Geometric Transformations for 3D Modeling
Written from a mathematical standpoint accessible to students, teachers, and professionals, this text provides a comprehensive introduction to the theory and application of transformations.
TABLE OF CONTENTS Geometric Transformations for 3D Modeling
Chapter 1: Geometry
Here we look at geometry from three different points of view. First, we examine various attempts to define it and try to develop an appropriate attitude toward the subject. Next, we review its history and explore its scope and diversity, discovering that there are many geometries. Finally, we discover how a single powerful principle codifies, unites and simplifies our understanding of geometry. We see change and permanence transformation and invariance emerge as agents of this principle.
1.1 What is Geometry?
What kind of answer?, fractals, Kock snowflake, limits of intuition and visualization.
Arrange three straight sticks end to end so that they form a triangle. If you randomly choose the sticks from an assortment of varying lengths, you won't always succeed in your construction. You will soon observe that if the length of any one of the three sticks exceeds the total length of the remaining two, then it is impossible to form a triangle. You have discovered a simple yet fundamental principle of the geometry of triangles. Next, leap to a study of Einstein's theory of general relativity. In it, you find that gravitational forces are attributable to curvature in the four-dimensional geometry of spacetime. How are two such seemingly distinct and diverse phenomena encompassed by a single discipline? Indeed, what is geometry?
Euclid and his students would have had no trouble answering this question, but does geometry mean the same thing today as it did more than two thousand years ago? Does it mean the same...
Copyright Industrial Press Inc. 2007 under license agreement with Books24x7
