The Intersection of Rays with Algebraic Surfaces

被引：1

作者：

Parkin, Spencer T.

机构：

[1] 102 W. 500 S, Salt Lake City, 84101, UT

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2014年 / 24卷 / 03期

关键词：

Taylor Series; Ray Casting Algebraic Surfaces; Geometric Algebra;

D O I：

10.1007/s00006-014-0460-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Although a well known result in the traditional language of multi-variable calculus, in this paper it is shown, using the language of geometric algebra, that for any real-valued polynomial defined over n-dimensional euclidean space, that the image of any line through the domain of such a function is determined entirely by all orders of directional derivatives of this function at any one point along the line and in the direction of the line. This result is applied to the problem of casting rays through algebraic surfaces.

引用

页码：809 / 815

页数：7