样条曲线功能体素模型的构建

A. Tolok, N. Tolok, A. Sycheva
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引用次数: 2

摘要

解析模型是最精确的几何信息表示方法。参数化光滑曲线不能用于解析几何领域,这就解释了寻找这类曲线解析表示的必要性。本文讨论了以解析形式表示的光滑曲线的构造和求参数贝塞尔曲线解析模型的几种方法。А以功能区域的形式表示函数被选为分析模型的原型。选择的表示形式是在De Casteljau的贝塞尔曲线构造方法和集合论建模的基础上形成的。Rvachev函数(r -函数)被用作函数域上集合论运算的数学工具。函数体素法可以简化r -函数过程的计算。在此基础上,提出了一种构造贝塞尔曲线功能区的算法。所得结果表明该方法的充分性及其在构建更复杂结构方面的发展前景。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Construction of the Functional Voxel Model for a Spline Curve
Analytical models are the most accurate method of geometric information representation. Parameterized smooth curves cannot be used in the field of analytical geometry, which explains the necessity for finding of analytical representation of such curves. The article considered the construction of a smooth curve presented in an analytical form and some approaches to finding an analytical model for a parametric Bezier curve. А presentation of a function in the form of its functional areas was chosen as prototype of the analytical model. The selected representation formed on the basis of the De Casteljau's method of constructing the Bezier curve and set-theoretic modeling. The Rvachev functions (R-functions) are used as the mathematical apparatus of set-theoretic operations on function areas. The functional-voxel method makes it possible to simplify the computation of R-functional procedures. An algorithm for constructing the functional area of the Bezier curve is developed on the basis of the presented combined R-voxel approach. The obtained results allow for the conclusions about the adequacy of this approach and its development protentional to construct more complicated structures.
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