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116
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
NURBS Approximation of ASplines and APatches
, 1991
"... Given Aspline curves and Apatch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for Aspline curves and a parametric tensorproduct NURBS form for Apatch surfaces. We concentrate on cubic Apatches, provid ..."
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Cited by 1 (0 self)
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Given Aspline curves and Apatch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for Aspline curves and a parametric tensorproduct NURBS form for Apatch surfaces. We concentrate on cubic Apatches
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
Smooth Low Degree Approximations of Polyhedra
, 1994
"... We present an efficient algorithm to construct an inner simplicial hull \Sigma based on a given polyhedron P in three dimensional space. Piecewise smooth C 1 and C 2 Apatches can then be constructed within \Sigma to approximate polyhedron P. An Apatch is a smooth and functional zerocontour pa ..."
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patches with restricted singularity to model C 0 features. 1 Introduction In this paper, we present an efficient algorithm to construct an inner simplicial hull based on cornercutting a given polyhedron P in three dimensions. Both a C 1 smooth mesh with cubic Apatches and a C 2 smooth mesh
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
A Vlasov solver based on local cubic spline interpolation on patches
 J. Comput. Phys
"... A method for computing the numerical solution of Vlasov type equations on massively parallel computers is presented. In contrast with Particle In Cell methods which are known to be noisy, the method is based on a semiLagrangian algorithm that approaches the Vlasov equation on a grid of phase space. ..."
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Cited by 8 (5 self)
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. As this kind of method requires a huge computational effort, the simulations are carried out on parallel machines. To that purpose, we present a local cubic splines interpolation method based on a decomposition domain, each subdomain being devoted to a processor. Hermite boundary conditions between the domains
Construction of Cubic Triangular Patches with � 1 Continuity around a Corner
"... This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with � 1 continuity around a common corner vertex. A � 1 continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing ..."
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This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with � 1 continuity around a common corner vertex. A � 1 continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing
lipidic cubic phases
, 2001
"... Abstract Crystals of transmembrane proteins may be grown from detergent solutions or in a matrix of membranous lipid bilayers existing in a liquid crystalline state and forming a cubic phase (in cubo). While crystallization in micellar solutions appears analogous to that for soluble proteins, crysta ..."
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Abstract Crystals of transmembrane proteins may be grown from detergent solutions or in a matrix of membranous lipid bilayers existing in a liquid crystalline state and forming a cubic phase (in cubo). While crystallization in micellar solutions appears analogous to that for soluble proteins
Shape Optimization of Piecewise Rational Cubics
, 1995
"... An interpolation scheme for planar curves is described, obtained by patching together parametric rational cubics approximating logarithmic spiral segments. The resulting spline curves are G 2 continuous, their curvature radius plot is close to piecewise linear. The presented method is globally con ..."
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An interpolation scheme for planar curves is described, obtained by patching together parametric rational cubics approximating logarithmic spiral segments. The resulting spline curves are G 2 continuous, their curvature radius plot is close to piecewise linear. The presented method is globally
Results 1  10
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116