Dynamic meshes for accurate polygonization of implicit surfaces with sharp features (original) (raw)
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JSME International Journal Series C, 2005
In this paper, we introduce a new approach to surface mesh improvement problem. In contrast to previous methods we do not tend to preserve new mesh vertices on the original discrete surface. Instead our technique keeps mesh nodes very close to a smooth or piecewisesmooth surface approximated by an initial mesh. As a result, the algorithm is able to improve mesh quality while preserving essential surface characteristics and features. Proposed approach can be applied iteratively not only to polygonal meshes but also to 2D and 3D curves that allows to treat sharp edges and surface boundaries. We demonstrate effectiveness of our method using various triangular and quadrilateral meshes. Also we compare our algorithm with some commonly used techniques and analyze their advantages and disadvantages.
Creating smooth implicit surfaces from polygonal meshes
1999
Implicit surfaces have long been used for a myriad of tasks in computer graphics, including modeling soft or organic objects, morphing, and constructive solid geometry. Although operating on implicit surfaces is usually straightforward , creating them is not-interactive techniques are impractical for complex models, and automatic techniques have been largely unexplored. We introduce a practical method for creating implicit surfaces from polygonal models that produces high-quality results for complex models. Whereas much previous work has been done with primitives such as "blobbies," we use surfaces based on a variational interpolation technique (the 3D generalization of thin-plate interpolation). Given a polygonal mesh, we convert the data to a volumetric representation and use this as a guide to create the implicit surface iteratively. Carefully chosen metrics evaluate each intermediate surface and control further refinement. We have applied this method successfully to a variety of polygonal meshes.
Polygonization of implicit surfaces with sharp features by edge-spinning
The Visual Computer, 2005
This paper presents an adaptive approach for polygonization of implicit surfaces. The algorithm generates a well-shaped triangular mesh with respect to a given approximation error. The error is proportional to a local surface curvature estimation. Polygonization of surfaces of high curvature, as well as surfaces with sharp features, is possible using a simple technique combined with a particle system approach. The algorithm is based on a surface tracking scheme, and it is compared with other algorithms based on a similar principle, such as the marching cube and the marching triangle algorithms.
Physically-Based Methods for Polygonization of Implicit Surfaces
1992
We present d i s c r e t e p h ysically-based methods for generating polygonal approximations of implicit surfaces. These methods not only generate a combinatorial manifold approximating the surface, but also produce a structure that is well suited to numerical simulations in physically-based modeling and animation systems.
Variational implicit surface meshing
Computers & Graphics, 2009
In this paper, we propose a new algorithm to mesh implicit surfaces which produces meshes both with a good triangle aspect ratio as well as a good approximation quality. The number of vertices of the output mesh is defined by the end-user. For this goal, we perform a two-stage processing : an initialization step followed by an iterative optimization step. The initialization step consists in capturing the surface topology and allocating the vertex budget. The optimization algorithm is based on a variational vertices relaxation and triangulation update. In addition a gradation parameter can be defined to adapt the mesh sampling to the curvature of the implicit surface. We demonstrate the efficiency of the approach on synthetic models as well as real-world acquired data, and provide comparisons with previous approaches.
Polygonization of Implicit Surfaces with Constructive Solid Geometry
International Journal of Shape Modeling, 1996
A polygonisation algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects. The result is a surface definition (to be called Boolean Compound Soft Object, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference operators. The geometric primitives that form the operands are soft objects bounded by the iso-surfaces resulting from suitable potential fields. These potential fields are parameterized by configurations of so called skeletal elements. The resulting system, unlike most CSG systems, combines blended and unblended primitives. The polygonisation algorithm produces a mesh of triangles to facilitate fast viewing and rendering.
Fast Polygonization of Implicit Surfaces
Wscg, 2001
Our work is centered on the use of implicit surfaces in interactive applications (at least 10 frames per sec) running on high-end consumer architecture (modeling, simulation, deformable body animation, games). We focus on the Marching Cubes algorithm that we tried to implement in an optimized way. We restrict our work to blended iso-surfaces generated by skeletons, since this kind of implicit surfaces is the most handy to use for animations. Our implementation optimizations deal with the following features: simplifying the field function, accelerating its evaluation for each point (voxel-based technique), generating automatically the triangles for any case of the Marching Cubes. Another point we have considered concerns tesselation ambiguities often resulting in holes appearing in the surface. We have coded a library which is very easy to use and can be downloaded freely. All these optimizations allow us to sample implicit surfaces composed of 200 points in 45 ms on a 450 MHz Pentium II Xeon.