SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Interactive multiresolution mesh editing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Out-of-core simplification of large polygonal models
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the sixth ACM symposium on Solid modeling and applications
Sphere-tree construction using dynamic medial axis approximation
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation
Adaptive medial-axis approximation for sphere-tree construction
ACM Transactions on Graphics (TOG)
BD-tree: output-sensitive collision detection for reduced deformable models
ACM SIGGRAPH 2004 Papers
Variational shape approximation
ACM SIGGRAPH 2004 Papers
Shape Simplification Based on the Medial Axis Transform
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Graphical Models
Variational sphere set approximation for solid objects
The Visual Computer: International Journal of Computer Graphics
Automatic rigging and animation of 3D characters
ACM SIGGRAPH 2007 papers
ACM SIGGRAPH 2008 papers
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Quadric surface extraction by variational shape approximation
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Medial Spheres for Shape Approximation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Characterizing shape using conformal factors
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
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Shape approximation algorithms aim at computing simple geometric descriptions of dense surface meshes. Many such algorithms are based on mesh decimation techniques, generating coarse triangulations while optimizing for a particular metric which models the distance to the original shape. This approximation scheme is very efficient when enough polygons are allowed for the simplified model. However, as coarser approximations are reached, the intrinsic piecewise linear point interpolation which defines the decimated geometry fails at capturing even simple structures. We claim that when reaching such extreme simplification levels, highly instrumental in shape analysis, the approximating representation should explicitly and progressively model the volumetric extent of the original shape. In this paper, we propose Sphere-Meshes, a new shape representation designed for extreme approximations and substituting a sphere interpolation for the classic point interpolation of surface meshes. From a technical point-of-view, we propose a new shape approximation algorithm, generating a sphere-mesh at a prescribed level of detail from a classical polygon mesh. We also introduce a new metric to guide this approximation, the Spherical Quadric Error Metric in R4, whose minimizer finds the sphere that best approximates a set of tangent planes in the input and which is sensitive to surface orientation, thus distinguishing naturally between the inside and the outside of an object. We evaluate the performance of our algorithm on a collection of models covering a wide range of topological and geometric structures and compare it against alternate methods. Lastly, we propose an application to deformation control where a sphere-mesh hierarchy is used as a convenient rig for altering the input shape interactively.