An area-oriented analytical visibility method for displaying parametrically defined tensor-product surfaces

Authors:
Christoph Hornung;Wolfgang Lellek;Peter Rehwald;Wolfgang Strasser
Affiliations:
Krupp Atlas-Elektronik, D-2800 Bremen, Fed. Rep. Germany;GTS-Gral, D-6100 Darmstadt, Fed. Rep. Germany;VW-GEDAS, D-1000 Berlin, Fed. Rep. Germany;Graphisch-Interaktive Systeme, TH Darmstadt, Fed. Rep. Germany
Venue:
Computer Aided Geometric Design
Year:
1985

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Abstract

An analytical method to determine the visible parts of parametrically defined tensor-product surfaces in described. All visibility calculations are strictly oriented on the (u, v)-parameter plane. This leads to substantial advantages over visibility algorithms based on the approximation of curved surfaces by sets of planar polygons. The new algorithm allows the calculation and the display of boundaries and contour curves with high precision in a minimal way. All critical points of a surface (contours, overlapping contours and penetrations) can be detected with machine precision. The results can be displayed both on vector and raster devices and are invariant under image transformations.