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37
Cone Spline Surfaces and Spatial Arc Splines
, 1998
"... The design of developable surfaces is of fundamental importance for many applications in Computer Aided Geometric Design. The aim of this thesis is to derive different algorithms to approximate developable surfaces by cone spline surfaces, which are G¹surfaces composed of segments of right circular ..."
Abstract

Cited by 7 (2 self)
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The design of developable surfaces is of fundamental importance for many applications in Computer Aided Geometric Design. The aim of this thesis is to derive different algorithms to approximate developable surfaces by cone spline surfaces, which are G¹surfaces composed of segments of right
Approximation of Developable Surfaces with Cone Spline Surfaces
 ComputerAided Design
, 1998
"... Developable surfaces are modelled with pieces of right circular cones. These cone spline surfaces are wellsuited for applications: They possess degree two parametric and implicit representations. Bending sequences and the development can be explicitly computed and the offsets are of the same typ ..."
Abstract

Cited by 26 (6 self)
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Developable surfaces are modelled with pieces of right circular cones. These cone spline surfaces are wellsuited for applications: They possess degree two parametric and implicit representations. Bending sequences and the development can be explicitly computed and the offsets are of the same
Cone spline approximation via fat conic spline fitting
, 2006
"... Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error b ..."
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Cited by 2 (0 self)
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Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error
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
Homogeneous Simplex Splines
 J. Comput. Appl. Math
"... . Homogeneous simplex splines, also known as cone splines or multivariate truncated power functions, are discussed from a perspective of homogeneous divided differences and polar forms. This makes it possible to derive the basic properties of these splines in a simple and economic way. In addition, ..."
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Cited by 9 (3 self)
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. Homogeneous simplex splines, also known as cone splines or multivariate truncated power functions, are discussed from a perspective of homogeneous divided differences and polar forms. This makes it possible to derive the basic properties of these splines in a simple and economic way. In addition
Distance extrema for spline models using tangent cones
 In Graphics Interface
, 2005
"... We present a robust search for distance extrema from a point to a curve or a surface. The robustness comes from using geometric operations rather than numerical methods to find all local extrema. Tangent cones are used to search for regions where distance extrema conditions are satisfied and patch r ..."
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Cited by 6 (0 self)
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refinement hierarchically improves the search. Instead of preprocessing and storing a large hierarchy, elements are computed as needed and retained only if useful. However, for spatially coherent queries, this provides a significant speedup. Key words: Tangent cones, minimum distance, spline models.
A spectral sequence for splines
 ADVANCES IN APPLIED MATHEMATICS
, 1997
"... We define a complex R=J of graded modules on a ddimensional simplicial complex #, so that the top homology module of this complex consists of piecewise polynomial functions (splines) of smoothness r on the cone of #. In a series of papers ([4], [5], [6]), Billera and Rose used a similar approach to ..."
Abstract

Cited by 8 (4 self)
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We define a complex R=J of graded modules on a ddimensional simplicial complex #, so that the top homology module of this complex consists of piecewise polynomial functions (splines) of smoothness r on the cone of #. In a series of papers ([4], [5], [6]), Billera and Rose used a similar approach
Isotonic, Convex and Related Splines l
"... In this paper, we consider the estimation of isotonic, convex or related functions by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, we give an existence and characterizat ..."
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In this paper, we consider the estimation of isotonic, convex or related functions by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, we give an existence
On normals and control nets
 IN THE MATHEMATICS OF SURFACES XI
, 2005
"... This paper characterizes when the normals of a spline curve or spline surface lie in the more easily computed cone of the normals of the segments of the spline control net. ..."
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Cited by 2 (1 self)
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This paper characterizes when the normals of a spline curve or spline surface lie in the more easily computed cone of the normals of the segments of the spline control net.
Results 1  10
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37