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119
Modeling with Cubic APatches
, 1995
"... We present a sufficient criterion for the Bernstein Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smoothand singlesheeted algebraic surface patch, We call this an Apatch. We present algorithms to build a mesh of cubic ..."
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Cited by 68 (37 self)
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We present a sufficient criterion for the Bernstein Bezier (BB) form of a trivariate polynomial within a tetrahedron, such that the real zero contour of the polynomial defines a smoothand singlesheeted algebraic surface patch, We call this an Apatch. We present algorithms to build a mesh of cubic
Free Form Surface Design with APatches
 In Proceedings of Graphics Interface '94
, 1994
"... We present a sufficient criterion for the BernsteinBezier (BB)form of a trivariate polynomialwithina tetrahedron, such that the real zero contour of the polynomial defines a smooth and single sheeted algebraic surface patch. We call this an Apatch. We present algorithms to build a mesh of cubic A ..."
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Cited by 14 (5 self)
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We present a sufficient criterion for the BernsteinBezier (BB)form of a trivariate polynomialwithina tetrahedron, such that the real zero contour of the polynomial defines a smooth and single sheeted algebraic surface patch. We call this an Apatch. We present algorithms to build a mesh of cubic Apatches
Interactive Shape Control and Rapid Display of Apatches
 In Implicit Surfaces'95
, 1995
"... Apatches are implicit surfaces in BernsteinB'ezier(BB) form that are smooth and singlesheeted. In this paper, we present algorithms to utilize the extra degrees of freedom of each Apatch for local shape control. A ray shooting scheme is also given to rapidly generate polygonal approximations ..."
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Cited by 1 (1 self)
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surface, rendering, polygonization, computeraided geometric design, solid modeling. 1 Introduction The Apatch is a smooth and singlesheeted zerocontour patch of a trivariate polynomial in BernsteinB'ezier(BB) form defined within a tetrahedron[BCX94a], where the "A" stands
Implicit Surface Patches
, 1997
"... Contents 1 Introduction 2 2 Mathematical Preliminaries 2 3 Curvlinear Mesh Scheme 5 4 Simplex and Box Based Schemes 7 4.1 Smooth Interpolation of a Polyhedron with C 1 Apatches : : : : : : : : : : : : : : : : : 7 4.2 Smooth Interpolation with C 2 Apatches : : : : : : : : : : : : : : : : : : ..."
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Cited by 8 (5 self)
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: : : : : : : : : : : : : : : : : : : : : : : : : : : 12 4.3 Smooth Reconstruction of Surfaces and FunctionsonSurfaces from Scattered Data : : : 12 5 Subdivision Based Schemes 15 6 Conclusion 20 B1: APatches 2 1 Introduction While it is possible to model a general closed surface of arbitrary genus as a single implicit surface patch, the geometry
TESSELLATING ALGEBRAIC CURVES AND SURFACES USING APATCHES
"... This work approaches the problem of triangulating algebraic curves and surfaces with a subdivisionstyle algorithm using Apatches. An algebraic curve or surface is converted from the monomial basis to the BernsteinBezier basis over a simplex. If the coefficients are all positive or all negative, t ..."
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Cited by 2 (0 self)
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This work approaches the problem of triangulating algebraic curves and surfaces with a subdivisionstyle algorithm using Apatches. An algebraic curve or surface is converted from the monomial basis to the BernsteinBezier basis over a simplex. If the coefficients are all positive or all negative
C¹ Modeling with APatches from Rational Trivariate Functions
, 2001
"... We approximate a manifold triangulation in R³ using smooth implicit algebraic surface patches, which we call Apatches. Here each Apatch is a real isocontour of a trivariate rational function defined within a tetrahedron. The rational trivariate function provides increased degrees of freedom so t ..."
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Cited by 9 (4 self)
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that the number of surface patches needed for freeform shape modeling is significantly reduced compared to earlier similar approaches. Furthermore, the surface patches have quadratic precision, that is they exactly recover quadratic surfaces. We give conditions under which a C¹ smooth and single sheeted surface
Polyhedral Subdivision for FreeForm Algebraic Surfaces
"... We present a robust algorithm to construct an "inner" simplicial hull S as a single step of subdivision of an input polyhedron P in three dimensional space. Similar to traditional subdivision schemes P becomes the `control net' for freeform modeling while an inner surface triangulati ..."
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triangulation T of S is a second level mesh. FreeForm C 1 cubic Apatches and C 2 quintic Apatches can then be constructed within S to approximate P. An Apatch is a smooth and functional algebraic surface (zerocontour of a trivariate polynomial) in BernsteinB ezier (BB) form defined within each
Polyhedral Subdivision for FreeForm Algebraic Surfaces
"... We present a robust algorithm to construct an "inner" simplicial hull S as a single step of subdivision of an input polyhedron P in three dimensional space. Similar to traditional subdivision schemes P becomes the `control net' for freeform modeling while an inner surface triangulati ..."
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triangulation T of S is a second level mesh. FreeForm C 1 cubic Apatches and C 2 quintic Apatches can then be constructed within S to approximate P. An Apatch is a smooth and functional algebraic surface (zerocontour of a trivariate polynomial) in BernsteinB ezier (BB) form defined within each
Surface Approximation Using Geometric Hermite Patches
, 1992
"... A highorderofapproximation surface patch is used to construct continuous, approximating surfaces. This patch, together with a relaxation of tangent plane continuity, is used to approximate offset surfaces, algebraic surfaces, and Spatches. ..."
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Cited by 15 (6 self)
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A highorderofapproximation surface patch is used to construct continuous, approximating surfaces. This patch, together with a relaxation of tangent plane continuity, is used to approximate offset surfaces, algebraic surfaces, and Spatches.
Results 1  10
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119