Matrices

Table of Contents

• About
• Classes
  • 2D Matrices
  • 3D Matrices
  • 4D Matrices
• Creation
• Utility
• Further Reading

About

The matrix classes of the MAXON API are based on these generic matrix templates:

• maxon::Mat2: Template for a 2D matrix.
• maxon::Mat3: Template for a 3D matrix.
• maxon::SqrMat2: Template for a general 2x2 matrix composed of two vectors.
• maxon::SqrMat3: Template for a general 3x3 matrix composed of three vectors.
• maxon::SqrMat4: Template for a general 4x4 matrix composed of four vectors.

Classes

2D Matrices

maxon::Mat2 based matrices contains these members:

• maxon::Mat2::off: The translation vector.
• maxon::Mat2::sqmat: The maxon::SqrMat2 for rotation, scale and shear.

maxon::Mat2 based matrix classes are:

• maxon::Matrix2d32: maxon::Float32 matrix.
• maxon::Matrix2d64: maxon::Float64 matrix.
• maxon::Matrix2d: maxon::Float matrix.

maxon::SqrMat2 based matrix classes are:

• maxon::SquareMatrix2d32: maxon::Float32 matrix.
• maxon::SquareMatrix2d64: maxon::Float64 matrix.
• maxon::SquareMatrix2d: maxon::Float matrix.

3D Matrices

maxon::Mat3 based matrices contains these members:

• maxon::Mat3::off: The translation vector.
• maxon::Mat3::sqmat: The maxon::SqrMat3 for rotation, scale and shear.

maxon::Mat3 based matrix classes are:

• maxon::Matrix32: maxon::Float32 matrix.
• maxon::Matrix64: maxon::Float64 matrix.
• maxon::Matrix: maxon::Float matrix.

maxon::SqrMat3 based matrix classes are:

• maxon::SquareMatrix32: maxon::Float32 matrix.
• maxon::SquareMatrix64: maxon::Float64 matrix.
• maxon::SquareMatrix: maxon::Float matrix.

4D Matrices

maxon::SqrMat4 based matrix classes are:

• maxon::SquareMatrix4d32: maxon::Float32 matrix.
• maxon::SquareMatrix4d64: maxon::Float64 matrix.
• maxon::SquareMatrix4d: maxon::Float matrix.

Creation

A new matrix object is simply created using the above matrix classes. It is can easily be configured with SetIdentity():

• maxon::Mat3::SetIdentity(): Sets the matrix to an identity matrix.

    // This example creates a matrix and prints its data to the debug console.
 
    maxon::Matrix matrix;
    matrix.SetIdentity();
 
    DiagnosticOutput("V1: @", matrix.sqmat.v1);
    DiagnosticOutput("V2: @", matrix.sqmat.v2);
    DiagnosticOutput("V3: @", matrix.sqmat.v3);
    DiagnosticOutput("Off: @", matrix.off);

The following operators can be applied to a matrix:

• maxon::Mat3::operator*(): Multiplies two matrices or transforms a vector by a matrix.
• maxon::Mat3::operator/(): Divides all matrix components by the given scalar value.
• maxon::Mat3::operator==(): Returns true if all components of the given matrix are identical.
• maxon::Mat3::operator!=(): Returns true if a component of the given matrix is not identical.
• maxon::Mat3::operator~(): Calculates the inverse matrix.
• maxon::Mat3::GetNormalized(): Returns this matrix with all axis vectors normalized.

    // This example uses the given matrix to transform a point.
 
    maxon::Vector point(10, 10, 10);
 
    // apply matrix
    point = matrix * point;
 
    DiagnosticOutput("New Point: @", point);

Further utility functions are:

• maxon::Mat3::ToString(): Returns a string representation of the matrix.
• maxon::Mat3::GetHashCode(): Returns a hash value of the matrix.

Special functions of maxon::SqrMat2, maxon::SqrMat3 and maxon::SqrMat4 are:

• maxon::SqrMat3::Det(): Calculates the determinant of this matrix.
• maxon::SqrMat3::operator[](): Returns the value for the given index.

Special functions of maxon::SqrMat3 and maxon::SqrMat4 are:

• maxon::SqrMat3::GetTransposed(): Calculates the transposed matrix.

Utility

These utility functions are used to create transformation matrices:

• maxon::GetTranslationMatrix(): Calculates a matrix to move / translate for the given translation vector.
• maxon::GetScaleMatrix(): Calculates a matrix to scale for the given vector.
• maxon::GetRotationMatrixX(): Calculates a matrix to rotate around the X axis for the given angle.
• maxon::GetRotationMatrixY(): Calculates a matrix to rotate around the Y axis for the given angle.
• maxon::GetRotationMatrixZ(): Calculates a matrix to rotate around the Z axis for the given angle.
• maxon::GetRotationMatrixFromAxis(): Calculates the matrix from the given axis and rotation.

    // This example creates a scale matrix and uses it to transform a given point.
 
    const maxon::Vector scale(1.0, 10.0, 1.0);
 
    maxon::Matrix matrix;
    matrix.sqmat = maxon::GetScaleMatrix(scale);
 
    // scale
    point = matrix * point;
 
    DiagnosticOutput("New Point: @", point);

Further Reading

• Data & Algorithms
• Vectors
• Basic Data Types