AffineTransformation3D—The 3D version of AffineTransformation2D is a 4x4 matrix and supports definition of general affine transformations from control points. It will not determine conformal affine transformations. Using an affine transformation The following code example uses an affine transformation to tr...
vertexCmp returns -1 if vertex i is to the right of vertex j with respect to the given direction. isExtreme just follows my definition, but in case when there are two extreme vertices on the same line, it returns true only for the first in counter-clockwise order (true for 1 and 5,...
Definition and Basic Properties(定义和基本属性)(155) 2. Computing the Voronoi Diagram(计算 Voronoi 图)(158) 3. Voronoi Diagrams of Line Segments(线段Voronoi图)(167) 4. Farthest-Point Voronoi Diagrams(最远点 Voronoi 图)(170) 5. Notes and Comments(注释和评论)(174) 8. Arrangements and ...
interest is the tropical geometric representation of the space of phylogenetic trees. In particular, there has very recently been active work in using tropical geometry as a data analytic tool for sets of phylogenetic trees [33,37,45,50]. In this paper, we study the tropical projective torus,...
子午线定义(Definition of a meridian.)。给定一个球体和它相应的柱面坐标系统,球的一个子午线是一个包含了所有相同 θ 的点的一个圆弧(极点是其端点)。一个包含两极的平面定义了两个子午线,分别在两个极点连线的两侧。 一个向量M,其方向与前面定义的直线方向不同,它定义了唯一的球体子午线。子午线所在平面由M的...
Up to closure, we may assume that this factor is a linear form, so there are \left( {\begin{array}{c}d\\ 2\end{array}}\right) -1+2 degrees of freedom. This shows that the family of nonreduced curves A has codimension 2d-1=\bigl (\left( {\begin{array}{c}d+2\\ 2\end{...
However, one cannot guarantee the existence of a subdivision where all simplices are unimodular when the dimension is greater than 2. This leads us to our next definition: Definition 2.4 Let P be a d-dimensional lattice polytope given by \(P = {{\,\mathrm{conv}\,}}(V)\) for some ...
Vectors in CGare defined as entities that convey direction within a three-dimensional space, represented by three numerical values. This definition narrows down from the broader mathematical perspective of vectors, which can exist in any dimension. ...
Definition of Affine Geometry by a Group of Transformations point of view, about an affine plane, in order to be able to describe its points by pairs of elements of a field, and its lines by linear ... J Lipman - 《Canadian Mathematical Bulletin》 被引量: 8发表: 1961年 ...
Chapter 1: Introduction to Discrete Differential Geometry: The Geometry of Plane Curves 。 A better approximation than the tangent is the circle of curvature. 。 If the curve is sufficiently smooth (“【curvature-continuous at P】”) then the circle thus approaches a definite position known as ...