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//
// Filename : GeomUtils.h
// Author(s) : Stephane Grabli
// Purpose : Various tools for geometry
// Date of creation : 12/04/2002
//
///////////////////////////////////////////////////////////////////////////////
//
// Copyright (C) : Please refer to the COPYRIGHT file distributed
// with this source distribution.
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 2
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
//
///////////////////////////////////////////////////////////////////////////////
#ifndef GEOMUTILS_H
# define GEOMUTILS_H
# include <vector>
# include "../system/FreestyleConfig.h"
# include "Geom.h"
using namespace std;
using namespace Geometry;
namespace GeomUtils {
//
// Templated procedures
//
/////////////////////////////////////////////////////////////////////////////
/*! Computes the distance from a point P to a segment AB */
template<class T>
real distPointSegment( const T& P, const T& A , const T& B) {
T AB, AP, BP;
AB = B - A;
AP = P - A;
BP = P - B;
real c1(AB * AP);
if (c1 <= 0)
return AP.norm();
real c2(AB * AB);
if (c2 <= c1)
return BP.norm();
real b = c1 / c2;
T Pb, PPb;
Pb = A + b * AB;
PPb = P - Pb;
return PPb.norm();
}
//
// Non-templated procedures
//
/////////////////////////////////////////////////////////////////////////////
typedef enum {
DONT_INTERSECT,
DO_INTERSECT,
COLINEAR,
COINCIDENT
} intersection_test;
LIB_GEOMETRY_EXPORT
intersection_test intersect2dSeg2dSeg(const Vec2r& p1, const Vec2r& p2, // first segment
const Vec2r& p3, const Vec2r& p4, // second segment
Vec2r& res); // found intersection point
LIB_GEOMETRY_EXPORT
intersection_test intersect2dLine2dLine(const Vec2r& p1, const Vec2r& p2, // first segment
const Vec2r& p3, const Vec2r& p4, // second segment
Vec2r& res); // found intersection point
LIB_GEOMETRY_EXPORT
intersection_test intersect2dSeg2dSegParametric(const Vec2r& p1, const Vec2r& p2, // first segment
const Vec2r& p3, const Vec2r& p4, // second segment
real& t, // I = P1 + t * P1P2)
real& u, // I = P3 + u * P3P4
real epsilon = M_EPSILON);
/*! check whether a 2D segment intersect a 2D region or not */
LIB_GEOMETRY_EXPORT
bool intersect2dSeg2dArea(const Vec2r& min,
const Vec2r& max,
const Vec2r& A,
const Vec2r& B);
/*! check whether a 2D segment is included in a 2D region or not */
LIB_GEOMETRY_EXPORT
bool include2dSeg2dArea(const Vec2r& min,
const Vec2r& max,
const Vec2r& A,
const Vec2r& B);
/*! Box-triangle overlap test, adapted from Tomas Akenine-Möller code */
LIB_GEOMETRY_EXPORT
bool overlapTriangleBox(Vec3r& boxcenter,
Vec3r& boxhalfsize,
Vec3r triverts[3]);
/*! Fast, Minimum Storage Ray-Triangle Intersection,
* adapted from Tomas Möller and Ben Trumbore code.
*/
LIB_GEOMETRY_EXPORT
bool intersectRayTriangle(const Vec3r& orig, const Vec3r& dir,
const Vec3r& v0, const Vec3r& v1, const Vec3r& v2,
real& t, // I = orig + t * dir
real& u, real& v, // I = (1-u-v)*v0+u*v1+v*v2
const real epsilon = M_EPSILON); // the epsilon to use
/*! Intersection between plane and ray
* adapted from Graphics Gems, Didier Badouel
*/
LIB_GEOMETRY_EXPORT
intersection_test intersectRayPlane(const Vec3r& orig, const Vec3r& dir, // ray origin and direction
const Vec3r& norm, const real d, // plane's normal and offset (plane = { P / P.N + d = 0 })
real& t, // I = orig + t * dir
const real epsilon = M_EPSILON); // the epsilon to use
/*! Intersection Ray-Bounding box (axis aligned).
* Adapted from Williams et al, "An Efficient Robust Ray-Box Intersection Algorithm",
* JGT 10:1 (2005), pp. 49-54.
* Returns
*/
LIB_GEOMETRY_EXPORT
bool intersectRayBBox(const Vec3r& orig, const Vec3r& dir, // ray origin and direction
const Vec3r& boxMin, const Vec3r& boxMax, // the bbox
real t0, real t1, // the interval in which at least on of the intersections must happen
real& tmin, real& tmax, // Imin=orig+tmin*dir is the first intersection, Imax=orig+tmax*dir is the second intersection
real epsilon = M_EPSILON); // the epsilon to use
/*! Checks whether 3D point P lies inside or outside of the triangle ABC */
LIB_GEOMETRY_EXPORT
bool includePointTriangle(const Vec3r& P,
const Vec3r& A,
const Vec3r& B,
const Vec3r& C);
LIB_GEOMETRY_EXPORT
void transformVertex(const Vec3r& vert,
const Matrix44r& matrix,
Vec3r& res);
LIB_GEOMETRY_EXPORT
void transformVertices(const vector<Vec3r>& vertices,
const Matrix44r& trans,
vector<Vec3r>& res);
LIB_GEOMETRY_EXPORT
Vec3r rotateVector(const Matrix44r& mat, const Vec3r& v);
//
// Coordinates systems changing procedures
//
/////////////////////////////////////////////////////////////////////////////
/*! From world to image
* p
* point's coordinates expressed in world coordinates system
* q
* vector in which the result will be stored
* model_view_matrix
* The model view matrix expressed in line major order (OpenGL
* matrices are column major ordered)
* projection_matrix
* The projection matrix expressed in line major order (OpenGL
* matrices are column major ordered)
* viewport
* The viewport: x,y coordinates followed by width and height (OpenGL like viewport)
*/
LIB_GEOMETRY_EXPORT
void fromWorldToImage(const Vec3r& p,
Vec3r& q,
const real model_view_matrix[4][4],
const real projection_matrix[4][4],
const int viewport[4]);
/*! From world to image
* p
* point's coordinates expressed in world coordinates system
* q
* vector in which the result will be stored
* transform
* The transformation matrix (gathering model view and projection),
* expressed in line major order (OpenGL matrices are column major ordered)
* viewport
* The viewport: x,y coordinates followed by width and height (OpenGL like viewport)
*/
LIB_GEOMETRY_EXPORT
void fromWorldToImage(const Vec3r& p,
Vec3r& q,
const real transform[4][4],
const int viewport[4]);
/*! Projects from world coordinates to camera coordinates
* Returns the point's coordinates expressed in the camera's
* coordinates system.
* p
* point's coordinates expressed in world coordinates system
* q
* vector in which the result will be stored
* model_view_matrix
* The model view matrix expressed in line major order (OpenGL
* matrices are column major ordered)
*/
LIB_GEOMETRY_EXPORT
void fromWorldToCamera(const Vec3r& p,
Vec3r& q,
const real model_view_matrix[4][4]);
/*! Projects from World Coordinates to retina coordinates
* Returns the point's coordinates expressed in Retina system.
* p
* point's coordinates expressed in camera system
* q
* vector in which the result will be stored
* projection_matrix
* The projection matrix expressed in line major order (OpenGL
* matrices are column major ordered)
*/
LIB_GEOMETRY_EXPORT
void fromCameraToRetina(const Vec3r& p,
Vec3r& q,
const real projection_matrix[4][4]);
/*! From retina to image.
* Returns the coordinates expressed in Image coorinates system.
* p
* point's coordinates expressed in retina system
* q
* vector in which the result will be stored
* viewport
* The viewport: x,y coordinates followed by width and height (OpenGL like viewport).
*/
LIB_GEOMETRY_EXPORT
void fromRetinaToImage(const Vec3r& p,
Vec3r& q,
const int viewport[4]);
/*! From image to retina
* p
* point's coordinates expressed in image system
* q
* vector in which the result will be stored
* viewport
* The viewport: x,y coordinates followed by width and height (OpenGL like viewport).
*/
LIB_GEOMETRY_EXPORT
void fromImageToRetina(const Vec3r& p,
Vec3r& q,
const int viewport[4]);
/*! computes the coordinates of q in the camera coordinates system,
* using the known z coordinates of the 3D point.
* That means that this method does not inverse any matrices,
* it only computes X and Y from x,y and Z)
* p
* point's coordinates expressed in retina system
* q
* vector in which the result will be stored
* projection_matrix
* The projection matrix expressed in line major order (OpenGL
* matrices are column major ordered)
*/
LIB_GEOMETRY_EXPORT
void fromRetinaToCamera(const Vec3r& p,
Vec3r& q,
real z,
const real projection_matrix[4][4]);
/*! Projects from camera coordinates to world coordinates
* Returns the point's coordinates expressed in the world's
* coordinates system.
* p
* point's coordinates expressed in the camera coordinates system
* q
* vector in which the result will be stored
* model_view_matrix
* The model view matrix expressed in line major order (OpenGL
* matrices are column major ordered)
*/
LIB_GEOMETRY_EXPORT
void fromCameraToWorld(const Vec3r& p,
Vec3r& q,
const real model_view_matrix[4][4]);
} // end of namespace GeomUtils
#endif // GEOMUTILS_H
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