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Mesh optimization
, 1993
"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
Abstract

Cited by 394 (8 self)
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).
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 ..."
Abstract

Cited by 295 (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.
Chapter 5
"... Introduction 97 The goal of this chapter is to develop techniques for constraining the volume bounded by a surface. We discuss the motivation for developing such a constraint, derive expressions for the constraint function, and describe techniques for generating fair, volume constrained surfaces. T ..."
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Introduction 97 The goal of this chapter is to develop techniques for constraining the volume bounded by a surface. We discuss the motivation for developing such a constraint, derive expressions for the constraint function, and describe techniques for generating fair, volume constrained surfaces. To measure fairness we use both the linearized thin plate and the exact thin plate formulations. We use Loop's Bezier patch scheme and the CatmullClark subdivision scheme as surface representations, and draw comparisons between the two. In Section 2.3 and the previous chapter, we surveyed techniques for designing surfaces using constrained optimization. The physical situation simulated by most of these techniques is a pliable surface being coerced into shape by userdefined constraints. In some applications, or in certain phases of design, a designer may prefer to construct an object from a lump of clay than from an elastic membrane. This suggests that we should extend existing surfa
Reconstructing Curved Surfaces From Specular Reflection Patterns Using Spline Surface Fitting of Normals ABSTRACT CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling; J.6 [ComputerAided
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"... We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy f ..."
Abstract
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We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh wH, produce a mesh w, of the same topological type as wH, that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles).