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546
A.: Interactive animation of structured deformable objects
- In Proc. of SIGGRAPH 99 (1999), ACM
"... In this paper, we propose a stable and efficient algorithm for animating mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a pr ..."
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Cited by 156 (5 self)
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In this paper, we propose a stable and efficient algorithm for animating mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a predictor-corrector approach: We first compute a rapid approximation of the implicit integration, then we correct this estimate in a post-step process to preserve momentum. Combined with an inverse kinematics process to implement collisions and other constraints, this method provides a simple, stable and tunable model for deformable objects suitable for virtual reality. An implementation in a VR environment demonstrates this approach. 1
Feature Sensitive Surface Extraction from Volume Data
"... The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) ..."
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Cited by 154 (11 self)
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The representation of geometric objects based on volumetric data structures has advantages in many geometry processing applications that require, e.g., fast surface interrogation or boolean operations such as intersection and union. However, surface based algorithms like shape optimization (fairing) or freeform modeling often need a topological manifold representation where neighborhood information within the surface is explicitly available. Consequently, it is necessary to find effective conversion algorithms to generate explicit surface descriptions for the geometry which is implicitly defined by a volumetric data set. Since volume data is usually sampled on a regular grid with a given step width, we often observe severe alias artifacts at sharp features on the extracted surfaces. In this paper we present a new technique for surface extraction that performs feature sensitive sampling and thus reduces these alias effects while keeping the simple algorithmic structure of the standard Marching Cubes algorithm. We demonstrate the effectiveness of the new technique with a number of application examples ranging from CSG modeling and simulation to surface reconstruction and remeshing of polygonal models. 1
Normal Meshes
, 2000
"... Normal meshes are new fundamental surface descriptions inspired by differential geometry. A normal mesh is a multiresolution mesh where each level can be written as a normal offset from a coarser version. Hence the mesh can be stored with a single float per vertex. We present an algorithm to approxi ..."
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Cited by 150 (9 self)
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Normal meshes are new fundamental surface descriptions inspired by differential geometry. A normal mesh is a multiresolution mesh where each level can be written as a normal offset from a coarser version. Hence the mesh can be stored with a single float per vertex. We present an algorithm to approximate any surface arbitrarily closely with a normal semi-regular mesh. Normal meshes can be useful in numerous applications such as compression, filtering, rendering, texturing, and modeling.
Diffusion Wavelets
, 2004
"... We present a multiresolution construction for efficiently computing, compressing and applying large powers of operators that have high powers with low numerical rank. This allows the fast computation of functions of the operator, notably the associated Green’s function, in compressed form, and their ..."
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Cited by 149 (18 self)
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We present a multiresolution construction for efficiently computing, compressing and applying large powers of operators that have high powers with low numerical rank. This allows the fast computation of functions of the operator, notably the associated Green’s function, in compressed form, and their fast application. Classes of operators satisfying these conditions include diffusion-like operators, in any dimension, on manifolds, graphs, and in non-homogeneous media. In this case our construction can be viewed as a far-reaching generalization of Fast Multipole Methods, achieved through a different point of view, and of the non-standard wavelet representation of Calderón-Zygmund and pseudodifferential operators, achieved through a different multiresolution analysis adapted to the operator. We show how the dyadic powers of an operator can be used to induce a multiresolution analysis, as in classical Littlewood-Paley and wavelet theory, and we show how to construct, with fast and stable algorithms, scaling function and wavelet bases associated to this multiresolution analysis, and the corresponding downsampling operators, and use them to compress the corresponding powers of the operator. This allows to extend multiscale signal processing to general spaces (such as manifolds and graphs) in a very natural way, with corresponding fast algorithms.
Bilateral Mesh Denoising
- ACM TRANSACTIONS ON GRAPHICS
, 2003
"... We present an anisotropic mesh denoising algorithm that is effective, simple and fast. This is accomplished by filtering vertices of the mesh in the normal direction using local neighborhoods. Motivated by the impressive results of bilateral filtering for image denoising, we adopt it to denoise 3D m ..."
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Cited by 143 (4 self)
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We present an anisotropic mesh denoising algorithm that is effective, simple and fast. This is accomplished by filtering vertices of the mesh in the normal direction using local neighborhoods. Motivated by the impressive results of bilateral filtering for image denoising, we adopt it to denoise 3D meshes; addressing the specific issues required in the transition from two-dimensions to manifolds in three dimensions. We show that the proposed method successfully removes noise from meshes while preserving features. Furthermore, the presented algorithm excels in its simplicity both in concept and implementation.
M.: Laplace-beltrami eigenfunctions for deformation invariant shape representation
- In SGP’07 (2007
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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 finite-differences 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 116 (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 finite-differences approach for estimating curvatures on irregular triangle meshes that may be thought of as an extension of a common method for estimating per-vertex 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 higher-order surface differentials.
Topological Noise Removal
"... Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial to ..."
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Cited by 113 (5 self)
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Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial topology from meshes. Using a local wave front traversal, we discover the local topologies of the mesh and identify features such as small tunnels. We then identify non-separating cuts along which we cut and seal the mesh, reducing the genus and thus the topological complexity of the mesh.
Anisotropic Geometric Diffusion in Surface Processing
, 2000
"... INTRODUCTION Geometric evolution problems for curves and surfaces and especially curvature flow problems are an exciting and already classical mathematical research field. They lead to interesting systems of nonlinear partial differential equations and allow the appropriate mathematical modelling o ..."
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Cited by 111 (0 self)
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INTRODUCTION Geometric evolution problems for curves and surfaces and especially curvature flow problems are an exciting and already classical mathematical research field. They lead to interesting systems of nonlinear partial differential equations and allow the appropriate mathematical modelling of physical processes such as material interface propagation, fluid free boundary motion, crystal growth. On the other hand, curves and surfaces are essential objects in computer aided geometric design and computer graphics. Here, issues are fairing, modelling, deformation, and motion. Recently, geometric evolution problems and variational approaches have entered this research field as well and have turned out to be powerful tools. The aim of our work in the field of surface fairing and surface modelling is to modify "classical" curvature motion in a suitable way and apply it in computer graphics. 2 A GENERAL SCHEME Consider an image I :# R. A well known approach to image processing c
An Intuitive Framework for Real-Time 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 109 (11 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 9-dof 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 real-time response in an interactive design session even for complex meshes by precomputing a set of scalar-valued basis functions that correspond to the degrees of freedom of the manipulator by which the user controls the modification.
