Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
An interactive computer graphics approach to surface representation
Communications of the ACM
Digital Signal Analysis
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Digital Image Restoration
B-spline surfaces for ship hull design
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Spline-based color sequences for univariate, bivariate and trivariate mapping
VIS '90 Proceedings of the 1st conference on Visualization '90
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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.