A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas. The book discusses fundamental tools in analytical geometry and linear algebra. It covers a wide range of topics, from matrix decomposition to curvature analysis and principal component analysis to dimensionality reduction.

Written by a team of highly respected professors, the book can be used in a one-semester, intermediate-level course in computer science. It takes a practical problem-solving approach, avoiding detailed proofs and analysis. Suitable for readers without a deep academic background in mathematics, the text explains how to solve non-trivial geometric problems. It quickly gets readers up to speed on a variety of tools employed in visual computing and applied geometry.

Table of Contents

Chapter 1: Analytical Geometry
Chapter 2: Linear Algebra?
Chapter 3: Least-Squares Solutions
Chapter 4: PCA and SVD
Chapter 5: Spectral Transform
Chapter 6: Solution of Linear Systems
Chapter 7: Laplace and Poisson
Chapter 8: Curvatures: A Differential Geometry Tool
Chapter 9: Dimensionality Reduction
Chapter 10: Scattered-Data Interpolation
Chapter 11: Topology: How Are Objects Connected?
Chapter 12: Graphs and Images
Chapter 13: Skewing Schemes