Polygonization of implicit surfaces
Computer Aided Geometric Design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Physically-based methods for polygonization of implicit surfaces
Proceedings of the conference on Graphics interface '92
An implicit surface polygonizer
Graphics gems IV
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Simple and efficient polygonization of implicit surfaces
Journal of Graphics Tools
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This paper describes an adaptive and efficient algorithm for polygonization of implicit surfaces, which consists of two steps: initial polygonization and adaptive refinement. The algorithm first generates an initial coarse triangular mesh from implicit surface using a variation of the traditional Marching Cubes (MC) Algorithm. And then the triangles in the coarse mesh are iteratively subdivided by employing a sampling rate that varies spatially according to local complexity of the surface. The new created vertices in refined mesh are projected onto the implicit surface by gradient descent method. Consequently, the algorithm produces the minimum number of polygons required to approximate the surface with a desired precision and the final mesh is simplicial complex. Our algorithm can be used in the real-time environment of visualization of implicit surfaces.