Curve and surface computer modelling is far more complex than what you see on screen. It is quite a feat to convert a data set into a visual image, and a bigger trick to convert it into a recognisable dimensional object that you can turn as if you're holding it in your hand. The mathematical heroes who paved the road to this point are eloquently acknowledged in David Rogers's An Introduction to NURBS with Historical Perspective
Rogers himself is a figure in computer graphics history, having penned Mathematical Elements for Computer Graphics and Procedural Elements for Computer Graphics. In An Introduction to NURBS he takes us on a mathematical journey that introduces the concept and details of non-uniform rational B-splines while at the same time shedding light on the mathematical wizards that make NURBS possible.
This is a hardcover textbook (not light reading), with enough equations and pseudocode to satisfy even the hungriest of math theorists. With seven chapters, starting with "Curve and Surface Representation" through "B-Spline Curves" to "Bezier Surfaces," the book is a thorough primer for those working toward understanding computer graphic modelling.
What really sets this book apart from other texts, though, is the closing portion of each chapter, in which readers get a historical perspective of the current state of the art in curve and surface mathematics in passages written by such luminaries as Robin Forrest (Bezier Curves), Rich Riesenfeld (B-splines), Lewis Knapp (Rational B-splines), and others. --Mike Caputo, Amazon.com
About the Author
David F. Rogers, Ph.D., is the author of two computer graphics classics, Mathematical Elements for Computer Graphics and Procedural Elements for Computer Graphics, as well as works on fluid dynamics. His early research on the use of B-splines and NURBS for dynamic manipulation of ship hull surfaces led to significant commercial and scientific advances in a number of fields. Founder and former director of the Computer Aided Design/Interactive Graphics Group at the U.S. Naval Academy, Dr. Rogers was an original member of the USNA's Aerospace Engineering Department. He sits on the editorial boards of The Visual Computer and Computer Aided Design and serves on committees for SIGGRAPH, Computer Graphics International, and other conferences.