Results 1  10
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21
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fai ..."
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Cited by 654 (15 self)
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In this paper we describe a new tool for interactive freeform fair surface design. By generalizing classical discrete Fourier analysis to twodimensional discrete surface signals  functions defined on polyhedral surfaces of arbitrary topology , we reduce the problem of surface smoothing, or fairing, to lowpass filtering. We describe a very simple surface signal lowpass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimizationbased fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique.
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.
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.
Geometric signal processing on polygonal meshes”. Eurographics State of the Art Report.
, 2000
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Visualizing Geometric Uncertainty of Surface Interpolants
 of Surface Interpolants,” Proc. Graphics Interface
, 1996
"... Evaluating and comparing the quality of surface interpolants is an important problem in computer graphics, computer aided geometric design and scientific visualization. We introduce geometric uncertainty as a measure of interpolation error, level of confidence or quality of an interpolant. Geometric ..."
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Cited by 19 (5 self)
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Evaluating and comparing the quality of surface interpolants is an important problem in computer graphics, computer aided geometric design and scientific visualization. We introduce geometric uncertainty as a measure of interpolation error, level of confidence or quality of an interpolant. Geometric uncertainty can be estimated as a scalar or a vectorvalued function that depends upon geometric characteristics of interpolants associated with the underlying data. These characteristics include position, normals, isophotes, principal curvatures and directions, mean and Gaussian curvatures. We present several new techniques for visualizing geometric uncertainty of surface interpolants, that combine the strengths of traditional techniques such as pseudocoloring, differencing, overlay, and transparency with new glyph and texturebased techniques. The viewer can control an interactive querydriven toolbox to create a wide variety of graphics that allow probing of geometric information in useful and convenient ways. We demonstrate the effectiveness of these techniques by visualizing geometric uncertainty of surfaces obtained by different interpolation techniques bilinear, C 0
Surface Approximation Using Geometric Hermite Patches
, 1992
"... A highorderofapproximation surface patch is used to construct continuous, approximating surfaces. This patch, together with a relaxation of tangent plane continuity, is used to approximate offset surfaces, algebraic surfaces, and Spatches. ..."
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Cited by 15 (6 self)
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A highorderofapproximation surface patch is used to construct continuous, approximating surfaces. This patch, together with a relaxation of tangent plane continuity, is used to approximate offset surfaces, algebraic surfaces, and Spatches.
Variational Modeling with Wavelets
, 1994
"... In many geometric modeling paradigms the user sculpts a curve or surface by dragging around some type of control points (eg. Bezier or Bspline). A more intuitive modeling interface allows the user to directly manipulate curves and surfaces. This manipulation defines some set of constraints that the ..."
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Cited by 14 (0 self)
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In many geometric modeling paradigms the user sculpts a curve or surface by dragging around some type of control points (eg. Bezier or Bspline). A more intuitive modeling interface allows the user to directly manipulate curves and surfaces. This manipulation defines some set of constraints that the curve or surface must satisfy (such as interpolation and tangent constraints). Direct manipulation, however, usually leads to an underconstrained problem since there are, in general, many possible surfaces meeting some set of constraints. Finding the "best" solution requires solving a variational problem. Unfortunately, this can be costly to compute. In particular, iterative descent methods converge slowly when a finite element basis such as Bsplines is used. This paper discusses how geometric variational modeling problems can be solved more efficiently by using a wavelet basis. Because the wavelet basis is hierarchical, the iterative methods converge rapidly. And because the wavelet coeff...
FeatureBased Reverse Engineering of Mechanical Parts
 IEEE Transactions on Robotics and Automation
, 1999
"... Reverse engineering of mechanical parts requires extraction of information about an instance of a particular part sufficient to replicate the part using appropriate manufacturing techniques. This is important in a wide variety of situations, since functional CAD models are often unavailable or unusa ..."
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Cited by 12 (0 self)
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Reverse engineering of mechanical parts requires extraction of information about an instance of a particular part sufficient to replicate the part using appropriate manufacturing techniques. This is important in a wide variety of situations, since functional CAD models are often unavailable or unusable for parts which must be duplicated or modified. Computer vision techniques applied to 3–D data acquired using noncontact, threedimensional position digitizers have the potential for significantly aiding the process. Serious challenges must be overcome, however, if sufficient accuracy is to be obtained and if models produced from sensed data are truly useful for manufacturing operations. This paper describes a prototype of a reverse engineering system which uses manufacturing features as geometric primitives. This approach has two advantages over current practice. The resulting models can be directly imported into featurebased CAD systems without loss of the semantics and topological information inherent in featurebased representations. In addition, the featurebased approach facilitates methods capable of producing highly accurate models, even when the original 3–D sensor data has substantial errors.
Curvature and Continuity Control in ParticleBased Surface Models
 In SPIE Geometric Methods in Computer Vision II
, 1993
"... This paper develops techniques to locally control curvature and continuity in particlebased surface models. Such models are a generalization of traditional spline surfaces built out of triangular patches. Traditional splines require the topology of the triangular mesh to be specified ahead of time. ..."
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Cited by 11 (4 self)
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This paper develops techniques to locally control curvature and continuity in particlebased surface models. Such models are a generalization of traditional spline surfaces built out of triangular patches. Traditional splines require the topology of the triangular mesh to be specified ahead of time. In contrast, particlebased surface models compute the topology dynamically as a function of the relative node positions, and can add or delete nodes as required. Such models are particularly important in computer vision and other inverse problems, where the topology of the surface being reconstructed is usually not known a priori. We develop techniques for both locally controlling the curvature of the surface (through additional state at each node), and for adapting the triangulation to surface curvature (by concentrating more particles in areas of high curvature). We show how the same ideas can also be applied to 3D curves, which results in a flexible version of traditional dynamic contours (snakes). 1.
Subdivision Surfaces  Can they be Useful for Geometric Modeling Applications?
, 2001
"... This report summarizes the findings and recommendations of the authors concerning the usefulness of subdivision surfaces for geometric modeling, and in particular for engineering applications. The work described is a result of a threemonth collaboration of the authors during the visit of the sec ..."
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Cited by 5 (0 self)
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This report summarizes the findings and recommendations of the authors concerning the usefulness of subdivision surfaces for geometric modeling, and in particular for engineering applications. The work described is a result of a threemonth collaboration of the authors during the visit of the second author to Boeing in the Summer of 2001.