planar_projection.h

// Description: Projections onto a plane
// Documentation: projection.txt

#ifndef PASTELGEOMETRY_PLANAR_PROJECTION_H
#define PASTELGEOMETRY_PLANAR_PROJECTION_H

#include "pastel/sys/mytypes.h"

#include "pastel/geometry/shape/alignedbox.h"

#include "pastel/math/matrix/matrix.h"

namespace Pastel
{

    template <typename Real, integer N>
    Vector<Real, N> wDivide(const Vector<Real, N>& that);

    //! Returns a homogeneous 3D perspective projection matrix.
    /*!
   Preconditions:
   xMin != xMax
   yMin != yMax
   zMin >= 0
   zMax >= 0
   zMin < zMax

   Let the center of projection be at the origin.
   The geometry of the view volume is given by
   the intersection of six half-spaces. These
   are (boundaries in parentheses):

   z >= zMin (near plane)
   z <= zMax (far plane)
   x >= z (xMin / zMin) (left plane)
   x <= z (xMax / zMin) (right plane)
   y >= z (yMin / zMin) (bottom plane)
   y <= z (yMax / zMin) (top plane)

   The view volume will be mapped to the range [-1, 1]^3.
   */

    template <typename Real>
    Matrix<Real> perspectiveProjection(
        const AlignedBox<Real, 2>& window,
        const NoDeduction<Real>& zMin,
        const NoDeduction<Real>& zMax);

    //! Returns a homogeneous 3D orthogonal projection matrix.
    /*!
   Preconditions:
   zMin < zMax
   */
    template <typename Real>
    Matrix<Real> orthogonalProjection(
        const AlignedBox<Real, 2>& window,
        const NoDeduction<Real>& zMin,
        const NoDeduction<Real>& zMax);

    //! Returns a projective transformation relating the given quadrilaterals.
    /*!
   It is assumed that the points in the 'from' point set have
   homogeneous coordinate 1.
   */
    template <typename Real>
    Matrix<Real> projectiveTransformation(
        const Tuple<Vector<Real, 2>, 4>& from,
        const Tuple<Vector<Real, 2>, 4>& to);

}

#include "pastel/geometry/planar_projection.hpp"

#endif