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42
A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control
 ACM TRANSACTIONS ON GRAPHICS
, 1990
"... A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is C¹ for a specified range of the tension parameter, with a few ..."
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Cited by 393 (7 self)
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A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is C¹ for a specified range of the tension parameter, with a few exceptions. Application of the butterfly scheme and the role of the tension parameter are demonstrated by several examples.
Piecewise smooth surface reconstruction
, 1994
"... We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of t ..."
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Cited by 303 (13 self)
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We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering — the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.
Subdivision for Modeling and Animation
 SIGGRAPH ’99 Courses, no. 37. ACM SIGGRAPH
, 1999
"... ..."
Efficient, Fair Interpolation using CatmullClark Surfaces
, 1993
"... We describe an efficient method for constructing a smooth surface that interpolates the vertices of a mesh of arbitrary topological type. Normal vectors can also be interpolated at an arbitrary subset of the vertices. The method improves on existing interpolation techniques in that it is fast, robus ..."
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Cited by 205 (9 self)
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We describe an efficient method for constructing a smooth surface that interpolates the vertices of a mesh of arbitrary topological type. Normal vectors can also be interpolated at an arbitrary subset of the vertices. The method improves on existing interpolation techniques in that it is fast, robust and general. Our approach is to compute a control mesh whose CatmullClark subdivision surface interpolates the given data and minimizes a smoothness or "fairness" measure of the surface. Following Celniker and Gossard, the norm we use is based on a linear combination of thinplate and membrane energies. Even though CatmullClark surfaces do not possess closedform parametrizations, we show that the relevant properties of the surfaces can be computed efficiently and without approximation. In particular, we show that (1) simple, exact interpolation conditions can be derived, and (2) the fairness norm and its derivatives can be computed exactly, without resort to numerical integration.
Interactive Techniques for Implicit Modeling
, 1990
"... Recent research has demonstrated the usefulness of implicit surfaces for modeling geometric objects. The interactive design of such surfaces has not, however, received the same attention as has the design of parametric surfaces. Principally this is due to the difficulty of controlling the shape of i ..."
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Cited by 150 (13 self)
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Recent research has demonstrated the usefulness of implicit surfaces for modeling geometric objects. The interactive design of such surfaces has not, however, received the same attention as has the design of parametric surfaces. Principally this is due to the difficulty of controlling the shape of implicit surfaces while displaying the changes quickly enough for use within an interactive design environment. This paper describes progress towards interactive control of implicit surfaces and introduces new techniques useful to the designer.
Modeling the Mighty Maple
"... A method is presented for representing botanical trees, given threedimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A freeform surface connects branching limbs. "Blobby" techniques are used to model th ..."
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Cited by 114 (1 self)
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A method is presented for representing botanical trees, given threedimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A freeform surface connects branching limbs. "Blobby" techniques are used to model the tree trunk as a series of noncircular cross sections. Bark is simulated with a bump map digitized from real world bark; leaves are textures mapped onto simple surfaces.
Piecewise Smooth Subdivision Surfaces with Normal Control
"... In this paper we introduce improved rules for CatmullClark and Loop subdivision that overcome several problems with the original schemes, namely, lack of smoothness at extraordinary boundary vertices and folds near concave corners. In addition, our approach to rule modification allows the generatio ..."
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Cited by 109 (11 self)
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In this paper we introduce improved rules for CatmullClark and Loop subdivision that overcome several problems with the original schemes, namely, lack of smoothness at extraordinary boundary vertices and folds near concave corners. In addition, our approach to rule modification allows the generation of surfaces with prescribed normals, both on the boundary and in the interior, which considerably improves control of the shape of surfaces.
Analysis and Application of Subdivision Surfaces
, 1996
"... Subdivision surfaces are a convenient representation for modeling objects of arbitrary topological type. In this dissertation, we investigate the analysis of a piecewise smooth subdivision scheme, and we apply the scheme to reconstruct objects from nonuniformly sampled data points. Defined as the ..."
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Cited by 72 (0 self)
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Subdivision surfaces are a convenient representation for modeling objects of arbitrary topological type. In this dissertation, we investigate the analysis of a piecewise smooth subdivision scheme, and we apply the scheme to reconstruct objects from nonuniformly sampled data points. Defined as the limit of repeated refinement of a mesh of 3D control points, subdivision surfaces require analysis to establish convergence to a welldefined, tangent plane smooth G1 surface. Recent research has focused on analyzing smooth surface schemes in which the rules are symmetrical about each vertex and edge. However, a scheme for creating surfaces with sharp features has rules that do not exhibit this symmetry. In this dissertation, we extend the use of eigenanalysis and characteristic maps to analyze a piecewise smoot...
Nonuniform recursive subdivision surfaces
 Proceedings of SIGGRAPH
"... DooSabin and CatmullClark subdivision surfaces are based on the notion of repeated knot insertion of uniform tensor product Bspline surfaces. This paper develops rules for nonuniform DooSabin and CatmullClark surfaces that generalize nonuniform tensor product Bspline surfaces to arbitrary to ..."
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Cited by 63 (9 self)
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DooSabin and CatmullClark subdivision surfaces are based on the notion of repeated knot insertion of uniform tensor product Bspline surfaces. This paper develops rules for nonuniform DooSabin and CatmullClark surfaces that generalize nonuniform tensor product Bspline surfaces to arbitrary topologies. This added flexibility allows, among other things, the natural introduction of features such as cusps, creases, and darts, while elsewhere maintaining the same order of continuity as their uniform counterparts.
Approximating CatmullClark subdivision surfaces with bicubic patches
 ACM Transactions on Graphics
"... We present a simple and computationally efficient algorithm for approximating CatmullClark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the ..."
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Cited by 36 (8 self)
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We present a simple and computationally efficient algorithm for approximating CatmullClark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the shape and silhouette of the CatmullClark surface and are smooth everywhere except along patch edges containing an extraordinary vertex where the patches are C0.Tomake the patch surface appear smooth, we provide a pair of tangent patches that approximate the tangent fields of the CatmullClark surface. These tangent patches are used to construct a continuous normal field (through their crossproduct) for shading and displacement mapping. Using this bifurcated representation, we are able to define an accurate proxy for CatmullClark surfaces that is efficient to evaluate on nextgeneration GPU architectures that expose a programmable tessellation unit.