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Curve Discretization

To estimate the number of segments to be used to discretize a curve a binary tree is built in the parametric space of that curve. This tree structure is used to evaluate the mass curve by integrating the required element density (Fig. 1). The number of segments can be expressed as

where is the element density along the curve, is the centerline parameterized by in range from to and brackets stand for integer part of the enclosed quantity. The actual discretization of the curve is then obtained by splitting the mass curve to pieces which are projected back to the model curve (Fig. 1). Since the octree is employed for the mesh size control a gradual and very smooth discretization is achieved which does not need further optimization.



Next: Surface Discretization Up: Mesh Generation Previous: Mesh Generation

Daniel Rypl
2005-12-03