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geometryrotationcgal

CGAL: Transformation Matrix for Rotation given two lines/vectors/directions

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.

Solution

  • 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.