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Scattered Data Interpolation with Multilevel Splines
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 1997
"... This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequen ..."
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Cited by 106 (9 self)
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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequence of bicubic Bspline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using Bspline refinement to reduce the sum of these functions into one equivalent Bspline function. Experimental results demonstrate that highfidelity reconstruction is possible from a selected set of sparse and irregular samples.
Matrixvalued subdivision schemes for generating surfaces with extraordinary vertices
 Comput. Aided Geom. Design
"... Subdivision templates of numerical values are replaced by templates of matrices in this paper to allow the introduction of shape control parameters for the feasibility of achieving desirable geometric shapes at those points on the subdivision surfaces that correspond to extraordinary control vertice ..."
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Cited by 9 (6 self)
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Subdivision templates of numerical values are replaced by templates of matrices in this paper to allow the introduction of shape control parameters for the feasibility of achieving desirable geometric shapes at those points on the subdivision surfaces that correspond to extraordinary control vertices. Formulation of the matrixvalued subdivision surface is derived. Based on refinable bivariate spline function vectors for matrixvalued subdivisions, the notion of characteristic map introduced by Reif is extended from (scalar) surface subdivisions to matrixvalued subdivisions. The C 1 and C kcontinuity of Reif and Prautzsch for matrixvalued subdivisions are discussed. To illustrate the general theory, the smoothness of matrixvalued triangular subdivision schemes for extraordinary vertices with valences 3 and 4 is analyzed. The issue of effective choices of the shape control parameters will also be discussed in this paper. Keywords: Matrixvalued surface subdivision, matrixvalued templates, surface shape control, extraordinary vertices, characteristic map, C kcontinuity 1
Constructing Curvaturecontinuous Surfaces by Blending
, 2006
"... In this paper we describe an approach to the construction of curvaturecontinuous surfaces with arbitrary control meshes using subdivision. Using a simple modification of the widely used Loop subdivision algorithm we obtain perturbed surfaces which retain the overall shape and appearance of Loop sub ..."
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Cited by 6 (2 self)
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In this paper we describe an approach to the construction of curvaturecontinuous surfaces with arbitrary control meshes using subdivision. Using a simple modification of the widely used Loop subdivision algorithm we obtain perturbed surfaces which retain the overall shape and appearance of Loop subdivision surfaces but no longer have flat spots or curvature singularities at extraordinary vertices. Our method is computationally efficient and can be easily added to any existing subdivision code.
xcmodel: an aCADemic system
, 2000
"... xcmodel is a CAD system realized and usable in an academic environment. It integrates four packages: a 2D and a 3D modeller, an object composer and a realistic scene renderer; these subsystems can be regarded as being in constant evolution i.e. a continuous work in progress. The system summarises ou ..."
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Cited by 1 (1 self)
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xcmodel is a CAD system realized and usable in an academic environment. It integrates four packages: a 2D and a 3D modeller, an object composer and a realistic scene renderer; these subsystems can be regarded as being in constant evolution i.e. a continuous work in progress. The system summarises our knowledge and experience in geometric modelling and NURBS curves and surfaces acquired over ten years of research. xcmodel and its subsystems were designed to represent a research and teaching laboratory to experiment and learn; it is an ideal environment to develop, perfect and compare methods and algorithms in geometric modelling and graphic visualization.
Multiple Knot BSpline Representation of Incompressible Flow
, 1996
"... this paper that we are given a set of normal fluid fluxes defined across the face centers of some tensor product cartesian mesh. Other velocity data may require preprocessing to obtain the desired format. x i\Gamma1 x i ..."
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Cited by 1 (1 self)
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this paper that we are given a set of normal fluid fluxes defined across the face centers of some tensor product cartesian mesh. Other velocity data may require preprocessing to obtain the desired format. x i\Gamma1 x i
ManifoldBased Surfaces with Boundaries
"... We present a manifoldbased surface construction extending the C ∞ construction of Ying and Zorin (2004a). Our surfaces allow for pircewisesmooth boundaries, have usercontrolled arbitrary degree of smoothness and improved derivative and visual behavior. 2flexibility of our surface construction is ..."
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We present a manifoldbased surface construction extending the C ∞ construction of Ying and Zorin (2004a). Our surfaces allow for pircewisesmooth boundaries, have usercontrolled arbitrary degree of smoothness and improved derivative and visual behavior. 2flexibility of our surface construction is confirmed numerically for a range of local mesh configurations. Key words: Geometric modeling, manifolds, highorder surfaces