Page 71

Publication Type	technical report
School or College	College of Engineering
Department	Computing, School of
Creator	Catmull, Edwin E.
Title	A Subdivision Algorithm for Computer Display of Curved Surfaces
Date	1974-12
Description	This report presents a method for producing computer shaded pictures of curved surfaces. Three-dimensional curved patches are used, as contrasted with conventional methods using polygons. The method subdivides a patch into successively smaller subpatches until a subpatch is as small as a raster- element, at which time it can be displayed. In general this method could be very time consuming because of the great number of subdivisions that must take place; however, there is at least one very useful class of patches - the bicubic patch - that can be subdivided very quickly. Pictures produced with the method accurately portray the shading and silhouette of curved surfaces. In addition, photographs can be 'mapped' onto patches thus providing a means for putting texture on computer-generated pictures. Doctoral thesis
Type	Text
Language	eng
Series	University of Utah Computer Science Technical Report
Relation is Part of	ARPANET
Format Medium	application/pdf
Format Extent	5,958,407 bytes
File Name	ADA004968.pdf
ARK	ark:/87278/s6cg2j21
Setname	ir_computersa
ID	104071
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6cg2j21

Title	Page 71
Setname	ir_computersa
ID	104057
OCR Text	Show M APPENDIX C APPROXIMATING .'HE BICUBIC NORMAL EQUATION The normal vector to a bicubic patch can be found by taking the cross product of the tangent vector in the the u direction and the tangent vector in the v direction and can be shown to be quintic. It is desirable to approximate :he quintic normal equation with a bicubic equation because a bicubic equation is easier to work with. The x component of the surface vector is: x -[u» u7 u 1]M. where M, is the matrix of coefficients for x. The derivative in the u direction is: xu - [Su3 2u 1 0] M« and the derivative in the v direction is: x, -[u» u» u .1]M. 3v» 2v 1 0 . For simplicity we shall define: U - [u3 u' u 1] U' - [3u? 2u 1 0] U" - [6u 2 0 0] tMM^MMMl ii ii ■i«-<-if^Miiii*Mm i
Reference URL	https://collections.lib.utah.edu/ark:/87278/s6cg2j21/104057