NURBS for Curve and Surface Design
from Projective Geometry to Practical Use
2nd edition

by Gerald Farin

Published in 1999 by AK Peters, Ltd.
267 Pages
ISBN 1-56881-084-9

NURB curves and surfaces are the industry standard for geometry description in CAD/CAM or  Computer Graphics. 

NURBS  are piecewise rational; they are the logical extension of B-spline or Bezier entitities. 

While those have their roots in affine geometry, NURBS cannot be understood without paying attention to their foundations in projective geometry - this constitutes the first part of the book.

After these foundations have been laid, rational conics and Bezier curves are introduced;
rational B-spline curves (NURBS) follow. As a further extension, the surfaces
corresponding to these curves are also introduced. Applications include Pythagorean Hodograph curves and developable surfaces.

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More books by the author
Mathematical Principles for Scientific Computing and Visualization
by Gerald Farin and Dianne Hansford
The Essentials of Computer Aided Geometric Design
by Gerald Farin & Dianne Hansford
Practical Linear Algebra - A Geometry Toolbox
by Gerald Farin and Dianne Hansford
Curves and Surfaces for CAGD
by Gerald Farin
Linear Algebra: Ein geometrischer Zugang
by Gerald Farin & Dianne Hansford
Published by Springer Verlag, Heidelberg, 2003
(A German translation of The Geometry Toolbox)