Tutorial Geometric Computing in Computer （教程几何计算在计算机）.pdf

Dietmar Hildenbrand / Geometric Computing in Computer Graphics 1 Tutorial Geometric Computing in Computer Graphics using Conformal Geometric Algebra Dietmar Hildenbrand Interactive Graphics Systems Group, TU Darmstadt, Germany Abstract Early in the development of Computer Graphics it was realized that projective geometry was well suited for the representation of transformations. Now, it seems that another change of paradigm is lying ahead of us based on Geometric Computing using Conformal Geometric Algebra. Due to its geometric intuitiveness, elegance and simplicity, the underlying Conformal Geometric Algebra appears to be a promising mathematical tool for Computer Graphics and Animations. In this tutorial paper we introduce into the basics of the Conformal Geometric Algebra and show its advantages based on two Computer Graphics applications. First, we will present an algorithm for the Inverse Kinematics of a robot that you are able to comprehend without prior knowledge of Geometric Algebra. We expect that here you will obtain the basic knowledge for developing your own algorithm afterwards. Second, we will show how easy it is in Conformal Geometric Algebra, to fit the best suitable object in a set of points , whether it is a plane or a sphere. 2 Dietmar Hildenbrand / Geometric Computing in Computer Graphics 1. Introduction Table 1: list of the conformal geometric entities In this tutorial paper, we focus on the introduction of the 5D Conformal Geometric Algebra which is an extension of entity representation 1 representation