CGAL：给定两行/矢量/方向的旋转变换矩阵 [英] CGAL: Transformation Matrix for Rotation given two lines/vectors/directions

问题描述

如何通过CGAL中两条直线/矢量/方向之间的角度生成旋转点/其他点的变换矩阵？

2D是我需要的。 3D是我喜欢的。根据 Kernel_23_ref / Class_Aff_transformation_2.htmlrel =nofollow noreferrer>手册，您可以使用这些工具：

Aff_transformation_2<内核> t（const Rotation，Direction_2 d，Kernel :: RT num，Kernel :: RT den = RT（1））

近似于由方向d表示的角度上的旋转，使得由d给出的旋转的正弦和余弦与近似旋转之间的差值每个最大为num / den。
前提条件：num / den> 0且d！= 0。

Aff_transformation_2< Kernel> t.operator *（s）组成两个仿射变换。

Aff_transformation_2< Kernel> t.inverse（）给出了逆变换。

使用它们，您应该能够计算与两个方向相对应的矩阵，并使用以下几行的标识：

  Mat（d1-d2）=== Mat（d1）* Inv（Mat（d2））
  

可以得到您想要的。

How do I generate a transformation matrix for rotating points/others by the angle between two lines/vectors/directions in CGAL?

2D is what I need. 3D is what I love.

解决方案

According to the manual you have these tools to work with:

Aff_transformation_2<Kernel> t ( const Rotation, Direction_2<Kernel> d, Kernel::RT num, Kernel::RT den = RT(1))

approximates the rotation over the angle indicated by direction d, such that the differences between the sines and cosines of the rotation given by d and the approximating rotation are at most num/den each. Precondition: num/den>0 and d != 0.

Aff_transformation_2<Kernel> t.operator* ( s) composes two affine transformations.

Aff_transformation_2<Kernel> t.inverse () gives the inverse transformation.

With them you should be able to compute the matrices corresponding to the two directions and use an identity along the lines of:

Mat(d1-d2) === Mat(d1)*Inv(Mat(d2))

to get what you want.

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