/// <summary>
/// Multiply a float with the matrix
/// </summary>
/// <param name="value">The float to multiply to the matrix</param>
/// <returns>Returns the multiplied matrix</returns>
public Matrix3x3 Mult(float value)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = this.m11 * value;
newMatrix.m12 = this.m12 * value;
newMatrix.m13 = this.m13 * value;
newMatrix.m21 = this.m21 * value;
newMatrix.m22 = this.m22 * value;
newMatrix.m23 = this.m23 * value;
newMatrix.m31 = this.m31 * value;
newMatrix.m32 = this.m32 * value;
newMatrix.m33 = this.m33 * value;
return newMatrix;
}
/// <summary>
/// Transpose the matrix
/// </summary>
/// <returns>Returns transposed matrix</returns>
public Matrix3x3 Transpose()
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = this.m11;
newMatrix.m12 = this.m21;
newMatrix.m13 = this.m31;
newMatrix.m21 = this.m12;
newMatrix.m22 = this.m22;
newMatrix.m23 = this.m32;
newMatrix.m31 = this.m13;
newMatrix.m32 = this.m23;
newMatrix.m33 = this.m33;
return newMatrix;
}
/// <summary>
/// Calculate the coefficient of the matrix
/// </summary>
/// <returns>Returns the coefficient</returns>
public Matrix3x3 Coefficient()
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = + ((this.m22 * this.m33) - (this.m23 * this.m32));
newMatrix.m12 = - ((this.m21 * this.m33) - (this.m23 * this.m31));
newMatrix.m13 = + ((this.m21 * this.m32) - (this.m22 * this.m31));
newMatrix.m21 = - ((this.m12 * this.m33) - (this.m13 * this.m32));
newMatrix.m22 = + ((this.m11 * this.m33) - (this.m13 * this.m31));
newMatrix.m23 = - ((this.m11 * this.m32) - (this.m12 * this.m31));
newMatrix.m31 = + ((this.m12 * this.m23) - (this.m13 * this.m22));
newMatrix.m32 = - ((this.m11 * this.m23) - (this.m13 * this.m21));
newMatrix.m33 = + ((this.m11 * this.m22) - (this.m12 * this.m21));
return newMatrix;
}
/// <summary>
/// Multiply another matrix to this matrix
/// </summary>
/// <param name="secondMatrix">The second matrix</param>
/// <returns>Returns the multiplied matrix</returns>
public Matrix3x3 Mult(Matrix3x3 secondMatrix)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = ((this.m11 * secondMatrix.m11) + (this.m12 * secondMatrix.m21) + (this.m13 * secondMatrix.m31));
newMatrix.m12 = ((this.m11 * secondMatrix.m12) + (this.m12 * secondMatrix.m22) + (this.m13 * secondMatrix.m32));
newMatrix.m13 = ((this.m11 * secondMatrix.m13) + (this.m12 * secondMatrix.m23) + (this.m13 * secondMatrix.m33));
newMatrix.m21 = ((this.m21 * secondMatrix.m11) + (this.m22 * secondMatrix.m21) + (this.m23 * secondMatrix.m31));
newMatrix.m22 = ((this.m21 * secondMatrix.m12) + (this.m22 * secondMatrix.m22) + (this.m23 * secondMatrix.m32));
newMatrix.m23 = ((this.m21 * secondMatrix.m13) + (this.m22 * secondMatrix.m23) + (this.m23 * secondMatrix.m33));
newMatrix.m31 = ((this.m31 * secondMatrix.m11) + (this.m32 * secondMatrix.m21) + (this.m33 * secondMatrix.m31));
newMatrix.m32 = ((this.m31 * secondMatrix.m12) + (this.m32 * secondMatrix.m22) + (this.m33 * secondMatrix.m32));
newMatrix.m33 = ((this.m31 * secondMatrix.m13) + (this.m32 * secondMatrix.m23) + (this.m33 * secondMatrix.m33));
return newMatrix;
}
/// <summary>
/// Returns the view matrix for the given parameters
/// </summary>
/// <param name="right">The camera's right vector</param>
/// <param name="up">The camera's up vector</param>
/// <param name="position">The camera's position</param>
/// <returns>View matrix</returns>
public static Matrix3x3 ViewTransform(Vector2 right, Vector2 up, Vector2 position)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = right.x;
newMatrix.m12 = right.y;
newMatrix.m21 = up.x;
newMatrix.m22 = up.y;
newMatrix.m31 = -(right * position);
newMatrix.m32 = -(up * position);
return newMatrix;
}
/// <summary>
/// Returns a world matrix for the given vectors
/// </summary>
/// <param name="right">The right vector</param>
/// <param name="up">The up vector</param>
/// <param name="position">The position vector</param>
/// <returns></returns>
public static Matrix3x3 WorldTransform(Vector2 right, Vector2 up, Vector2 position)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = right.x;
newMatrix.m12 = right.y;
newMatrix.m21 = up.x;
newMatrix.m22 = up.y;
newMatrix.m31 = position.x;
newMatrix.m32 = position.y;
return newMatrix;
}
/// <summary>
/// Returns a translation matrix for the given vector
/// </summary>
/// <param name="translation">Translation vector</param>
/// <returns>Returns translated matrix</returns>
public static Matrix3x3 TranslateTransform(Vector2 translation)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m31 = translation.x;
newMatrix.m32 = translation.y;
return newMatrix;
}
/// <summary>
/// Calculate the determinant of a matrix
/// </summary>
/// <param name="matrix">Matrix to calculate determinant of</param>
/// <returns>Returns the determinant</returns>
public static float Determinant(Matrix3x3 matrix)
{
return
+ (matrix.m11 * matrix.m22 * matrix.m33)
+ (matrix.m12 * matrix.m23 * matrix.m31)
+ (matrix.m13 * matrix.m21 * matrix.m32)
- (matrix.m13 * matrix.m22 * matrix.m31)
- (matrix.m12 * matrix.m21 * matrix.m33)
- (matrix.m11 * matrix.m23 * matrix.m32);
}
/// <summary>
/// Returns a scale matrix for the given vector
/// </summary>
/// <param name="translation">Scale vector</param>
/// <returns>Returns scale matrix</returns>
public static Matrix3x3 ScaleTransform(Vector2 scale)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = scale.x;
newMatrix.m22 = scale.y;
return newMatrix;
}
/// <summary>
/// Returns transformation matrix for shearing along Y axis
/// </summary>
/// <param name="shear">Shearing value</param>
/// <returns>Returns transformation matrix for shearing along Y axis</returns>
public static Matrix3x3 ShearYTransform(float shear)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m21 = shear;
return newMatrix;
}
/// <summary>
/// Returns the rotation matrix of a clockwise rotation by an angle given in radians
/// </summary>
/// <param name="angle">The angle in radians</param>
/// <returns>Returns the rotation matrix</returns>
public static Matrix3x3 RotateTransform(float angle)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = (float)(Math.Cos(angle));
newMatrix.m12 = (float)(Math.Sin(angle));
newMatrix.m21 = (float)(-Math.Sin(angle));
newMatrix.m22 = (float)(Math.Cos(angle));
return newMatrix;
}
/// <summary>
/// Multiply a float with a matrix
/// </summary>
/// <param name="matrix">The matrix to multiplay the float to</param>
/// <param name="value">The float to multiply to the matrix</param>
/// <returns>Returns the multiplied matrix</returns>
public static Matrix3x3 Mult(Matrix3x3 matrix, float value)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = matrix.m11 * value;
newMatrix.m12 = matrix.m12 * value;
newMatrix.m13 = matrix.m13 * value;
newMatrix.m21 = matrix.m21 * value;
newMatrix.m22 = matrix.m22 * value;
newMatrix.m23 = matrix.m23 * value;
newMatrix.m31 = matrix.m31 * value;
newMatrix.m32 = matrix.m32 * value;
newMatrix.m33 = matrix.m33 * value;
return newMatrix;
}
/// <summary>
/// Calculate the inverse of a matrix
/// </summary>
/// <param name="matrix">Matrix to calculate inverse of</param>
/// <returns>Returns inverse of matrix</returns>
public static Matrix3x3 Inverse(Matrix3x3 matrix)
{
float determinant = matrix.Determinant();
Matrix3x3 newMatrix = matrix.Coefficient();
newMatrix = newMatrix.Transpose();
newMatrix = newMatrix / determinant;
return newMatrix;
}
/// <summary>
/// Multiply a Matrix3x3 to a vector (ignoring the third dimension of the matrix)
/// </summary>
/// <param name="matrix">The Matrix3x3 to multiply to the vector</param>
/// <returns>Returns the multiplied vector</returns>
public static Vector2 Mult(Vector2 vector, Matrix3x3 matrix)
{
Vector2 newVector = new Vector2();
newVector.x = ((matrix.m11 * vector.x) + (matrix.m12 * vector.y));
newVector.y = ((matrix.m21 * vector.x) + (matrix.m22 * vector.y));
return newVector;
}
/// <summary>
/// Transpose a matrix
/// </summary>
/// <param name="matrix">Matrix to transpose</param>
/// <returns>Returns transposed matrix</returns>
public static Matrix3x3 Transpose(Matrix3x3 matrix)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = matrix.m11;
newMatrix.m12 = matrix.m21;
newMatrix.m13 = matrix.m31;
newMatrix.m21 = matrix.m12;
newMatrix.m22 = matrix.m22;
newMatrix.m23 = matrix.m32;
newMatrix.m31 = matrix.m13;
newMatrix.m32 = matrix.m23;
newMatrix.m33 = matrix.m33;
return newMatrix;
}
/// <summary>
/// Multiply a Matrix3x3 to the vector (ignoring the third dimension of the matrix)
/// </summary>
/// <param name="matrix">The Matrix3x3 to multiply to the vector</param>
/// <returns>Returns the multiplied vector</returns>
public Vector2 Mult(Matrix3x3 matrix)
{
Vector2 newVector = new Vector2();
newVector.x = ((matrix.m11 * this.x) + (matrix.m12 * this.y));
newVector.y = ((matrix.m21 * this.x) + (matrix.m22 * this.y));
return newVector;
}
/// <summary>
/// Calculate the coefficient of a matrix
/// </summary>
/// <param name="matrix">Matrix to calculate coefficient of</param>
/// <returns>Returns the coefficient</returns>
public static Matrix3x3 Coefficient(Matrix3x3 matrix)
{
Matrix3x3 newMatrix = new Matrix3x3();
newMatrix.m11 = + ((matrix.m22 * matrix.m33) - (matrix.m23 * matrix.m32));
newMatrix.m12 = - ((matrix.m21 * matrix.m33) - (matrix.m23 * matrix.m31));
newMatrix.m13 = + ((matrix.m21 * matrix.m32) - (matrix.m22 * matrix.m31));
newMatrix.m21 = - ((matrix.m12 * matrix.m33) - (matrix.m13 * matrix.m32));
newMatrix.m22 = + ((matrix.m11 * matrix.m33) - (matrix.m13 * matrix.m31));
newMatrix.m23 = - ((matrix.m11 * matrix.m32) - (matrix.m12 * matrix.m31));
newMatrix.m31 = + ((matrix.m12 * matrix.m23) - (matrix.m13 * matrix.m22));
newMatrix.m32 = - ((matrix.m11 * matrix.m23) - (matrix.m13 * matrix.m21));
newMatrix.m33 = + ((matrix.m11 * matrix.m22) - (matrix.m12 * matrix.m21));
return newMatrix;
}