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Contour Interpolation and Smooth Surface Reconstruction Using Partial Differential Equations

机译:使用偏微分方程的轮廓插值和平滑曲面重构

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摘要

It is one of important issues to acquire the reasonable sub-contour lines from a contour terrain map in order to reconstruct a 3--D terrain model as smooth as possible. Although in the fields of computer graphics and geographic information CAD systems many approaches have been developed to solve this problem, it still remains open. TO acquire reasonably interpolated sub--contour lines and reconstruct the smooth surface throughout the whole region of contour lines, we propose the following method: (l) employing the gradient controlled partial differential equations (PDE) in which the local parameters in each region held by every neighboring contour lines are controllable; (2) applying the two step iterative convergence algorithm which satisfies both the given elevation and smoothness with C continuity on every contour line. Usefulness of the proposed method is testified by some examples, the smooth saddle shapes with plural branches in one region and the reasonable sub--contour lines of a terrain map.
机译:从等高线地形图获取合理的子轮廓线,以尽可能平滑地重建3-D地形模型是重要的问题之一。尽管在计算机图形和地理信息CAD系统领域中,已经开发出许多方法来解决此问题,但它仍然是开放的。为了获得合理插值的子轮廓线并在轮廓线的整个区域上重建平滑表面,我们提出以下方法:(l)使用梯度控制的偏微分方程(PDE),其中每个区域的局部参数均保持不变每个相邻的轮廓线都是可控的; (2)应用两步迭代收敛算法,该算法同时满足给定的高程和平滑度,并且每条轮廓线上都具有C连续性。通过一些实例证明了该方法的有效性,例如在一个区域中具有多个分支的平滑鞍形以及地形图的合理子轮廓线。

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