
Blossoming Development of Splines
Stephen Mann(Author)
Morgan & Claypool Publishers
Published on 1. November 2006
Book
Paperback/Softback
108 pages
978-1-59829-116-2 (ISBN)
Description
In this lecture, we study Bézier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bézier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface.
The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bézier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.
The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bézier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.
More details
Series
Language
English
Place of publication
San Rafael
United States
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 187 mm
ISBN-13
978-1-59829-116-2 (9781598291162)
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Schweitzer Classification
Content
- Introduction and Background
- Polynomial Curves
- B-Splines
- Surfaces
- Polynomial Curves
- B-Splines
- Surfaces