Curves and Surfaces for Geometric Design offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work-whether you're a graduate student, scientist, or practitioner.
Inside, the focus is on "blossoming"-the process of converting a polynomial to its polar form-as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for far more than its theoretical elegance, for the author proceeds to demonstrate the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more.
The product of groundbreaking research by a noteworthy computer scientist and mathematician, this book is destined to emerge as a classic work on this complex subject. It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning.
Jean Gallier received the degree of Civil Engineer from the Ecole Nationale des Ponts et Chaussees in 1972 and a Ph.D. in Computer Science from UCLA in 1978. That same year he joined the University of Pennsylvania, where he is presently a professor in CIS with a secondary appointment in Mathematics. In 1983, he received the Linback Award for distinguished teaching. Gallier's research interests range from constructive logics and automated theorem proving to geometry and its applications to computer graphics, animation, computer vision, and motion planning. The author of Logic in Computer Science, he enjoys hiking (especially the Alps) and swimming. He also enjoys classical music (Mozart), jazz (Duke Ellington, Oscar Peterson), and wines from Burgundy, especially Volnay.
There are fewer graphics programmers who have an adequate understanding of the underlying mathematical concepts. This book can partially help the graphics programmers to cross over to that select group. Problems at the end of each chapter enhance the value of the book. The material is updated with latest developments in the field such as subdivision surfaces.
People interested in Computer Graphics, Geometric Modeling, Computer Vision, and Robotics will benefit from studying this book.