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BSpline Surface Approximation to CrossSections Using Distance Maps
, 1999
"... this paper, we present a method of surface approximation to crosssections with multiple branching problems. In this method, we first decompose each multiple branching problem into a set of single branching problems by providing a set of intermediate contours using distance maps. For each single bra ..."
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this paper, we present a method of surface approximation to crosssections with multiple branching problems. In this method, we first decompose each multiple branching problem into a set of single branching problems by providing a set of intermediate contours using distance maps. For each single branching region, a procedure then performs the skinning of contour curves represented by cubic Bspline curves on a common knot vector, each of which is fitted to its contour points within a given accuracy. In order to acquire a more compact representation for the surface, the method includes an algorithm for reducing the number of knots in the common knot vector. The approximation surface to the crosssections is represented by a set of bicubic Bspline surfaces. This method provides a smooth surface model, yet realises efficient data reduction.
A New Modeling Method for Objects with Branching Problem Using Nonuniform BSpline *
"... Abstract. In many applications, objects are reconstructed from crosssections for visualization, finite element and dynamic analysis. Although crosssection of an object may contain multiple contours, a few papers have dealt with branching problem. Moreover ends of branches are described flatly. In ..."
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Abstract. In many applications, objects are reconstructed from crosssections for visualization, finite element and dynamic analysis. Although crosssection of an object may contain multiple contours, a few papers have dealt with branching problem. Moreover ends of branches are described flatly. In this paper, as a basic study for dynamic analysis of a human knee joint, we present a new modeling method which proposes a dataset for solving branching problem and handling convexendcondition of branches. We select an initial standard point from lowest slice and decide a nearest standard point of the next slice and the next, in turns. Based on standard points, we complete the dataset by applying contour alignment. For 3D reconstruction, the surface is approximated by bicubic nonuniform Bspline surface fitting. This method provides the smooth surface model with C 2 continuity and describes the convexity of ends of branches. 1
Computer Aided Geometric Design 23 (2006) 573–581 Class
, 2006
"... www.elsevier.com/locate/cagd We discuss 3D Bézier curves with monotone curvature and torsion, generalizing a 2D class of curves by Y. Mineur et al. © 2006 Elsevier B.V. All rights reserved. 1. ..."
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www.elsevier.com/locate/cagd We discuss 3D Bézier curves with monotone curvature and torsion, generalizing a 2D class of curves by Y. Mineur et al. © 2006 Elsevier B.V. All rights reserved. 1.
Abstract Joining Polyhedral Objects using Implicitly Defined Surfaces
"... Complex polyhedral objects are often constructed from simpler polyhedral objects using CSG, booleans and various blend operations that produce fillets and chamfers. Skinning and shrink wrapping techniques provide alternatives to generating a smooth composite object from individual object parts. This ..."
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Complex polyhedral objects are often constructed from simpler polyhedral objects using CSG, booleans and various blend operations that produce fillets and chamfers. Skinning and shrink wrapping techniques provide alternatives to generating a smooth composite object from individual object parts. This paper presents an effective and general technique for incrementally building complex polyhedral objects from simpler parts. We provide a procedural implicit function definition for a region of a polyhedral object that is starshaped with respect to a skeletal point, called a blend center. We extend this definition to provide a single implicit function definition for an arbitrary polyhedral object, where every region is starshaped with respect to a proximal blend center, chosen from an arbitrary set of blend centers. This allows the application of implicit function based modeling techniques in constructing transition surfaces between arbitrary polyhedral object parts. Generalizations of our approach allow the algebraic combination of arbitrarily shaped and positioned, disjoint object parts, and is thus a significant superset of CSG, booleans, and other blending techniques. At the same time original detail and character of object parts are preserved in regions where they are not involved in constructing transition surfaces or do not interact with other object parts. A complete implemetation of the presented concepts show polyhedral implicit primitives to be a general and efficient technique for building complex polyhedral objects from a modular set of polyhedral object parts. 1