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中文摘要：
为了通过并行化技术提高隐式曲面绘制和网格化的速度,提出一种基于GPU并行计算架构的区间分析方法来网格化和绘制隐式曲面.首先按照给定的绘制分辨率将绘制空间离散成体素表示,充分利用GPU的并行计算能力,采取区间分析方法并行计算隐函数在所有体素上的取值区间,从而确定出包含隐函数零等值面的特征体素;进一步,抽取特征体素的外表面对其进行拓扑校正,确保得到的网格是二维流形;然后使用Laplace操作对这个网格进行光滑处理,得到隐式曲面的网格表示.大量实验结果表明,隐式曲面的网格化和绘制时间一般小于0.1 s,达到了实时化的水平.
英文摘要：
Implicit surface has a simple expression,and meets the smoothness requirements naturally.However,rendering implicit surface is computationally complex and inefficient.More importantly,it is difficult to control and adjust the shape of the implicit surface.Therefore,the modeling technology of implicit surface is far from being practical.To overcome these deficiencies,this paper presents an interval analysis method for rendering and polygonizing implicit surfaces based on GPU parallel computing architecture,which greatly improves the computational efficiency and rendering speed.The method first divides the rendering-space into voxels with a given resolution.Then,taking full advantage of GPU＇s parallel computing ability,the algorithm uses an interval analysis method to compute the range of implicit function in every voxel in parallel to find the feature-voxels which contain the zero-isosurface of the implicit function.Next,we extract the outer surface of feature-voxels,and handle it with topology-correction operations to ensure that the mesh is two-dimensional manifold;at last,using Laplace operation to smooth the mesh,we get the mesh representation of the implicit surface.A large number of experiments have been done,and the results show that the time of the implicit surface rendering and mesh smoothing are usually in millisecond magnitude which achieves the real-time level.
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