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首页> 外文期刊>IEEE transactions on visualization and computer graphics >Approximating digital 3D shapes by rational Gaussian surfaces
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Approximating digital 3D shapes by rational Gaussian surfaces

机译：通过有理高斯曲面逼近数字3D形状

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摘要

A method for approximating spherical topology digital shapes by rational Gaussian (RaG) surfaces is presented. Points in a shape are parametrized by approximating the shape with a triangular mesh, determining parameter coordinates at mesh vertices, and finding parameter coordinates at shape points from interpolation of parameter coordinates at mesh vertices. Knowing the locations and parameter coordinates of the shape points, the control points of a RaG surface are determined to approximate the shape with a required accuracy. The process starts from a small set of control points and gradually increases the control points until the error between the surface and the digital shape reduces to a required tolerance. Both triangulation and surface approximation proceed from coarse to fine. Therefore, the method is particularly suitable for multiresolution creation and transmission of digital shapes over the Internet. Application of the proposed method in editing of 3D shapes is demonstrated.
机译：提出了一种通过有理高斯（RaG）曲面逼近球形拓扑数字形状的方法。通过用三角形网格近似形状，确定网格顶点处的参数坐标并从网格顶点处的参数坐标内插中找到形状点处的参数坐标，可以对形状中的点进行参数化。在知道形状点的位置和参数坐标的情况下，确定RaG表面的控制点以所需的精度近似形状。该过程从一小组控制点开始，然后逐渐增加控制点，直到表面和数字形状之间的误差减小到所需的公差为止。三角剖分和表面近似都从粗略进行到精细。因此，该方法特别适合于多分辨率创建和通过互联网传输数字形状。演示了该方法在3D形状编辑中的应用。

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