Convexification of Unstructured Grids
نویسندگان
چکیده
Unstructured tetrahedral grids are a common data representation of three-dimensional scalar fields. For convex unstructured meshes efficient rendering methods are known. For concave or cyclic meshes, however, a significant overhead is required to sort the grid cells in back to front order. In this paper we apply methods known from computational geometry to transform concave into convex grids. While this issue has been studied in theory it has not yet been applied to the specific area of unstructured volume rendering. This is mainly due to the complexity of the required geometrical operations. We demonstrate that the convexification of concave grids can be achieved by a combination of simple operations on triangle meshes. For convexified meshes the experimental results show that the performance penalty is only about 70% in comparison to approximately 300% for the fastest known concave sorting algorithm. In order to achieve high-quality visualizations we also adapt the preintegrated lighting technique to cell projection.
منابع مشابه
On the Convexification of Unstructured Grids From A Scientific Visualization Perspective
Unstructured grids are extensively used in modern computational solvers and, thus, play an important role in scientific visualization. They come in many different types. One of the most general types are non-convex meshes, which may contain voids and cavities. The lack of convexity presents a problem for several algorithms, often causing performance issues. One way around the complexity of non-...
متن کاملAutomatic Convexification of Space using BSP-trees
Convex representations of shapes have several nice properties that can be exploited to generate efficient geometric algorithms. At the same time, extending algorithms from convex to non-convex shapes is non-trivial and often leads to more expensive solutions. An alternative and sometimes more efficient solution is to transform the non-convex problem into a collection of convex problems using a ...
متن کاملA New Implicit Dissipation Term for Solving 3D Euler Equations on Unstructured Grids by GMRES+LU-SGS Scheme
Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...
متن کاملA New Implicit Dissipation Term for Solving 3D Euler Equations on Unstructured Grids by GMRES+LU-SGS Scheme
Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...
متن کامل