s;
+            x = (matrix[2][0] + matrix[0][2])*s;
-            y = (array[1][2] + array[2][1])*s;
+            y = (matrix[1][2] + matrix[2][1])*s;
             z = 0.5 * r;
-            w = (array[1][0] - array[0][1])*s;
+            w = (matrix[1][0] - matrix[0][1])*s;
         }
         else {
-            r = sqrt(array[0][0] - array[1][1] - array[2][2] + 1.0);
+            r = sqrt(matrix[0][0] - matrix[1][1] - matrix[2][2] + 1.0);
             s = 0.5 / r;
 
             // Compute the quaternion
             x = 0.5 * r;
-            y = (array[0][1] + array[1][0])*s;
+            y = (matrix[0][1] + matrix[1][0])*s;
-            z = (array[2][0] - array[0][2])*s;
+            z = (matrix[2][0] - matrix[0][2])*s;
-            w = (array[2][1] - array[1][2])*s;
+            w = (matrix[2][1] - matrix[1][2])*s;
         }
     }
     else {
@@ -118,9 +111,9 @@ Quaternion::Quaternion(const Matrix3x3& matrix) {
         s = 0.5/r;
 
         // Compute the quaternion
-        x = (array[2][1]-array[1][2])*s;
+        x = (matrix[2][1] - matrix[1][2]) * s;
-        y = (array[0][2]-array[2][0])*s;
+        y = (matrix[0][2] - matrix[2][0]) * s;
-        z = (array[1][0]-array[0][1])*s;
+        z = (matrix[1][0] - matrix[0][1]) * s;
         w = 0.5 * r;
     }
 }

src/mathematics/Quaternion.h

@@ -70,12 +70,21 @@ struct Quaternion {
         // Destructor
         ~Quaternion();
 
+        /// Set all the values
+        void setAllValues(decimal newX, decimal newY, decimal newZ, decimal newW);
+
+        /// Set the quaternion to zero
+        void setToZero();
+
         // Return the vector v=(x y z) of the quaternion
-        Vector3 vectorV() const;
+        Vector3 getVectorV() const;
 
         // Return the length of the quaternion
         decimal length() const;
 
+        /// Normalize the quaternion
+        void normalize();
+
         // Return the unit quaternion
         Quaternion getUnit() const;
 
@@ -113,6 +122,9 @@ struct Quaternion {
         // Overloaded operator for the multiplication
         Quaternion operator*(const Quaternion& quaternion) const;
 
+        /// Overloaded operator for the multiplication with a vector
+        Vector3 operator*(const Vector3& point);
+
         // Overloaded operator for assignment
         Quaternion& operator=(const Quaternion& quaternion);
 
@@ -120,8 +132,24 @@ struct Quaternion {
         bool operator==(const Quaternion& quaternion) const;
 };
 
+/// Set all the values
+inline void Quaternion::setAllValues(decimal newX, decimal newY, decimal newZ, decimal newW) {
+    x = newX;
+    y = newY;
+    z = newZ;
+    w = newW;
+}
+
+/// Set the quaternion to zero
+inline void Quaternion::setToZero() {
+    x = 0;
+    y = 0;
+    z = 0;
+    w = 0;
+}
+
 // Return the vector v=(x y z) of the quaternion
-inline Vector3 Quaternion::vectorV() const {
+inline Vector3 Quaternion::getVectorV() const {
 
     // Return the vector v
     return Vector3(x, y, z);
@@ -132,6 +160,20 @@ inline decimal Quaternion::length() const {
     return sqrt(x*x + y*y + z*z + w*w);
 }
 
+// Normalize the quaternion
+inline void Quaternion::normalize() {
+
+    decimal l = length();
+
+    // Check if the length is not equal to zero
+    assert (l > MACHINE_EPSILON);
+
+    x /= l;
+    y /= l;
+    z /= l;
+    w /= l;
+}
+
 // Return the unit quaternion
 inline Quaternion Quaternion::getUnit() const {
     decimal lengthQuaternion = length();
@@ -193,9 +235,16 @@ inline Quaternion Quaternion::operator*(decimal nb) const {
 
 // Overloaded operator for the multiplication of two quaternions
 inline Quaternion Quaternion::operator*(const Quaternion& quaternion) const {
-    return Quaternion(w * quaternion.w - vectorV().dot(quaternion.vectorV()),
+    return Quaternion(w * quaternion.w - getVectorV().dot(quaternion.getVectorV()),
-                      w * quaternion.vectorV() + quaternion.w * vectorV() +
+                      w * quaternion.getVectorV() + quaternion.w * getVectorV() +
-                      vectorV().cross(quaternion.vectorV()));
+                      getVectorV().cross(quaternion.getVectorV()));
+}
+
+// Overloaded operator for the multiplication with a vector.
+/// This methods rotates a point given the rotation of a quaternion.
+inline Vector3 Quaternion::operator*(const Vector3& point) {
+    Quaternion p(point.x, point.y, point.z, 0.0);
+    return (((*this) * p) * getConjugate()).getVectorV();
 }
 
 // Overloaded operator for the assignment

src/mathematics/Transform.h

@@ -100,6 +100,9 @@ class Transform {
                                                const Transform& newTransform,
                                                decimal interpolationFactor);
 
+        /// Return the identity transform
+        static Transform identity();
+
         // Return the transformed vector
         Vector3 operator*(const Vector3& vector) const;
 
@@ -154,12 +157,12 @@ inline void Transform::setFromOpenGL(decimal* openglMatrix) {
 // Get the OpenGL matrix of the transform
 inline void Transform::getOpenGLMatrix(decimal* openglMatrix) const {
     const Matrix3x3& matrix = mOrientation.getMatrix();
-    openglMatrix[0] = matrix.getValue(0, 0); openglMatrix[1] = matrix.getValue(1, 0);
+    openglMatrix[0] = matrix[0][0]; openglMatrix[1] = matrix[1][0];
-    openglMatrix[2] = matrix.getValue(2, 0); openglMatrix[3] = 0.0;
+    openglMatrix[2] = matrix[2][0]; openglMatrix[3] = 0.0;
-    openglMatrix[4] = matrix.getValue(0, 1); openglMatrix[5] = matrix.getValue(1, 1);
+    openglMatrix[4] = matrix[0][1]; openglMatrix[5] = matrix[1][1];
-    openglMatrix[6] = matrix.getValue(2, 1); openglMatrix[7] = 0.0;
+    openglMatrix[6] = matrix[2][1]; openglMatrix[7] = 0.0;
-    openglMatrix[8] = matrix.getValue(0, 2); openglMatrix[9] = matrix.getValue(1, 2);
+    openglMatrix[8] = matrix[0][2]; openglMatrix[9] = matrix[1][2];
-    openglMatrix[10] = matrix.getValue(2, 2); openglMatrix[11] = 0.0;
+    openglMatrix[10] = matrix[2][2]; openglMatrix[11] = 0.0;
     openglMatrix[12] = mPosition.x; openglMatrix[13] = mPosition.y;
     openglMatrix[14] = mPosition.z; openglMatrix[15] = 1.0;
 }
@@ -186,6 +189,11 @@ inline Transform Transform::interpolateTransforms(const Transform& oldTransform,
     return Transform(interPosition, interOrientation);
 }
 
+// Return the identity transform
+inline Transform Transform::identity() {
+    return Transform(Vector3(0, 0, 0), Quaternion::identity());
+}
+
 // Return the transformed vector
 inline Vector3 Transform::operator*(const Vector3& vector) const {
     return (mOrientation.getMatrix() * vector) + mPosition;

src/mathematics/Vector3.h

@@ -67,6 +67,9 @@ struct Vector3 {
         // Set all the values of the vector
         void setAllValues(decimal newX, decimal newY, decimal newZ);
 
+        /// Set the vector to zero
+        void setToZero();
+
         // Return the lenght of the vector
         decimal length() const;
 
@@ -140,6 +143,13 @@ struct Vector3 {
         friend Vector3 operator/(const Vector3& vector, decimal number);
 };
 
+// Set the vector to zero
+inline void Vector3::setToZero() {
+    x = 0;
+    y = 0;
+    z = 0;
+}
+
 // Set all the values of the vector
 inline void Vector3::setAllValues(decimal newX, decimal newY, decimal newZ) {
     x = newX;