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Simplification Envelopes
"... We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a user-specifiable distance # from the original model and that all points of the original m ..."
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Cited by 206 (17 self)
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We propose the idea of simplification envelopes for generating a hierarchy of level-of-detail approximations for a given polygonal model. Our approach guarantees that all points of an approximation are within a user-specifiable distance # from the original model and that all points of the original model are within a distance # from the approximation. Simplificationenvelopes provide a general framework within which a large collection of existing simplification algorithms can run. We demonstrate this technique in conjunction with two algorithms, one local, the other global. The local algorithm provides a fast method for generating approximations to large input meshes (at least hundreds of thousands of triangles). The global algorithm provides the opportunity to avoid local "minima" and possibly achieve better simplifications as a result. Each approximation attempts to minimize the total number of polygons required to satisfy the above # constraint. The key advantages of our approach are...
Dynamic View-Dependent Simplification for Polygonal Models
, 1996
"... We present an algorithm for performing view-dependent simplifications of a triangulated polygonal model in real-time. The simplifications are dependent on viewing direction, lighting, and visibility and are performed by taking advantage of image-space, objectspace, and frame-to-frame coherences. A c ..."
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Cited by 186 (1 self)
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We present an algorithm for performing view-dependent simplifications of a triangulated polygonal model in real-time. The simplifications are dependent on viewing direction, lighting, and visibility and are performed by taking advantage of image-space, objectspace, and frame-to-frame coherences. A continuous level-of-detail representation for an object is first constructed off-line. This representation is then used at run-time to guide the selection of appropriate triangles for display. The list of displayed triangles is updated incrementally from one frame to the next. Our approach is more effective than the current level-of-detail-based rendering approaches for most scientific visualization applications where there are a limited number of highly complex objects that stay relatively close to the viewer. 1 Introduction The scientific visualization and virtual reality communities have always faced the problem that their "desirable" visualization dataset sizes are one or more orders of...
Displaced subdivision surfaces
- Siggraph 2000, Computer Graphics Proceedings, Annual Conference Series, pages 85–94. ACM Press / ACM SIGGRAPH
, 2000
"... In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalar-valued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivisio ..."
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Cited by 158 (2 self)
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In this paper we introduce a new surface representation, the displaced subdivision surface. It represents a detailed surface model as a scalar-valued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact. Additional Keywords: geometry compression, multiresolution geometry, displacement maps, bump maps, multiresolution editing, animation.
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 148 (16 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.
CHARMS: A Simple Framework for Adaptive Simulation
- ACM Transactions on Graphics
, 2002
"... Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations. Although adaptive solvers can be of great value in reducing the often high computational cost of simulations they are not employed broadly. Indeed, bui ..."
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Cited by 146 (11 self)
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Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations. Although adaptive solvers can be of great value in reducing the often high computational cost of simulations they are not employed broadly. Indeed, building adaptive solvers can be a daunting task especially for 3D finite elements. In this paper we are introducing a new approach to produce conforming, hierarchical, adaptive refinement methods (CHARMS). The basic principle of our approach is to refine basis functions, not elements. This removes a number of implementation headaches associated with other approaches and is a general technique independent of domain dimension (here 2D and 3D), element type (e.g., triangle, quad, tetrahedron, hexahedron), and basis function order (piecewise linear, higher order B-splines, Loop subdivision, etc.). The (un-)refinement algorithms are simple and require little in terms of data structure support. We demonstrate the versatility of our new approach through 2D and 3D examples, including medical applications and thin-shell animations.
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 144 (8 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.
Adaptive Real-Time Level-of-detail-based Rendering for Polygonal Models
, 1997
"... We present an algorithm for performing adaptive real-time level-of-detail-based rendering for triangulated polygonal models. The simplifications are dependent on viewing direction, lighting, and visibility and are performed by taking advantage of image-space, object-space, and frame-to-frame coheren ..."
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Cited by 96 (11 self)
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We present an algorithm for performing adaptive real-time level-of-detail-based rendering for triangulated polygonal models. The simplifications are dependent on viewing direction, lighting, and visibility and are performed by taking advantage of image-space, object-space, and frame-to-frame coherences. In contrast to the traditional approaches of precomputing a fixed number of level-of-detail representations for a given object our approach involves statically generating a continuous level-ofdetail representation for the object. This representation is then used at run-time to guide the selection of appropriate triangles for display. The list of displayed triangles is updated incrementally from one frame to the next. Our approach is more effective than the current level-of-detail-based rendering approaches for most scientific visualization applications where there are a limited number of highly complex objects that stay relatively close to the viewer. Our approach is applicable for scalar (such as distance from the viewer) as well as vector (such as normal direction) attributes.
Interactive Multiresolution Surface Viewing
, 1996
"... Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and level-of-detail control of complex meshes in a unified and theoretically sound way. ..."
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Cited by 90 (5 self)
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Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and level-of-detail control of complex meshes in a unified and theoretically sound way.
