Results 1  10
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129
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 523 (13 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. CR Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/image generation  display algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling  curve, surface, solid, and object representations;J.6[Com puter Applications]: ComputerAided Engineering  computeraided design General Terms: Algorithms, Graphics. 1
Multiresolution Signal Processing for Meshes
, 1999
"... We generalize basic signal processing tools such as downsampling, upsampling, and filters to irregular connectivity triangle meshes. This is accomplished through the design of a nonuniform relaxation procedure whose weights depend on the geometry and we show its superiority over existing schemes wh ..."
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Cited by 212 (12 self)
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We generalize basic signal processing tools such as downsampling, upsampling, and filters to irregular connectivity triangle meshes. This is accomplished through the design of a nonuniform relaxation procedure whose weights depend on the geometry and we show its superiority over existing schemes whose weights depend only on connectivity. This is combined with known mesh simplification methods to build subdivision and pyramid algorithms. We demonstrate the power of these algorithms through a number of application examples including smoothing, enhancement, editing, and texture mapping.
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 180 (7 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.
Automatic reconstruction of Bspline surfaces of arbitrary topological type
 SIGGRAPH'96
, 1996
"... Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners in ..."
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Cited by 135 (0 self)
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Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product Bspline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single Bspline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of Bspline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the Bspline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy userspecified error tolerances, and demonstrate our method on both synthetic and real data.
General Object Reconstruction based on Simplex Meshes
, 1999
"... In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconst ..."
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Cited by 100 (16 self)
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In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The di erent tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modi ed by creating holes or by increasing its genus. Finally, aniterativere nement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.
Discrete Fairing
 In Proceedings of the Seventh IMA Conference on the Mathematics of Surfaces
, 1997
"... We address the general problem of, given a triangular net of arbitrary topology in IR 3 , find a refined net which contains the original vertices and yields an improved approximation of a smooth and fair interpolating surface. The (topological) mesh refinement is performed by uniform subdivision o ..."
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Cited by 97 (16 self)
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We address the general problem of, given a triangular net of arbitrary topology in IR 3 , find a refined net which contains the original vertices and yields an improved approximation of a smooth and fair interpolating surface. The (topological) mesh refinement is performed by uniform subdivision of the original triangles while the (geometric) position of the newly inserted vertices is determined by variational methods, i.e., by the minimization of a functional measuring a discrete approximation of bending energy. The major problem in this approach is to find an appropriate parameterization for the refined net's vertices such that second divided differences (derivatives) tightly approximate intrinsic curvatures. We prove the existence of a unique optimal solution for the minimization of discrete functionals that involve squared second order derivatives. Finally, we address the efficient computation of fair nets. 1 Introduction One of the main problems in geometric modeling is the gen...
Dynamic NURBS with Geometric Constraints for Interactive Sculpting
, 1994
"... This article develops a dynamic generalization of the nonuniform rational Bspline (NURBS) model. NURBS have become a de facto standard in commercial modeling systems because of their power to represent freeform shapes as well as common analytic shapes. To date, however, they have been viewed as pu ..."
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Cited by 95 (27 self)
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This article develops a dynamic generalization of the nonuniform rational Bspline (NURBS) model. NURBS have become a de facto standard in commercial modeling systems because of their power to represent freeform shapes as well as common analytic shapes. To date, however, they have been viewed as purely geometric primitives that require the user to manually adjust multiple control points and associated weights in order to design shapes. Dynamic NURBS, or DNURBS, are physicsbased models that incorporate mass distributions, inertial deformation energies, and other physical quantities into the popular NURBS geometric substrate. Using DNURBS, a modeler can interactively sculpt curves and surfaces and design complex shapes to required specifications not only in the traditional indirect fashion, by adjusting control points and weights, but also through direct physical manipulation, by applying simulated forces and local and global shape constraints. DNURBS move and deform in a physically intuitive manner in response to the user's direct manipulations. Their dynamic behavior results from the numerical integration of a set of nonlinear differential equations that automatically evolve the control points and weights in response to the applied forces and constraints. To derive these equations, we employ Lagrangian mechanics and finiteelementlike discretization. Our approach supports the trimming of DNURBS surfaces using DNURBS curves. We demonstrate DNURBS models and constraints in applications including the rounding of solids, optimal surface fitting to unstructured data, surface design from crosssections, and freeform deformation. We also introduce a new technique for 2D shape metamorphosis using constrained DNURBS surfaces.
Geometric Surface Smoothing via Anisotropic Diffusion of Normals
, 2002
"... This paper introduces a method for smoothing complex, noisy surfaces, while preserving (and enhancing) sharp, geometric features. It has two main advantages over previous approaches to feature preserving surface smoothing. First is the use of level set surface models, which allows us to process very ..."
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Cited by 91 (13 self)
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This paper introduces a method for smoothing complex, noisy surfaces, while preserving (and enhancing) sharp, geometric features. It has two main advantages over previous approaches to feature preserving surface smoothing. First is the use of level set surface models, which allows us to process very complex shapes of arbitrary and changing topology. This generality makes it well suited for processing surfaces that are derived directly from measured data. The second advantage is that the proposed method derives from a wellfounded formulation, which is a natural generalization of anisotropic diffusion, as used in image processing. This formulation is based on the proposition that the generalization of image filtering entails filtering the normals of the surface, rather than processing the positions of points on a mesh.
An Intuitive Framework for RealTime Freeform Modeling
, 2004
"... We present a freeform modeling framework for unstructured triangle meshes which is based on constraint shape optimization. The goal is to simplify the user interaction even for quite complex freeform or multiresolution modifications. The user first sets various boundary constraints to define a custo ..."
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Cited by 89 (10 self)
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We present a freeform modeling framework for unstructured triangle meshes which is based on constraint shape optimization. The goal is to simplify the user interaction even for quite complex freeform or multiresolution modifications. The user first sets various boundary constraints to define a custom tailored (abstract) basis function which is adjusted to a given design task. The actual modification is then controlled by moving one single 9dof manipulator object. The technique can handle arbitrary support regions and piecewise boundary conditions with smoothness ranging continuously from C to C . To more naturally adapt the modification to the shape of the support region, the deformed surface can be tuned to bend with anisotropic stiffness. We are able to achieve realtime response in an interactive design session even for complex meshes by precomputing a set of scalarvalued basis functions that correspond to the degrees of freedom of the manipulator by which the user controls the modification.
Estimating Curvatures and Their Derivatives on Triangle Meshes
, 2004
"... The computation of curvature and other differential properties of surfaces is essential for many techniques in analysis and rendering. We present a finitedifferences approach for estimating curvatures on irregular triangle meshes that may be thought of as an extension of a common method for estimat ..."
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Cited by 84 (1 self)
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The computation of curvature and other differential properties of surfaces is essential for many techniques in analysis and rendering. We present a finitedifferences approach for estimating curvatures on irregular triangle meshes that may be thought of as an extension of a common method for estimating pervertex normals. The technique is efficient in space and time, and results in significantly fewer outlier estimates while more broadly offering accuracy comparable to existing methods. It generalizes naturally to computing derivatives of curvature and higherorder surface differentials.