Eurographics/ACM SIGGRAPH Symposium on Computer Animation(2006)Posters and Demos M.-P.Cani,J.O’Brien(Editors)
Robust Tetrahedral Meshing of Triangle Soups
J.Spillmann M.Wagner M.Teschner
羊肉火锅配料University of Freiburg,Germany
Abstract
We propo a novel approach to generate coar tetrahedral meshes which can be ud in interactive simulation
frameworks.The propod algorithm process unorientable and non-manifold triangle soups.
Since the volume bounded by an unconstrained surface is not defined,we tetrahedralize the pudo volume of the
surface,namely the space that is intuitively occupied by the surface.
Using our approach,we can generate coar tetrahedral meshes from damaged surfaces and even triangle soups
without any connectivity.Various examples underline the robustness of our approach.The usability of the resulting
meshes is illustrated in the context of interactive deformable modeling.
1.Introduction
Tetrahedral meshes are commonly ud to reprent the inte-rior of volumetric objects for physically-bad simulations, e.g.in order to reprent deformable objects.Generating a tetrahedral mesh from a boundary surface is a non-trivial task.Most mesh generators assume that the boundary sur-face is a clod[ACYD05]or oriented[SOS04]manifold. However,many surfaces do not obey the criteria and the enclod volume is not defisurfaces contain holes and cracks,are compod of interpenetrating subparts,or are modeled from unconnected triangles.While a human ob-rver can intuitively recognize the space occupied by this structure,a volumization approach fails to compute a plausi-ble volumetric reprentation which hinders the generation of a tetrahedral mesh.
We implemented a scheme for robust tetrahedral mesh generation from triangle soups.Fig.1illustrates the mesh generation pipeline.We do not impo any constraints on the object we can process unorientable and non-manifold surfaces.A signed distancefield is computed, where the voxels with negative sign conform to the space that is intuitively occupied by the input surface.Then this distancefield is tetrahedralized.The meshing process re-quires ur interaction and an intuitive way is provided to control the shape and size of the resulting mesh.Since a variety of arbitrarily triangulated object surface can be procesd,our approach is particularly interesting for game design.The resulting coar tetrahedral meshes can be ud in interactive simulations of rigid and deformable solids.2.Results
The torus surface shown in Fig.2is a clod manifold.Fig.2 illustrates that our approach can generate meshes at different resolutions.
The model illustrated in Fig.3consists of16K triangles and is compod of interpenetrating subparts.While a hu-man obrver can intuitively identify the volume,algorithms might have problems to consider the union of two interct-ing subparts as interior.However,our scheme produces plau-sible and well-shaped tetrahedral meshes for such object rep-rentations.
鸟语花香造句To illustrate that our approach can handle even badly dam-aged models,we have removed50%of the faces from a sur-face as shown in Fig.4.Note that the element size of the generated tetrahedral mesh do not significantly vary,which is an important criterion for efficient dynamic simulation of such meshes.
Since our approach can produce very coar and never-theless plausible tetrahedral meshes,they are are well-suited for interactive simulations and animations[THMG04].In Fig.5,we run an animation of four deformable robot mod-els falling onto a deformable tree model.The total num-ber of elements is3K.The simulation runs at about20 frames per cond including visualization and collision han-dling[ST05,HTK∗04].A massive scenario is depicted in the bottom row of Fig.5where125deformable robots at a total number of58K elements are falling onto a deformable tree model.
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拜年的图片Spillmann,Wagner,Teschner /Robust Tetrahedral Meshing of Triangle
Soups
老银匠银饰加盟
有声小说排行榜
(a)(b)(c)(d)
Figure 1:Generating a tetrahedral mesh from a triangle soup (a).First,a distance field is computed.A novel method generates the signs of the distance field values.Negative values reprent the space that is intuitively occupied by the he pudo volume (b).A tetrahedral lattice is laid onto the pudo volume (c)and a smoothing filter is applied to obtain a mesh (d)that is appropriate for interactive
simulations.
Figure 2:Torus.Our approach can generate tetrahedral meshes of varying resolutions.The left mesh consists of 139elements and the right mesh consists of 8K
elements.
Figure 3:The input model is compod of interpenetrating subparts.However,our approach still computes a plausible tetrahedral mesh for this object.The mesh consists of 2K
elements.
Figure 4:Our approach can be ud to build tetrahedral meshes from damaged surfaces.50%of the faces have been removed from the surface (left).However,a plausible tetra-hedral mesh can still be produced for this surface (right).The mesh consists of 1158
elements.
四个扎扎实实Figure 5:Simulation of deformable objects.The meshes have been generated using our approach.The scenario in the top row can be simulated at 20frames per cond us-ing [THMG04].A massive scenario,consisting of 125ob-jects and a total of 58K tetrahedra is shown in the bottom row.
References
[ACYD05]A LLIEZ P.,C OHEN -S TEINER D.,Y VINEC M.,D ES -BRUN M.:Variational tetrahedral meshing.ACM Transactions on Graphics (2005),617–625.[HTK ∗04]H EIDELBERGER B.,T ESCHNER M.,K EISER R.,M UELLER M.,G ROSS M.:Consistent penetration depth estima-tion for deformable collision respon.In Proc.Vision,Modeling,Visualization (2004),pp.339–346.
[SOS04]S HEN C.,O’B RIEN J.F.,S HEWCHUK J.R.:Interpo-lating and approximating implicit surfaces from polygon soup.In Proc.SIGGRAPH (2004),pp.896–904.[ST05]S PILLMANN J.,T ESCH
NER M.:Contact surface compu-tation for coarly sampled deformable objects.In Proc.Vision,Modeling,Visualization (2005),pp.289–296.[THMG04]T ESCHNER M.,H EIDELBERGER B.,M ÜLLER M.,G ROSS M.H.:A versatile and robust model for geometrically complex deformable solids.In Computer Graphics International (2004),pp.312–319.
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The Eurographics Association 2006.
