affine_rotation.h

// Description: Rotating affine transformation
// Documentation: affine_algorithms.txt

#ifndef PASTELMATH_AFFINE_ROTATION_H
#define PASTELMATH_AFFINE_ROTATION_H

#include "pastel/math/affine/affine_transformation.h"

namespace Pastel
{

    //! Returns a rotating affine transformation.
    /*!
   The rotation is from the standard basis axis 
   e_i towards axis e_j.

   n:
   The dimension of the rotation.

   i, j:
   The standard basis axes e_i and e_j to use as 
   the rotation plane.

   angle:
   The rotation angle.

   Preconditions:
   n >= 0
   0 <= i < n
   0 <= j < n
   */
    template <typename Real, int N>
    AffineTransformation<Real, N, N> affineRotation(
        integer n,
        integer i, integer j,
        const NoDeduction<Real>& angle)
    {
        PENSURE_OP(n, >=, 2);
        PENSURE_OP(i, >=, 0);
        PENSURE_OP(i, <, n);
        PENSURE_OP(j, >=, 0);
        PENSURE_OP(j, <, n);

        Real c = std::cos(angle);
        Real s = std::sin(angle);

        // For example, when
        // n = 2, i = 0, j = 1:
        //
        // [c -s]
        // [s  c]
        //
        // which is the counter-clockwise rotation
        // rotation of X to Y.
        //
        // If instead i = 1, and j = 0, then it is
        // the clockwise-rotation of Y to X.

        AffineTransformation<Real, N, N> result(n);

        result.matrix()(i, i) = c;
        result.matrix()(i, j) = -s;
        result.matrix()(j, i) = s;
        result.matrix()(j, j) = c;

        return result;
    }

}

#endif