BSplineMfd

Supported Versions

0

Subtype of

Manifold

Fields

The class is defined by the following fields:

Entity/Object	Variable	Description
integer		Version
integer	d	Space dimension
Transform		Transformation class
integer		Dimension (1 if curve, 2 if surface)
integer	p, q	Degree in each dimension (1 or 2 integers)
Boolean		If rational equal to1
integer		Number of knot vectors (1 for curves, 2 for surfaces)
integer	m1	Length of first knot vector
double[m1]	U	First knot vector
integer	m2	Length of second knot vector (not for curves)
double[m2]	V	Second knot vector (not for curves)
integer	n1	Number of control points in first parameter direction
integer	n2	Number of control points in second parameter dimension
integer	n3	Number of coordinates per control point
double [n1][n2][n3]	P	Matrix of coordinates where the last dimension is increased by 1 to store the weights if the manifold is rational

Description

The BSplineMfd type is the abstract base type for BSplineCurve and BSplineSurf, which represent general spline curves and surfaces, respectively.

They are represented using B-spline basis functions. Let U = {u0, …, um} be a nondecreasing sequence of real numbers; U is called the knot vector and the elements ui of U are called knots. The ith B-spline basis function of p-degree, , is defined as

A general B-spline can be described by

where

and

are the two knot vectors stored in the entry, and b and w are the control points coordinates and weights stored in P.

For periodic splines, the first and last parameter values in the knot vectors are not duplicated.