An adaptive subdivision method for surface-fitting from sampled data
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Geometric and solid modeling: an introduction
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Shape transformation for polyhedral objects
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A data reduction scheme for triangulated surfaces
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Multiresolution analysis of arbitrary meshes
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Hierarchical geometric approximations
Hierarchical geometric approximations
Interactive multiresolution surface viewing
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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Real-time, continuous level of detail rendering of height fields
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
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Mesh reduction with error control
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Surface simplification using quadric error metrics
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Fast and memory efficient polygonal simplification
Proceedings of the conference on Visualization '98
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SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Hierarchical geometric models for visible surface algorithms
Communications of the ACM
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IEEE Transactions on Visualization and Computer Graphics
Controlled Topology Simplification
IEEE Transactions on Visualization and Computer Graphics
Topology Simplification for Polygonal Virtual Environments
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IEEE Transactions on Visualization and Computer Graphics
Superfaces: Polygonal Mesh Simplification with Bounded Error
IEEE Computer Graphics and Applications
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WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
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CVRMed '95 Proceedings of the First International Conference on Computer Vision, Virtual Reality and Robotics in Medicine
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SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
Automatic generation of triangular irregular networks using greedy cuts
VIS '95 Proceedings of the 6th conference on Visualization '95
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'Meshsweeper': Dynamic Point-to-Polygonal-Mesh Distance and Applications
IEEE Transactions on Visualization and Computer Graphics
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IEEE Transactions on Visualization and Computer Graphics
An optimal algorithm for the minimum edge cardinality cut surface problem
Proceedings of the nineteenth annual symposium on Computational geometry
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Mesh Simplification with Hierarchical Shape Analysis and Iterative Edge Contraction
IEEE Transactions on Visualization and Computer Graphics
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Proceedings of the 2005 ACM symposium on Solid and physical modeling
A composite approach to meshing scattered data
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EURASIP Journal on Applied Signal Processing
Construction of Simplified Boundary Surfaces from Serial-sectioned Metal Micrographs
IEEE Transactions on Visualization and Computer Graphics
ASM: An adaptive simplification method for 3D point-based models
Computer-Aided Design
Deforming surface simplification based on feature preservation
ICEC'07 Proceedings of the 6th international conference on Entertainment Computing
Imperceptible Simplification on Mobile Displays
International Journal of Handheld Computing Research
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We present a technique for simplifying a triangulated surface. Simplifying consists of approximating the surface with another surface of lower triangle count. Our algorithm can preserve the volume of a solid to within machine accuracy; it favors the creation of near-equilateral triangles. We develop novel methods for reporting and representing a bound to the approximation error between a simplified surface and the original, and respecting a variable tolerance across the surface. A different positive error value is reported at each vertex. By linearly blending the error values in between vertices, we define a volume of space, called the error volume, as the union of balls of linearly varying radii. The error volume is built dynamically as the simplification progresses, on top of preexisting error volumes that it contains. We also build a tolerance volume to forbid simplification errors exceeding a local tolerance. The information necessary to compute error values is local to the star of a vertex; accordingly, the complexity of the algorithm is either linear or in $O(n \log n)$ in the original number of surface edges, depending on the variant. We extend the mechanisms of error and tolerance volumes to preserve during simplification scalar and vector attributes associated with surface vertices. Assuming a linear variation across triangles, error and tolerance volumes are defined in the same fashion as for positional error. For normals, a corrective term is applied to the error measured at the vertices to compensate for nonlinearities.