NDLI: Calculation of B-spline surfaces using digital filters

Content Provider	ACM Digital Library
Author	Schaffner, Stuart C.
Abstract	A (potentially large) MxN grid of B-spline control points is an attractive database for the representation of a curved surface. The properties of B-splines allow precise control over surface smoothness and ensure that local changes to the surface will require only local changes to the database. One difficulty in applying this technique is that the grid of control points does not in general lie on the surface it generates. Given an MxN grid of points, one would like to be able to generate a B-spline surface which passes through all points in the given grid.A straightforward but time-consuming solution to this problem would require the inversion of one MxM and one NxN matrix. Instead, we solve the problem with digital filters. The grid of surface points is passed through a set of first-order recursive digital filters to produce the grid of control points. This method requires time linear in the number of grid points, works without modification for all values of M and N, and has excellent stability.
Starting Page	437
Ending Page	457
Page Count	21
File Format	PDF
ISSN	00978930
DOI	10.1145/988428.988435
Journal	ACM SIGGRAPH Computer Graphics (COMG)
Volume Number	15
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1988-08-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computer Science Computer Graphics and Computer-Aided Design

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