NDLI: The Intersection of Rays with Algebraic Surfaces

Content Provider	Springer Nature Link
Author	Parkin, Spencer T.
Copyright Year	2014
Abstract	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.
Starting Page	809
Ending Page	815
Page Count	7
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	24
Issue Number	3
e-ISSN	16614909
Language	English
Publisher	Springer Basel
Publisher Date	2014-04-12
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Taylor Series Ray Casting Algebraic Surfaces Geometric Algebra Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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The Intersection of Rays with Algebraic Surfaces