688 lines
19 KiB
C++
688 lines
19 KiB
C++
/*
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----
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This file is part of SECONDO.
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Copyright (C) 2004, University in Hagen, Department of Computer Science,
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Database Systems for New Applications.
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SECONDO is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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SECONDO 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 General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with SECONDO; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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----
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01590 Fachpraktikum "Erweiterbare Datenbanksysteme"
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WS 2014 / 2015
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<our names here>
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//paragraph [1] Title: [{\Large \bf \begin{center}] [\end{center}}]
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//paragraph [10] Footnote: [{\footnote{] [}}]
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//[TOC] [\tableofcontents]
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[1] Implementation of a Spatial3D algebra
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[TOC]
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1 Includes and Defines
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*/
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#include "AuxiliaryTypes.h"
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#include "geometric_algorithm.h"
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#include<iostream>
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using namespace std;
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namespace spatial3d_geometric
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{
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/* TODO: Remove debugging helpers (Jens Breit) */
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void print(SimplePoint3d a)
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{
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std::cerr << "SimplePoint3d: (" << a.getX() << ","
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<< a.getY() << ","
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<< a.getZ() << ")";
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}
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void print(Vector3d a)
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{
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std::cerr << "Vector3d: (" << a.getX() << ","
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<< a.getY() << ","
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<< a.getZ() << ")";
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}
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void print(SimplePoint2d a, string name)
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{
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std::cerr << "Point2d \"" << name << "\": (" << a.getX() << ","
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<< a.getY() << ")" << endl;
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}
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void print(Triangle a)
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{
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std::cerr << "Triangle(";
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print(a.getA());
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print(a.getB());
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print(a.getC());
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std::cerr << ")" << endl;
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}
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void numeric_fail()
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{
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//assert(false);
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throw NumericFailure();
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}
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/* Helper functions */
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bool AlmostLte(double a, double b)
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{
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if (AlmostEqual(a, b))
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return true;
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return a < b;
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}
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/* Points */
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const SimplePoint3d origin(0,0,0);
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bool almostEqual(const SimplePoint3d& p1, const SimplePoint3d& p2)
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{
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return AlmostEqual(p1.getX(), p2.getX())
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&& AlmostEqual(p1.getY(), p2.getY())
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&& AlmostEqual(p1.getZ(), p2.getZ());
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}
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bool collinear(const SimplePoint3d& pA,
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const SimplePoint3d& pB,
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const SimplePoint3d& pC)
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{
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if (almostEqual(pB, pC))
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return true;
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// compute distance of pA to the line through pB und pC
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return AlmostEqual(0, distancePointToLine(pA, pB, pC));
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}
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double distance(const SimplePoint3d& p1, const SimplePoint3d& p2)
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{
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return length(Vector3d(p1, p2));
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}
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double distancePointToLine(const SimplePoint3d& distantPoint,
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const SimplePoint3d& linePoint1, const SimplePoint3d& linePoint2)
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{
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Vector3d v(origin, distantPoint);
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Vector3d v1(origin, linePoint1);
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Vector3d v2(origin, linePoint2);
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return length(crossProduct(v - v1, v - v2))
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/ length(v2 - v1);
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}
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/* Vectors */
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bool almostEqual(const Vector3d& p1, const Vector3d& p2)
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{
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return AlmostEqual(p1.getX(), p2.getX())
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&& AlmostEqual(p1.getY(), p2.getY())
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&& AlmostEqual(p1.getZ(), p2.getZ());
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}
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double length(const Vector3d& vector)
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{
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return sqrt(vector * vector);
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}
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bool collinear(const Vector3d& v1, const Vector3d& v2)
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{
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return collinear(origin, origin + v1, origin + v2);
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// TODO: Alternative: Kreuzprodukt = 0
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// oder inneres Produkt = Quadrat der Länge
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}
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bool orthogonal(const Vector3d& v1, const Vector3d& v2)
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{
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return AlmostEqual(v1 * v2, 0);
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}
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Vector3d operator+(const Vector3d& v1, const Vector3d& v2)
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{
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return Vector3d(v1.getX() + v2.getX(),
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v1.getY() + v2.getY(),
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v1.getZ() + v2.getZ());
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}
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Vector3d operator-(const Vector3d& v1, const Vector3d& v2)
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{
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return v1 + (-1 * v2);
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}
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Vector3d operator*(double scalar, const Vector3d& vector)
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{
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return Vector3d(scalar * vector.getX(),
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scalar * vector.getY(),
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scalar * vector.getZ());
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}
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double operator*(const Vector3d& v1, const Vector3d& v2)
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{
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return v1.getX() * v2.getX()
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+ v1.getY() * v2.getY()
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+ v1.getZ() * v2.getZ();
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}
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Vector3d crossProduct(const Vector3d& v1, const Vector3d& v2)
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{
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return Vector3d(v1.getY() * v2.getZ() - v1.getZ() * v2.getY(),
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v1.getZ() * v2.getX() - v1.getX() * v2.getZ(),
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v1.getX() * v2.getY() - v1.getY() * v2.getX());
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}
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SimplePoint3d operator+(const SimplePoint3d& p, const Vector3d& v)
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{
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return SimplePoint3d(p.getX() + v.getX(),
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p.getY() + v.getY(),
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p.getZ() + v.getZ());
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}
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/* Planes */
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bool almostEqual(const Plane3d& p1, const Plane3d& p2)
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{
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return AlmostEqual(p1.getDistanceToOrigin(), p2.getDistanceToOrigin())
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&& almostEqual(p1.getNormalVector(), p2.getNormalVector());
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}
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Vector3d normalVector(const SimplePoint3d& pA,
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const SimplePoint3d& pB,
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const SimplePoint3d& pC)
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{
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double ax = pA.getX(), ay = pA.getY(), az = pA.getZ();
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double bx = pB.getX(), by = pB.getY(), bz = pB.getZ();
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double cx = pC.getX(), cy = pC.getY(), cz = pC.getZ();
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double nx = (by-ay)*(cz-az)-(bz-az)*(cy-ay);
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double ny = (bz-az)*(cx-ax)-(bx-ax)*(cz-az);
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double nz = (bx-ax)*(cy-ay)-(by-ay)*(cx-ax);
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Vector3d direction = Vector3d(nx, ny, nz);
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return (1 / length(direction)) * direction;
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}
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double distance(const SimplePoint3d& point, const Plane3d& plane)
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{
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Vector3d pv = Vector3d(origin, point);
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Vector3d nv = plane.getNormalVector();
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double d = plane.getDistanceToOrigin();
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return pv * nv - d;
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}
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bool isPointInPlane(const SimplePoint3d& point, const Plane3d& plane)
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{
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return AlmostEqual(distance(point, plane), 0);
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}
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double planeDistanceToOrigin(const SimplePoint3d& pointInPlane,
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const Vector3d& normalVector)
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{
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return normalVector * Vector3d(origin, pointInPlane);
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}
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void planeHessianNormalForm(const SimplePoint3d& pA,
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const SimplePoint3d& pB,
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const SimplePoint3d& pC,
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double& out_distanceToOrigin,
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Vector3d& out_normalVector)
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{
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out_normalVector = normalVector(pA, pB, pC);
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out_distanceToOrigin = planeDistanceToOrigin(pA, out_normalVector);
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// Make sure the same plane always has the same representation.
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if (out_distanceToOrigin < 0)
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{
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out_distanceToOrigin *= -1;
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out_normalVector = -1.0 * out_normalVector;
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}
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else if (out_distanceToOrigin == 0)
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{
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if (out_normalVector.getX() != 0)
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{
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if (out_normalVector.getX() < 0)
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{
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out_normalVector = -1.0 * out_normalVector;
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}
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return;
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}
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if (out_normalVector.getY() != 0)
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{
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if (out_normalVector.getY() < 0)
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{
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out_normalVector = -1.0 * out_normalVector;
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}
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return;
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}
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if (out_normalVector.getZ() < 0)
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{
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out_normalVector = -1.0 * out_normalVector;
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}
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}
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}
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SimplePoint3d projectPointOntoPlane(const SimplePoint3d &point,
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const Plane3d& plane)
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{
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Vector3d v(plane.getPoint(), point);
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Vector3d n = plane.getNormalVector();
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return point + (-(n * v)) * n;
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}
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/* Triangles */
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// assumes directed triangles
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bool almostEqual(const Triangle& triangle1, const Triangle& triangle2)
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{
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SimplePoint3d points1[3] = { triangle1.getA(),
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triangle1.getB(),
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triangle1.getC() };
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SimplePoint3d points2[3] = { triangle2.getA(),
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triangle2.getB(),
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triangle2.getC() };
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for (int c = 0; c < 3; ++c)
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{
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bool differenceFound = false;
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for (int d = 0; d < 3; ++d)
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{
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if (!almostEqual(points1[d], points2[(d + c) % 3]))
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{
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differenceFound = true;
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break;
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}
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}
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if (!differenceFound)
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return true;
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}
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return false;
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}
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bool isValidTriangle(const SimplePoint3d& pA,
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const SimplePoint3d& pB,
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const SimplePoint3d& pC)
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{
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if (almostEqual(pA, pB) || almostEqual(pB, pC) || almostEqual(pC, pA))
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{
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return false;
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}
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if (collinear(pA, pB, pC))
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{
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return false;
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}
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return true;
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}
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bool isValidTriangle(const Triangle& triangle)
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{
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return isValidTriangle(triangle.getA(), triangle.getB(), triangle.getC());
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}
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// precondition: point is in the plane of the triangle.
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InsideResult pointInsideTriangle(const SimplePoint3d& pointToTest,
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const Triangle& triangle)
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{
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Vector3d w = Vector3d(triangle.getA(), pointToTest);
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Vector3d u = Vector3d(triangle.getA(), triangle.getB());
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Vector3d v = Vector3d(triangle.getA(), triangle.getC());
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double denominator = (u * v) * (u * v) - (u * u) * (v * v);
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double s = ((u * v) * (w * v) - (v * v) * (w * u)) / denominator;
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double t = ((u * v) * (w * u) - (u * u) * (w * v)) / denominator;
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if (AlmostEqual(s, 0) && AlmostEqual(t, 0))
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{
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return CORNER;
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}
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else if ((AlmostEqual(s, 0) || AlmostEqual(t, 0)) && AlmostEqual(s + t, 1))
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{
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return CORNER;
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}
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else if (AlmostEqual(s, 0) && t > 0 && t < 1)
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{
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return EDGE;
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}
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else if (AlmostEqual(t, 0) && s > 0 && s < 1)
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{
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return EDGE;
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}
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else if (AlmostEqual(s + t, 1) && s > 0 && t > 0)
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{
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return EDGE;
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}
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else if (s > 0 && t > 0 && s + t < 1)
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{
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return INSIDE;
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}
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else
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{
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return OUTSIDE;
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}
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}
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bool isCompletelyInside(const Triangle& t1, const Triangle& t2)
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{
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// if any corner is not inside, then the triangle is not completely inside
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if (pointInsideTriangle(t1.getA(), t2) == OUTSIDE)
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{
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return false;
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}
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if (pointInsideTriangle(t1.getB(), t2) == OUTSIDE)
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{
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return false;
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}
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if (pointInsideTriangle(t1.getC(), t2) == OUTSIDE)
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{
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return false;
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}
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return true;
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}
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/* 2D */
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bool almostEqual(const SimplePoint2d& p1, const SimplePoint2d& p2)
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{
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return AlmostEqual(p1.getX(), p2.getX())
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&& AlmostEqual(p1.getY(), p2.getY());
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}
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double distance(const SimplePoint2d& p1, const SimplePoint2d& p2)
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{
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return sqrt(distance_square(p1, p2));
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}
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double distance_square(const SimplePoint2d& p1, const SimplePoint2d& p2)
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{
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double lx = p1.getX() - p2.getX();
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double ly = p1.getY() - p2.getY();
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return lx * lx + ly * ly;
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}
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double getPolarAngle(const SimplePoint2d& point)
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{
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return atan2(point.getY(), point.getX());
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}
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// Positiv: Rechtsknick; Negativ: Linksknick
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double clockwise(const SimplePoint2d& p1,
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const SimplePoint2d& p2,
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const SimplePoint2d& p3)
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{
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return (p3.getX() - p1.getX()) * (p2.getY() - p1.getY()) -
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(p2.getX() - p1.getX()) * (p3.getY() - p1.getY());
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}
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// never true for parallel segments
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bool doSegmentsIntersect(const SimplePoint2d& a1, const SimplePoint2d& a2,
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const SimplePoint2d& b1, const SimplePoint2d& b2)
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{
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SimplePoint2d ip;
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bool r = lineIntersectionPoint(a1, a2, b1, b2, ip);
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if (r)
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{
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// Lines are not parallel, so we have an intersection point.
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// Just check whether the intersection is inside the segments.
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if (!AlmostLte(min(a1.getX(), a2.getX()), ip.getX()))
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return false;
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if (!AlmostLte(min(b1.getX(), b2.getX()), ip.getX()))
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return false;
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if (!AlmostLte(min(a1.getY(), a2.getY()), ip.getY()))
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return false;
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if (!AlmostLte(min(b1.getY(), b2.getY()), ip.getY()))
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return false;
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if (!AlmostLte(ip.getX(), max(a1.getX(), a2.getX())))
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return false;
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if (!AlmostLte(ip.getX(), max(b1.getX(), b2.getX())))
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return false;
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if (!AlmostLte(ip.getY(), max(a1.getY(), a2.getY())))
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return false;
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if (!AlmostLte(ip.getY(), max(b1.getY(), b2.getY())))
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return false;
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return true;
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}
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else
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{
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return false;
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}
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}
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bool lineIntersectionPoint(const SimplePoint2d& a1, const SimplePoint2d& a2,
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const SimplePoint2d& b1, const SimplePoint2d& b2,
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SimplePoint2d& out_intersection)
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{
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double denominator = (a1.getX() - a2.getX()) * (b1.getY() - b2.getY())
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- (a1.getY() - a2.getY()) * (b1.getX() - b2.getX());
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if (AlmostEqual(denominator, 0))
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return false;
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double X = (a1.getX() * a2.getY() - a1.getY() * a2.getX())
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* (b1.getX() - b2.getX()) -
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(a1.getX() - a2.getX())
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* (b1.getX() * b2.getY() - b1.getY() * b2.getX());
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double Y = (a1.getX() * a2.getY() - a1.getY() * a2.getX())
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* (b1.getY() - b2.getY()) -
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(a1.getY() - a2.getY())
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* (b1.getX() * b2.getY() - b1.getY() * b2.getX());
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out_intersection.set(X / denominator, Y / denominator);
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return true;
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}
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InsideResult pointInsideTriangle(const SimplePoint2d& pointToTest,
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const SimplePoint2d& pointA,
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const SimplePoint2d& pointB,
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const SimplePoint2d& pointC)
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{
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double cw0 = clockwise(pointA, pointB, pointToTest);
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double cw1 = clockwise(pointB, pointC, pointToTest);
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double cw2 = clockwise(pointC, pointA, pointToTest);
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if ( !(AlmostLte(cw0, 0) && AlmostLte(cw1, 0) && AlmostLte(cw2, 0))
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&& !(AlmostLte(0, cw0) && AlmostLte(0, cw1) && AlmostLte(0, cw2)))
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{
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return OUTSIDE;
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}
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int numberOfSegmentsThePointIsIn = 0;
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if (AlmostEqual(cw0, 0)) {
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++ numberOfSegmentsThePointIsIn;
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}
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if (AlmostEqual(cw1, 0)) {
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++ numberOfSegmentsThePointIsIn;
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}
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if (AlmostEqual(cw2, 0)) {
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++ numberOfSegmentsThePointIsIn;
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}
|
|
|
|
switch (numberOfSegmentsThePointIsIn) {
|
|
case 0:
|
|
return INSIDE;
|
|
case 1:
|
|
return EDGE;
|
|
default:
|
|
return CORNER;
|
|
}
|
|
}
|
|
|
|
InsideResult pointInsideSegment(const SimplePoint2d& pointToTest,
|
|
const SimplePoint2d& segmentPoint1,
|
|
const SimplePoint2d& segmentPoint2)
|
|
{
|
|
const SimplePoint2d& c = pointToTest;
|
|
const SimplePoint2d& a = segmentPoint1;
|
|
const SimplePoint2d& b = segmentPoint2;
|
|
|
|
// Idea from here: http://stackoverflow.com/a/328122
|
|
|
|
double crossproduct = (c.getY() - a.getY()) * (b.getX() - a.getX())
|
|
- (c.getX() - a.getX()) * (b.getY() - a.getY());
|
|
if (!AlmostEqual(crossproduct, 0))
|
|
return OUTSIDE;
|
|
|
|
double dotproduct = (c.getX() - a.getX()) * (b.getX() - a.getX())
|
|
+ (c.getY() - a.getY()) * (b.getY() - a.getY());
|
|
if (dotproduct < 0)
|
|
return OUTSIDE;
|
|
|
|
if (dotproduct > distance_square(a, b))
|
|
return OUTSIDE;
|
|
|
|
if (almostEqual(pointToTest, segmentPoint1) ||
|
|
almostEqual(pointToTest, segmentPoint2))
|
|
{
|
|
return CORNER;
|
|
}
|
|
else
|
|
{
|
|
return INSIDE;
|
|
}
|
|
}
|
|
|
|
// precondition: the segment does share a point with the triangle
|
|
SimplePoint2d firstPointInsideTriangle(const SimplePoint2d& from,
|
|
const SimplePoint2d& to,
|
|
const SimplePoint2d& t1,
|
|
const SimplePoint2d& t2,
|
|
const SimplePoint2d& t3)
|
|
{
|
|
if (pointInsideTriangle(from, t1, t2, t3) != OUTSIDE)
|
|
return from;
|
|
SimplePoint2d const * const triangle[3] = { &t1, &t2, &t3 };
|
|
bool intersectsEdge[3];
|
|
SimplePoint2d edgeIntersectionPoints[3];
|
|
for(int c = 0; c < 3; ++c)
|
|
{
|
|
intersectsEdge[c] = doSegmentsIntersect(from, to,
|
|
*triangle[c],
|
|
*triangle[(c + 1) % 3]);
|
|
if (intersectsEdge[c])
|
|
{
|
|
lineIntersectionPoint(from, to, *triangle[c], *triangle[(c + 1) % 3],
|
|
edgeIntersectionPoints[c]);
|
|
}
|
|
}
|
|
|
|
if (!(intersectsEdge[0] || intersectsEdge[1] || intersectsEdge[2]))
|
|
{
|
|
numeric_fail();
|
|
}
|
|
|
|
// Find the intersection with minimal distance. Initialise a variable
|
|
// with a value that is greater than that distance could be.
|
|
|
|
double min_distance_square = 2 * distance_square(from, to) + 1;
|
|
|
|
SimplePoint2d closest_point;
|
|
|
|
for(int c = 0; c < 3; ++c)
|
|
{
|
|
if (intersectsEdge[c])
|
|
{
|
|
SimplePoint2d p = edgeIntersectionPoints[c];
|
|
double this_distance_square = distance_square(from, p);
|
|
if (this_distance_square < min_distance_square)
|
|
{
|
|
min_distance_square = this_distance_square;
|
|
closest_point = p;
|
|
}
|
|
}
|
|
}
|
|
return closest_point;
|
|
}
|
|
|
|
SegmentTriangle2dIntersectionResult
|
|
intersection(const SimplePoint2d& segmentA, const SimplePoint2d& segmentB,
|
|
const SimplePoint2d* triangle)
|
|
{
|
|
// segmentAin is the point of the segment A<->B that is closest to A.
|
|
SimplePoint2d segmentAin, segmentBin;
|
|
bool intersectionFound = false;
|
|
bool segmentAinFound = false, segmentBinFound = false;
|
|
switch(pointInsideTriangle(segmentA, triangle[0], triangle[1], triangle[2]))
|
|
{
|
|
case INSIDE:
|
|
return SEGMENT;
|
|
case EDGE:
|
|
case CORNER:
|
|
segmentAin = segmentA;
|
|
segmentAinFound = true;
|
|
intersectionFound = true;
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
switch(pointInsideTriangle(segmentB, triangle[0], triangle[1], triangle[2]))
|
|
{
|
|
case INSIDE:
|
|
return SEGMENT;
|
|
case EDGE:
|
|
case CORNER:
|
|
segmentBin = segmentB;
|
|
segmentBinFound = true;
|
|
intersectionFound = true;
|
|
default:
|
|
break;
|
|
}
|
|
|
|
if (!intersectionFound)
|
|
{
|
|
// both points are outside. First, we have to find out whether any
|
|
// edge of the triangle intersects with the segment.
|
|
for (int c = 0; c < 3; ++c)
|
|
{
|
|
if (doSegmentsIntersect(segmentA, segmentB,
|
|
triangle[c], triangle[(c + 1) % 3]))
|
|
{
|
|
intersectionFound = true;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
if (intersectionFound)
|
|
{
|
|
if (!segmentAinFound)
|
|
{
|
|
segmentAin = firstPointInsideTriangle(segmentA, segmentB,
|
|
triangle[0], triangle[1], triangle[2]);
|
|
}
|
|
if (!segmentBinFound)
|
|
{
|
|
segmentBin = firstPointInsideTriangle(segmentB, segmentA,
|
|
triangle[0], triangle[1], triangle[2]);
|
|
}
|
|
if (!almostEqual(segmentAin, segmentBin))
|
|
{
|
|
return SEGMENT;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
return NONE;
|
|
}
|
|
return intersectionFound ? POINT : NONE;
|
|
}
|
|
}
|