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30
Analytic Signal Processing for Computer Graphics using Multivariate Polyhedral Splines
, 1995
"... Multivariate polyhedral splines can be used to solve a common image synthesis problem: multivariate integrals defined over multiple geometrically defined domains. The theory is extended from applications in geometric design; this involves both the loosening of some overly restrictive assumptions as ..."
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Cited by 6 (2 self)
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Multivariate polyhedral splines can be used to solve a common image synthesis problem: multivariate integrals defined over multiple geometrically defined domains. The theory is extended from applications in geometric design; this involves both the loosening of some overly restrictive assumptions
On the evaluation of box splines
"... The first (and for some still the only) multivariate Bspline is what today one would call the simplex spline, since it is derived from a simplex, and in distinction to other polyhedral splines, such as the cone spline and the box spline. The simplex spline was first talked about in 1976. However, i ..."
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Cited by 201 (8 self)
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The first (and for some still the only) multivariate Bspline is what today one would call the simplex spline, since it is derived from a simplex, and in distinction to other polyhedral splines, such as the cone spline and the box spline. The simplex spline was first talked about in 1976. However
Analytic Antialiasing with Prism Splines
, 1995
"... The theory of the multivariate polyhedral splines is applied to analytic antialiasing: a triangular simplex spline is used to represent surface intensity, while a box spline is used as a filter. Their continuous convolution is a prism spline that can be evaluated exactly via recurrence. Evaluation p ..."
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Cited by 17 (1 self)
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The theory of the multivariate polyhedral splines is applied to analytic antialiasing: a triangular simplex spline is used to represent surface intensity, while a box spline is used as a filter. Their continuous convolution is a prism spline that can be evaluated exactly via recurrence. Evaluation
Abstract Computing Exact Shadow Irradiance Using Splines
"... We present a solution to the general problem of characterizing shadows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a spline function. Studying generalized prismlike constructions generated by the emitter and ..."
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as curved emitters, occluders, and receivers. Spline functions are constructed from these prismlike objects. We call them generalized polyhedral splines because they extend the classical polyhedral splines to include curved boundaries and a density function. The approach can be applied to more general
Piecewise polynomials on polyhedral complexes
 ADVANCES IN APPLIED MATHEMATICS
, 2009
"... For a ddimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d = 2 and P is simplicial, in [1] Alfeld and Schumaker give a formula fo ..."
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Cited by 7 (3 self)
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For a ddimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d = 2 and P is simplicial, in [1] Alfeld and Schumaker give a formula
Graphs, Syzygies and Multivariate Splines
, 2004
"... The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism cl ..."
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Cited by 2 (0 self)
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The module of splines on a polyhedral complex can be viewed as the syzygy module of its dual graph with edges weighted by powers of linear forms. When the assignment of linear forms to edges meets certain conditions, we can decompose the graph into disjoint cycles without changing the isomorphism
The Simplified Surface Spline
, 2003
"... ii This thesis studies the problem of using surface splines as an approximation basis. The simplified surface spline basis, a slight simplification of the C 1surface spline construction of Jörg Peters, is presented. The simplified surface does not guarantee a C 1 surface, but has explicit formulas, ..."
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ii This thesis studies the problem of using surface splines as an approximation basis. The simplified surface spline basis, a slight simplification of the C 1surface spline construction of Jörg Peters, is presented. The simplified surface does not guarantee a C 1 surface, but has explicit formulas
Gröbner Basis Methods for Multivariate Splines
, 2006
"... In this paper we will consider various properties of the space of Cr piecewise polynomial functions, defined on finite polyhedral subdivisions of regions in Rd. For a given subdivision ∆, we define the space of all Cr piecewise polynomial functions of maximum degree k defined over ∆ as C r k (∆). W ..."
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In this paper we will consider various properties of the space of Cr piecewise polynomial functions, defined on finite polyhedral subdivisions of regions in Rd. For a given subdivision ∆, we define the space of all Cr piecewise polynomial functions of maximum degree k defined over ∆ as C r k
Modeling Surfaces of Arbitrary Topology using Manifolds
, 1995
"... We describe an extension of Bsplines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of Bsplines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral con ..."
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Cited by 89 (7 self)
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We describe an extension of Bsplines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of Bsplines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral
Generalized bspline subdivisionsurface wavelets for geometry compression
 VISUALIZATION AND COMPUTER GRAPHICS, IEEE TRANSACTIONS ON
, 2004
"... We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary twomanifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, Bspline wavelets, and the lifting scheme for biorthogon ..."
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Cited by 16 (4 self)
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We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary twomanifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, Bspline wavelets, and the lifting scheme
Results 1  10
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30