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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