1. The homogeneous module

class turberfield.utils.homogeneous.Homogeneous

This class provides homogeneous coordinates for use in graphical applications. The representation supports both points and vectors.

magnitude

Presents the magnitude of a vector (position vector in the case of a point).

Return type:number

The module consists of several functions which operate on Homogeneous coordinates to support 2D or 3D geometric calculations.

turberfield.utils.homogeneous.point(*args)

Factory function for homogeneous points.

Parameters:args – coordinates for the point
Returns:a new point object
Return type:Homogeneous
turberfield.utils.homogeneous.vector(*args)

Factory function for homogeneous vector.

Parameters:args – coordinates for the vector
Returns:a new vector object
Return type:Homogeneous
turberfield.utils.homogeneous.posvector(point)

Returns the position vector of a point.

Parameters:point (Homogeneous) – a point
Returns:a new vector object
Return type:Homogeneous
turberfield.utils.homogeneous.normalise(vec)

Scales a vector so its magnitude is unity.

Parameters:vec (Homogeneous) – a vector
Returns:a new vector object
Return type:Homogeneous
Requires:vec to be a vector
turberfield.utils.homogeneous.dot(one, tother)

Calculates the dot product of two vectors.

Parameters:
Returns:

the scalar product
Return type:

number
turberfield.utils.homogeneous.cross(one, tother)

Calculates the cross product of two vectors. Works in 3D only.

Parameters:
Returns:

a vector
Return type:

Homogeneous
turberfield.utils.homogeneous.premultiply(hom, *rows)

Performs a matrix transformation M{Mp} on a point or vector. The matrix is supplied as a number of tuples, each one being a row of the transformation matrix. The matrix must be properly sized to match a homogeneous array, ie: to transform a 3D (4-element) point, you need four rows each containing four values.

Parameters:
  • hom (Homogeneous) – a point or vector
  • rows (tuples) – matrix data
Returns:

a point or vector
Return type:

Homogeneous
Requires:

there must be as many rows as there are elements in hom, and each must be the length of hom
turberfield.utils.homogeneous.maxpick(one, tother)

Performs elementwise comparison of two points or vectors and keeps the larger of each corresponding element.

Parameters:
Returns:

a point or vector
Return type:

Homogeneous
turberfield.utils.homogeneous.minpick(one, tother)

Performs elementwise comparison of two points or vectors and keeps the smaller of each corresponding element.

Parameters:
Returns:

a point or vector
Return type:

Homogeneous