An object-oriented

implementation of T-splines

Data structures and Bézier extraction

T.H. Boschman

0629444

T-splines data structures

• Control points

• Line segments

• Faces

• Physical space

• Parameter space

• Index space

T-splines data structures

• Knot value configuration

• Local knot interval vector

• Local knot vector

T-spline data structures

• Local basis function domain

• T-spline basis functions

• Cox-de Boor recursion formula

Constant p=0

Higher order

T-splines data structures

• Elemental T-mesh

• Local basis function mesh

• Lines of reduced continuity

• Elements

T-splines data structures

• IEN array

• Global basis functions

• Local basis functions

T-splines Bézier extraction

• Bernstein basis

• Univariate

with

T-splines Bézier extraction

• Elemental extraction operators

• Bézier mesh with Bézier elements is created

T-splines Bézier extraction

• Construction of the elemental extraction operator

• Local, function by function

• Extended knot vector (p+1)

• Knot insertion in the extended knot vector

T-splines implementation

• Data structures

• Control points, line segments, faces

• Methods

• Index space, Parameter space, Physical space

• Local knot vector, Elemental T-mesh, IEN array

• Bezier extraction

• Elemental extraction operators

Examples

Examples