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Matrices.md

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Matrices

Design choices are still being made over the Vec3 and Vec4 classes. Mostly due to graphical rotation matrices supporting both Vec3 and Vec4 classes.
The matrix module currently consists of three classes, Mat2, Mat3 and Mat4.
The matrix itself is stored as a flat structure and implemented as row-major. e.g, the matrix,

| 0, 1 |
| 2, 3 |

is stored as,

[0, 1, 2, 3]

The current layout is also subject to change due to opengl using column-major matrices (functionality will most likely be put in place to support both matrice layouts).
Currently a large number of functions are not implemented, or are only implemented for some classes.

Functions

  1. Initalisation
  2. Standard
  3. Comparison
  4. [Extra functionality](#Extra Functionality)
  5. Mat3 Only Functions
  6. Mat4 Only Functions

Initalisation

Calling the matrix with out parameters will initalise a zero matrix

>>> pyclid.Mat2()
| 0 0 |
| 0 0 |

>>> pyclid.Mat3()
| 0 0 0 |
| 0 0 0 |
| 0 0 0 |

>>> pyclid.Mat4()
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |

Array parameters can be passed in as an array (subject to change)

>>> pyclid.Mat2([0, 1, 2, 3])
| 0 1 |
| 2 3 |

Standard

Addition

Addition is applied on an element by element basis

>>> a = pyclid.Mat2([1, 1, 1, 1])
>>> b = pyclid.Mat2([1, 2, 3, 4])
>>> a+b
| 2 3 |
| 4 5 |

Subtraction

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> b = pyclid.Mat2([1, 1, 1, 1])
>>> a-b
| 0 1 |
| 2 3 |

Multiplication

This can be used with a number, Vec2 or a matrix of the same size.

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> a*2
| 2 4 |
| 6 8 |

Multiplication by a vector must be applied in the correct order. A matrix multiplied by a vector is correct.

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> b = pyclid.Vec2(1, 2)
>>> a*b
<5, 11>

Multiplication by a matrix must use matrices of the same size

>>> a = pyclid.Mat2([1, 2, 4, 8])
>>> b = pyclid.Mat2([1, 2, 3, 4])
>>> a*b
|  7 10 |
| 28 40 |

Division

Division can only be used with a number

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> a/2.0
| 0.5 1.0 |
| 1.5 2.0 |

Comparison

Comparison is performed on an matrix element by element basis

Equal

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> b = pyclid.Mat2([1, 2, 3 ,4])
>>> a == b
True

Not Equal

>>> a = pyclid.Mat2([4, 3, 2, 1])
>>> b = pyclid.Mat2([1, 2, 3 ,4])
>>> a != b
True

Extra functionality

Matrix

Return the current matrix as a flat array (not a function call)

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> a.matrix
[1, 2, 3, 4]

Load Zero

Sets all elements in the matrix to zero

>>> a = pyclid.Mat2([1, 2, 3 ,4])
>>> a.load_zero()
| 0 0 |
| 0 0 |

Load Identity

Sets the matrix elements to the identity of the matrix

>>> a = pyclid.Mat2([1, 2, 3, 4])
>>> a.load_identity()
| 1 0 |
| 0 1 |

Transpose

>>> a = pyclid.Mat2([1, 2, 3 4])
>>> a
| 1 2 |
| 3 4 |
>>> a.transpose()
| 1 3 |
| 2 4 |

Rotate

Applies a rotation to the matrix based on an angle (Currently broken in Mat2 and Mat4). Uses the angle passed in to generate a rotation matrix, which is multiplied to the original matrix

>>> a = Mat3([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |

>>> a.rotate(1.5)
|   2.06572717488 -0.856020583269               3 |
|   5.27042373969  -3.63629393808               6 |
|   8.47512030451  -6.41656729289               9 |

Mat3 only functions

These functions need to be updated to work on Mat2 and Mat4

Set Value

Sets the value of an element within the matrix. element can be indexed with either by 1D or 2D [x, y]. Takes parameters (value, index)

>>> a = pyclid.Mat3()
>>> a
| 0 0 0 |
| 0 0 0 |
| 0 0 0 |

>>> a.set_value(1, 1)
>>> a
| 0 1 0 |
| 0 0 0 |
| 0 0 0 |

>>> a.set_value(2, [1, 1])
>>> a
| 0 1 0 |
| 0 2 0 |
| 0 0 0 |

Translate

Translates a matrix by parameters (x, y)

>>> a = pyclid.Mat3([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |

>>> a.translate(1, 0)
|  1  2  4 |
|  4  5 10 |
|  7  8 16 |

Scale

Scales a matrix by parameters (x, y)

>>> a = pyclid.Mat3([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a.scale(2.0, 1.0)
|  2.0  2.0    3 |
|  8.0  5.0    6 |
| 14.0  8.0    9 |

Share

Shares a matrix by parameters (x, y)

>>> a = pyclid.Mat3([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a.share(2.0, 1.0)
|  3.0  4.0    3 |
|  9.0 13.0    6 |
| 15.0 22.0    9 |

Convert 2D

This requires parameters (x, y) and returns the index of the element in 1D for the current matrix

>>> a = pyclid.Mat3([1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> a.convert_2d(0, 1)
3

Mat4 Only Functions

Rotate

The next set of functions apply only to Mat4 (Should also apply to Mat3). These apply rotations about the Euler angles x, y and z. An angle is supplied to the function (rotate_x, rotate_y, rotate_z depending on the require rotation) and the resulting rotation of the matrix is returned

>>> a = pyclid.Mat4()
>>> a.load_identity()
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
>>> a.rotate_x(1.5)
|               1             0.0             0.0               0 |
|               0 0.0707372016677  0.997494986604               0 |
|               0 -0.997494986604 0.0707372016677               0 |
|               0             0.0             0.0               0 |