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Spline Overlay Surfaces
 University of Waterloo
, 1991
"... We consider the construction of spline features on spline surfaces. 1 The approach taken is a generalization of the hierarchical surface introduced in [Forsey88]. Features are regarded as splinedefined vector displacement fields that are overlain on existing surfaces. No assumption is made that t ..."
Abstract

Cited by 8 (1 self)
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We consider the construction of spline features on spline surfaces. 1 The approach taken is a generalization of the hierarchical surface introduced in [Forsey88]. Features are regarded as splinedefined vector displacement fields that are overlain on existing surfaces. No assumption is made that the overlays are derived from the base surface. They may be applied with any orientation in a nonhierarchical fashion. In particular, we present a "cheap" version of the concept in which the displacement field is mapped to the base surface approximately, through the mapping of its control vectors alone. The result is a feature that occupies the appropriate position in space with respect to the base surface. It may be manipulated and rendered as an independent spline, thus avoiding the costs of a true displacement mapping. This approach is useful for prototyping and previewing during design. When a finished product is desired, of course, true displacement mapping is employed. 1 Introduction ...
From Degenerate Patches to Triangular and Trimmed Patches
 CURVES AND SURFACES
, 1997
"... CAD systems are usually based on a tensor product representation of free form surfaces. In this case, trimmed patches are used for modeling non rectangular zones. Trimmed patches provide a reasonable solution for the representation of general topologies, provided that the gap between equivalent trim ..."
Abstract

Cited by 1 (1 self)
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CAD systems are usually based on a tensor product representation of free form surfaces. In this case, trimmed patches are used for modeling non rectangular zones. Trimmed patches provide a reasonable solution for the representation of general topologies, provided that the gap between equivalent trimming curves in the euclidean space is small enough. Several commercial CAD systems, however, represent certain non rectangular surface regions through degenerate rectangular patches. Degenerate patches produce rendering artifacts and can lead to malfunctions in the subsequent geometric operations. In the present paper, two algorithms for converting degenerate tensorproduct patches into triangular and trimmed rectangular patches are presented. The algorithms are based on specific degree reduction algorithms for B'ezier curves. In both algorithms, the final surface approximates the initial one in a quadratic sense while inheriting its boundary curves. In the second one, " \Gamma G 1 cont...