477 lines
14 KiB
C++
477 lines
14 KiB
C++
/***************************************************************************
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* Copyright (c) 2005 Imetric 3D GmbH *
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* *
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* This file is part of the FreeCAD CAx development system. *
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* *
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* This library is free software; you can redistribute it and/or *
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* modify it under the terms of the GNU Library General Public *
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* License as published by the Free Software Foundation; either *
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* version 2 of the License, or (at your option) any later version. *
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* *
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* This library is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU Library General Public License for more details. *
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* *
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* You should have received a copy of the GNU Library General Public *
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* License along with this library; see the file COPYING.LIB. If not, *
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* write to the Free Software Foundation, Inc., 59 Temple Place, *
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* Suite 330, Boston, MA 02111-1307, USA *
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* *
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***************************************************************************/
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#include "PreCompiled.h"
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#ifndef _PreComp_
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# include <cstdlib>
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# include <set>
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#endif
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#include "Tools2D.h"
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#include "Vector3D.h"
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using namespace Base;
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double Vector2d::GetAngle (const Vector2d &rclVect) const
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{
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double fDivid, fNum;
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fDivid = Length() * rclVect.Length();
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if ((fDivid < -1e-10) || (fDivid > 1e-10))
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{
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fNum = (*this * rclVect) / fDivid;
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if (fNum < -1)
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return D_PI;
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else
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if (fNum > 1)
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return 0.0;
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else
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return acos(fNum);
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}
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else
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return -FLOAT_MAX; // division by zero
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}
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void Vector2d::ProjectToLine (const Vector2d &rclPt, const Vector2d &rclLine)
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{
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double l = rclLine.Length();
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double t1 = (rclPt * rclLine) / l;
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Vector2d clNormal = rclLine;
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clNormal.Normalize();
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clNormal.Scale(t1);
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*this = clNormal;
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}
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/********************************************************/
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/** BOUNDBOX2d ********************************************/
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bool BoundBox2d::Intersect(const Line2d &rclLine) const
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{
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Line2d clThisLine;
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Vector2d clVct;
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// first line
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clThisLine.clV1.x = MinX;
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clThisLine.clV1.y = MinY;
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clThisLine.clV2.x = MaxX;
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clThisLine.clV2.y = MinY;
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if (clThisLine.IntersectAndContain (rclLine, clVct))
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return true;
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// second line
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clThisLine.clV1 = clThisLine.clV2;
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clThisLine.clV2.x = MaxX;
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clThisLine.clV2.y = MaxY;
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if (clThisLine.IntersectAndContain (rclLine, clVct))
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return true;
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// third line
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clThisLine.clV1 = clThisLine.clV2;
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clThisLine.clV2.x = MinX;
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clThisLine.clV2.y = MaxY;
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if (clThisLine.IntersectAndContain (rclLine, clVct))
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return true;
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// fourth line
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clThisLine.clV1 = clThisLine.clV2;
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clThisLine.clV2.x = MinX;
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clThisLine.clV2.y = MinY;
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if (clThisLine.IntersectAndContain (rclLine, clVct))
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return true;
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return false;
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}
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bool BoundBox2d::Intersect(const BoundBox2d &rclBB) const
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{
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//// compare bb2-points to this
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//if (Contains (Vector2d (rclBB.fMinX, rclBB.fMinY))) return true;
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//if (Contains (Vector2d (rclBB.fMaxX, rclBB.fMinY))) return true;
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//if (Contains (Vector2d (rclBB.fMaxX, rclBB.fMaxY))) return true;
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//if (Contains (Vector2d (rclBB.fMinX, rclBB.fMaxY))) return true;
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//
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//// compare this-points to bb2
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//if (rclBB.Contains (Vector2d (fMinX, fMinY))) return true;
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//if (rclBB.Contains (Vector2d (fMaxX, fMinY))) return true;
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//if (rclBB.Contains (Vector2d (fMaxX, fMaxY))) return true;
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//if (rclBB.Contains (Vector2d (fMinX, fMaxY))) return true;
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if (MinX < rclBB.MaxX &&
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rclBB.MinX < MaxX &&
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MinY < rclBB.MaxY &&
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rclBB.MinY < MaxY )
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return true;
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else // no intersection
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return false;
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}
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bool BoundBox2d::Intersect(const Polygon2d &rclPoly) const
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{
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unsigned long i;
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Line2d clLine;
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// points contained in boundbox
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for (i = 0; i < rclPoly.GetCtVectors(); i++)
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if (Contains (rclPoly[i]))
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return true; /***** RETURN INTERSECTION *********/
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// points contained in polygon
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if (rclPoly.Contains (Vector2d (MinX, MinY)) ||
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rclPoly.Contains (Vector2d (MaxX, MinY)) ||
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rclPoly.Contains (Vector2d (MaxX, MaxY)) ||
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rclPoly.Contains (Vector2d (MinX, MaxY)))
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return true; /***** RETURN INTERSECTION *********/
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// test intersections of bound-lines
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if (rclPoly.GetCtVectors() < 3)
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return false;
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for (i = 0; i < rclPoly.GetCtVectors(); i++)
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{
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if (i == rclPoly.GetCtVectors() - 1)
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{
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clLine.clV1 = rclPoly[i];
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clLine.clV2 = rclPoly[0];
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}
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else
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{
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clLine.clV1 = rclPoly[i];
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clLine.clV2 = rclPoly[i + 1];
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}
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if (Intersect(clLine))
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return true; /***** RETURN INTERSECTION *********/
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}
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// no intersection
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return false;
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}
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/********************************************************/
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/** LINE2D **********************************************/
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BoundBox2d Line2d::CalcBoundBox () const
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{
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BoundBox2d clBB;
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clBB.MinX = std::min<double> (clV1.x, clV2.x);
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clBB.MinY = std::min<double> (clV1.y, clV2.y);
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clBB.MaxX = std::max<double> (clV1.x, clV2.x);
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clBB.MaxY = std::max<double> (clV1.y, clV2.y);
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return clBB;
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}
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bool Line2d::Intersect (const Line2d& rclLine, Vector2d &rclV) const
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{
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double m1, m2, b1, b2;
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// calc coefficients
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if (fabs (clV2.x - clV1.x) > 1e-10)
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m1 = (clV2.y - clV1.y) / (clV2.x - clV1.x);
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else
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m1 = DOUBLE_MAX;
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if (fabs (rclLine.clV2.x - rclLine.clV1.x) > 1e-10)
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m2 = (rclLine.clV2.y - rclLine.clV1.y) / (rclLine.clV2.x - rclLine.clV1.x);
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else
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m2 = DOUBLE_MAX;
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if (m1 == m2) /****** RETURN ERR (parallel lines) *************/
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return false;
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b1 = clV1.y - m1 * clV1.x;
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b2 = rclLine.clV1.y - m2 * rclLine.clV1.x;
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// calc intersection
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if (m1 == DOUBLE_MAX)
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{
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rclV.x = clV1.x;
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rclV.y = m2 * rclV.x + b2;
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}
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else
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if (m2 == DOUBLE_MAX)
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{
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rclV.x = rclLine.clV1.x;
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rclV.y = m1 * rclV.x + b1;
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}
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else
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{
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rclV.x = (b2 - b1) / (m1 - m2);
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rclV.y = m1 * rclV.x + b1;
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}
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return true; /*** RETURN true (intersection) **********/
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}
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bool Line2d::Intersect (const Vector2d &rclV, double eps) const
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{
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double dxc = rclV.x - clV1.x;
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double dyc = rclV.y - clV1.y;
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double dxl = clV2.x - clV1.x;
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double dyl = clV2.y - clV1.y;
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double cross = dxc * dyl - dyc * dxl;
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// is point on the infinite line?
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if (fabs(cross) > eps)
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return false;
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// point is on line but it is also between V1 and V2?
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double dot = dxc * dxl + dyc * dyl;
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double len = dxl * dxl + dyl * dyl;
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if (dot < -eps || dot > len + eps)
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return false;
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return true;
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}
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Vector2d Line2d::FromPos (double fDistance) const
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{
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Vector2d clDir(clV2 - clV1);
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clDir.Normalize();
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return Vector2d(clV1.x + (clDir.x * fDistance), clV1.y + (clDir.y * fDistance));
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}
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bool Line2d::IntersectAndContain (const Line2d& rclLine, Vector2d &rclV) const
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{
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bool rc = Intersect (rclLine, rclV);
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if (rc)
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rc = Contains (rclV) && rclLine.Contains (rclV);
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return rc;
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}
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/********************************************************/
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/** POLYGON2d ********************************************/
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BoundBox2d Polygon2d::CalcBoundBox () const
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{
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unsigned long i;
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BoundBox2d clBB;
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for (i = 0; i < _aclVct.size(); i++)
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{
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clBB.MinX = std::min<double> (clBB.MinX, _aclVct[i].x);
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clBB.MinY = std::min<double> (clBB.MinY, _aclVct[i].y);
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clBB.MaxX = std::max<double> (clBB.MaxX, _aclVct[i].x);
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clBB.MaxY = std::max<double> (clBB.MaxY, _aclVct[i].y);
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}
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return clBB;
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}
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static short _CalcTorsion (double *pfLine, double fX, double fY)
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{
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int sQuad[2], i; // Changing this from short to int allows the compiler to inline this function
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double fResX;
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// Classification of both polygon points into quadrants
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for (i = 0; i < 2; i++)
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{
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if (pfLine[i * 2] <= fX)
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sQuad[i] = (pfLine[i * 2 + 1] > fY) ? 0 : 3;
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else
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sQuad[i] = (pfLine[i * 2 + 1] > fY) ? 1 : 2;
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}
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// Abort at line points within a quadrant
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// Abort at non-intersecting line points
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if (abs (sQuad[0] - sQuad[1]) <= 1)
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return 0;
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// Both points to the left of ulX
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if (abs (sQuad[0] - sQuad[1]) == 3)
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return (sQuad[0] == 0) ? 1 : -1;
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// Remaining cases: Quadrant difference from 2
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// mathematical tests on intersection
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fResX = pfLine[0] + (fY - pfLine[1]) /
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((pfLine[3] - pfLine[1]) / (pfLine[2] - pfLine[0]));
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if (fResX < fX)
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// up/down or down/up
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return (sQuad[0] <= 1) ? 1 : -1;
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// Remaining cases?
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return 0;
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}
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bool Polygon2d::Contains (const Vector2d &rclV) const
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{
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// Using the number of turns method, determines
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// whether a point is contained within a polygon.
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// The sum of all turns indicates whether yes or no.
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double pfTmp[4];
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unsigned long i;
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short sTorsion = 0;
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// Error check
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if (GetCtVectors() < 3)
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return false;
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// for all polygon lines
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for (i = 0; i < GetCtVectors(); i++)
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{
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// Evidence of line structure
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if (i == GetCtVectors() - 1)
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{
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// Close polygon automatically
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pfTmp[0] = _aclVct[i].x;
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pfTmp[1] = _aclVct[i].y;
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pfTmp[2] = _aclVct[0].x;
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pfTmp[3] = _aclVct[0].y;
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}
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else
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{
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// accept point i and i+1
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pfTmp[0] = _aclVct[i].x;
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pfTmp[1] = _aclVct[i].y;
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pfTmp[2] = _aclVct[i + 1].x;
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pfTmp[3] = _aclVct[i + 1].y;
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}
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// Carry out a cut test and calculate the turn counter
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sTorsion += _CalcTorsion (pfTmp, rclV.x, rclV.y);
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}
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// Evaluate turn counter
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return sTorsion != 0;
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}
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void Polygon2d::Intersect (const Polygon2d &rclPolygon, std::list<Polygon2d> &rclResultPolygonList) const
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{
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// trim the passed polygon with the current one, the result is a list of polygons (subset of the passed polygon)
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// your own (trim) polygon is closed
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//
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if ((rclPolygon.GetCtVectors() < 2) || (GetCtVectors() < 2))
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return;
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// position of first points (in or out of polygon)
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bool bInner = Contains(rclPolygon[0]);
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Polygon2d clResultPolygon;
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if (bInner) // add first point if inner trim-polygon
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clResultPolygon.Add(rclPolygon[0]);
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// for each polygon segment
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size_t ulPolyCt = rclPolygon.GetCtVectors();
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size_t ulTrimCt = GetCtVectors();
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for (size_t ulVec = 0; ulVec < (ulPolyCt-1); ulVec++)
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{
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Vector2d clPt0 = rclPolygon[ulVec];
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Vector2d clPt1 = rclPolygon[ulVec+1];
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Line2d clLine(clPt0, clPt1);
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// try to intersect with each line of the trim-polygon
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std::set<double> afIntersections; // set of intersections (sorted by line parameter)
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Vector2d clTrimPt2; // second line point
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for (size_t i = 0; i < ulTrimCt; i++)
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{
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clTrimPt2 = At((i + 1) % ulTrimCt);
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Line2d clToTrimLine(At(i), clTrimPt2);
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Vector2d clV;
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if (clLine.IntersectAndContain(clToTrimLine, clV))
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{
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// save line parameter of intersection point
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double fDist = (clV - clPt0).Length();
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afIntersections.insert(fDist);
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}
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}
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if (afIntersections.size() > 0) // intersections founded
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{
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for (std::set<double>::iterator pF = afIntersections.begin(); pF != afIntersections.end(); ++pF)
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{
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// intersection point
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Vector2d clPtIS = clLine.FromPos(*pF);
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if (bInner)
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{
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clResultPolygon.Add(clPtIS);
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rclResultPolygonList.push_back(clResultPolygon);
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clResultPolygon.DeleteAll();
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bInner = false;
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}
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else
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{
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clResultPolygon.Add(clPtIS);
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bInner = true;
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}
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}
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if (bInner) // add line end point if inside
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clResultPolygon.Add(clPt1);
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}
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else
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{ // no intersections, add line (means second point of it) if inside trim-polygon
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if (bInner)
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clResultPolygon.Add(clPt1);
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}
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}
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// add last segment
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if (clResultPolygon.GetCtVectors() > 0)
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rclResultPolygonList.push_back(clResultPolygon);
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}
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bool Polygon2d::Intersect (const Polygon2d &other) const {
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if (other.GetCtVectors()<2 || GetCtVectors() < 2)
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return false;
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for (auto &v : _aclVct) {
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if (other.Contains(v))
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return true;
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}
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if (Contains(other[0]))
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return true;
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for (size_t j=1; j<other.GetCtVectors(); ++j) {
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auto &v0 = other[j-1];
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auto &v1 = other[j];
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if (Contains(v1))
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return true;
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Line2d line(v0, v1);
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for (size_t i=0; i<GetCtVectors(); ++i) {
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Line2d line2(At(i), At((i+1)%GetCtVectors()));
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Vector2d v;
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if (line.IntersectAndContain(line2, v))
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return true;
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}
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}
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return false;
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}
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bool Polygon2d::Intersect (const Vector2d &rclV, double eps) const
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{
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if (_aclVct.size() < 2)
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return false;
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size_t numPts = GetCtVectors();
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for (size_t i = 0; i < numPts; i++) {
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Vector2d clPt0 = (*this)[i];
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Vector2d clPt1 = (*this)[(i+1)%numPts];
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Line2d clLine(clPt0, clPt1);
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if (clLine.Intersect(rclV, eps))
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return true;
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}
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return false;
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}
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