Multi-level partition of unity implicits
Multi-level partition of unity implicits
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DOI：
10.1145/1201775.882293
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发表时间：
2003-07
期刊：
影响因子：
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通讯作者：
Y. Ohtake;A. Belyaev;M. Alexa;Greg Turk;H. Seidel
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文献类型：
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作者：
Y. Ohtake;A. Belyaev;M. Alexa;Greg Turk;H. Seidel
我们提出了一种新的形状表示，多级分区的单位隐式曲面，使我们能够构建表面模型，从非常大的点集。我们的方法有三个关键要素：1）捕捉表面的局部形状的分段二次函数，2）加权函数（单位的分割），将这些局部形状函数混合在一起，和3）八叉树细分方法，适应局部形状的复杂性的变化。我们的方法在局部形状函数的选择上给了我们相当大的灵活性，并且特别地，我们可以通过选择适当的形状函数来精确地表示诸如边缘和拐角的尖锐特征。误差控制细分导致自适应近似，其时间和存储器消耗取决于所需的精度。由于局部近似和局部混合的分离，该表示不是全局的，并且可以快速创建和评估。由于我们的曲面是使用隐式函数描述的，因此形状混合、偏移、变形和CSG等操作都很容易执行。
We present a new shape representation, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points. There are three key ingredients to our approach: 1) piecewise quadratic functions that capture the local shape of the surface, 2) weighting functions (the partitions of unity) that blend together these local shape functions, and 3) an octree subdivision method that adapts to variations in the complexity of the local shape.Our approach gives us considerable flexibility in the choice of local shape functions, and in particular we can accurately represent sharp features such as edges and corners by selecting appropriate shape functions. An error-controlled subdivision leads to an adaptive approximation whose time and memory consumption depends on the required accuracy. Due to the separation of local approximation and local blending, the representation is not global and can be created and evaluated rapidly. Because our surfaces are described using implicit functions, operations such as shape blending, offsets, deformations and CSG are simple to perform.