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secondo/Algebras/Spatial3D/geometric_algorithm.cpp
2026-01-23 17:03:45 +08:00

688 lines
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C++

/*
----
This file is part of SECONDO.
Copyright (C) 2004, University in Hagen, Department of Computer Science,
Database Systems for New Applications.
SECONDO 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.
SECONDO 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 SECONDO; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
----
01590 Fachpraktikum "Erweiterbare Datenbanksysteme"
WS 2014 / 2015
<our names here>
//paragraph [1] Title: [{\Large \bf \begin{center}] [\end{center}}]
//paragraph [10] Footnote: [{\footnote{] [}}]
//[TOC] [\tableofcontents]
[1] Implementation of a Spatial3D algebra
[TOC]
1 Includes and Defines
*/
#include "AuxiliaryTypes.h"
#include "geometric_algorithm.h"
#include<iostream>
using namespace std;
namespace spatial3d_geometric
{
/* TODO: Remove debugging helpers (Jens Breit) */
void print(SimplePoint3d a)
{
std::cerr << "SimplePoint3d: (" << a.getX() << ","
<< a.getY() << ","
<< a.getZ() << ")";
}
void print(Vector3d a)
{
std::cerr << "Vector3d: (" << a.getX() << ","
<< a.getY() << ","
<< a.getZ() << ")";
}
void print(SimplePoint2d a, string name)
{
std::cerr << "Point2d \"" << name << "\": (" << a.getX() << ","
<< a.getY() << ")" << endl;
}
void print(Triangle a)
{
std::cerr << "Triangle(";
print(a.getA());
print(a.getB());
print(a.getC());
std::cerr << ")" << endl;
}
void numeric_fail()
{
//assert(false);
throw NumericFailure();
}
/* Helper functions */
bool AlmostLte(double a, double b)
{
if (AlmostEqual(a, b))
return true;
return a < b;
}
/* Points */
const SimplePoint3d origin(0,0,0);
bool almostEqual(const SimplePoint3d& p1, const SimplePoint3d& p2)
{
return AlmostEqual(p1.getX(), p2.getX())
&& AlmostEqual(p1.getY(), p2.getY())
&& AlmostEqual(p1.getZ(), p2.getZ());
}
bool collinear(const SimplePoint3d& pA,
const SimplePoint3d& pB,
const SimplePoint3d& pC)
{
if (almostEqual(pB, pC))
return true;
// compute distance of pA to the line through pB und pC
return AlmostEqual(0, distancePointToLine(pA, pB, pC));
}
double distance(const SimplePoint3d& p1, const SimplePoint3d& p2)
{
return length(Vector3d(p1, p2));
}
double distancePointToLine(const SimplePoint3d& distantPoint,
const SimplePoint3d& linePoint1, const SimplePoint3d& linePoint2)
{
Vector3d v(origin, distantPoint);
Vector3d v1(origin, linePoint1);
Vector3d v2(origin, linePoint2);
return length(crossProduct(v - v1, v - v2))
/ length(v2 - v1);
}
/* Vectors */
bool almostEqual(const Vector3d& p1, const Vector3d& p2)
{
return AlmostEqual(p1.getX(), p2.getX())
&& AlmostEqual(p1.getY(), p2.getY())
&& AlmostEqual(p1.getZ(), p2.getZ());
}
double length(const Vector3d& vector)
{
return sqrt(vector * vector);
}
bool collinear(const Vector3d& v1, const Vector3d& v2)
{
return collinear(origin, origin + v1, origin + v2);
// TODO: Alternative: Kreuzprodukt = 0
// oder inneres Produkt = Quadrat der Länge
}
bool orthogonal(const Vector3d& v1, const Vector3d& v2)
{
return AlmostEqual(v1 * v2, 0);
}
Vector3d operator+(const Vector3d& v1, const Vector3d& v2)
{
return Vector3d(v1.getX() + v2.getX(),
v1.getY() + v2.getY(),
v1.getZ() + v2.getZ());
}
Vector3d operator-(const Vector3d& v1, const Vector3d& v2)
{
return v1 + (-1 * v2);
}
Vector3d operator*(double scalar, const Vector3d& vector)
{
return Vector3d(scalar * vector.getX(),
scalar * vector.getY(),
scalar * vector.getZ());
}
double operator*(const Vector3d& v1, const Vector3d& v2)
{
return v1.getX() * v2.getX()
+ v1.getY() * v2.getY()
+ v1.getZ() * v2.getZ();
}
Vector3d crossProduct(const Vector3d& v1, const Vector3d& v2)
{
return Vector3d(v1.getY() * v2.getZ() - v1.getZ() * v2.getY(),
v1.getZ() * v2.getX() - v1.getX() * v2.getZ(),
v1.getX() * v2.getY() - v1.getY() * v2.getX());
}
SimplePoint3d operator+(const SimplePoint3d& p, const Vector3d& v)
{
return SimplePoint3d(p.getX() + v.getX(),
p.getY() + v.getY(),
p.getZ() + v.getZ());
}
/* Planes */
bool almostEqual(const Plane3d& p1, const Plane3d& p2)
{
return AlmostEqual(p1.getDistanceToOrigin(), p2.getDistanceToOrigin())
&& almostEqual(p1.getNormalVector(), p2.getNormalVector());
}
Vector3d normalVector(const SimplePoint3d& pA,
const SimplePoint3d& pB,
const SimplePoint3d& pC)
{
double ax = pA.getX(), ay = pA.getY(), az = pA.getZ();
double bx = pB.getX(), by = pB.getY(), bz = pB.getZ();
double cx = pC.getX(), cy = pC.getY(), cz = pC.getZ();
double nx = (by-ay)*(cz-az)-(bz-az)*(cy-ay);
double ny = (bz-az)*(cx-ax)-(bx-ax)*(cz-az);
double nz = (bx-ax)*(cy-ay)-(by-ay)*(cx-ax);
Vector3d direction = Vector3d(nx, ny, nz);
return (1 / length(direction)) * direction;
}
double distance(const SimplePoint3d& point, const Plane3d& plane)
{
Vector3d pv = Vector3d(origin, point);
Vector3d nv = plane.getNormalVector();
double d = plane.getDistanceToOrigin();
return pv * nv - d;
}
bool isPointInPlane(const SimplePoint3d& point, const Plane3d& plane)
{
return AlmostEqual(distance(point, plane), 0);
}
double planeDistanceToOrigin(const SimplePoint3d& pointInPlane,
const Vector3d& normalVector)
{
return normalVector * Vector3d(origin, pointInPlane);
}
void planeHessianNormalForm(const SimplePoint3d& pA,
const SimplePoint3d& pB,
const SimplePoint3d& pC,
double& out_distanceToOrigin,
Vector3d& out_normalVector)
{
out_normalVector = normalVector(pA, pB, pC);
out_distanceToOrigin = planeDistanceToOrigin(pA, out_normalVector);
// Make sure the same plane always has the same representation.
if (out_distanceToOrigin < 0)
{
out_distanceToOrigin *= -1;
out_normalVector = -1.0 * out_normalVector;
}
else if (out_distanceToOrigin == 0)
{
if (out_normalVector.getX() != 0)
{
if (out_normalVector.getX() < 0)
{
out_normalVector = -1.0 * out_normalVector;
}
return;
}
if (out_normalVector.getY() != 0)
{
if (out_normalVector.getY() < 0)
{
out_normalVector = -1.0 * out_normalVector;
}
return;
}
if (out_normalVector.getZ() < 0)
{
out_normalVector = -1.0 * out_normalVector;
}
}
}
SimplePoint3d projectPointOntoPlane(const SimplePoint3d &point,
const Plane3d& plane)
{
Vector3d v(plane.getPoint(), point);
Vector3d n = plane.getNormalVector();
return point + (-(n * v)) * n;
}
/* Triangles */
// assumes directed triangles
bool almostEqual(const Triangle& triangle1, const Triangle& triangle2)
{
SimplePoint3d points1[3] = { triangle1.getA(),
triangle1.getB(),
triangle1.getC() };
SimplePoint3d points2[3] = { triangle2.getA(),
triangle2.getB(),
triangle2.getC() };
for (int c = 0; c < 3; ++c)
{
bool differenceFound = false;
for (int d = 0; d < 3; ++d)
{
if (!almostEqual(points1[d], points2[(d + c) % 3]))
{
differenceFound = true;
break;
}
}
if (!differenceFound)
return true;
}
return false;
}
bool isValidTriangle(const SimplePoint3d& pA,
const SimplePoint3d& pB,
const SimplePoint3d& pC)
{
if (almostEqual(pA, pB) || almostEqual(pB, pC) || almostEqual(pC, pA))
{
return false;
}
if (collinear(pA, pB, pC))
{
return false;
}
return true;
}
bool isValidTriangle(const Triangle& triangle)
{
return isValidTriangle(triangle.getA(), triangle.getB(), triangle.getC());
}
// precondition: point is in the plane of the triangle.
InsideResult pointInsideTriangle(const SimplePoint3d& pointToTest,
const Triangle& triangle)
{
Vector3d w = Vector3d(triangle.getA(), pointToTest);
Vector3d u = Vector3d(triangle.getA(), triangle.getB());
Vector3d v = Vector3d(triangle.getA(), triangle.getC());
double denominator = (u * v) * (u * v) - (u * u) * (v * v);
double s = ((u * v) * (w * v) - (v * v) * (w * u)) / denominator;
double t = ((u * v) * (w * u) - (u * u) * (w * v)) / denominator;
if (AlmostEqual(s, 0) && AlmostEqual(t, 0))
{
return CORNER;
}
else if ((AlmostEqual(s, 0) || AlmostEqual(t, 0)) && AlmostEqual(s + t, 1))
{
return CORNER;
}
else if (AlmostEqual(s, 0) && t > 0 && t < 1)
{
return EDGE;
}
else if (AlmostEqual(t, 0) && s > 0 && s < 1)
{
return EDGE;
}
else if (AlmostEqual(s + t, 1) && s > 0 && t > 0)
{
return EDGE;
}
else if (s > 0 && t > 0 && s + t < 1)
{
return INSIDE;
}
else
{
return OUTSIDE;
}
}
bool isCompletelyInside(const Triangle& t1, const Triangle& t2)
{
// if any corner is not inside, then the triangle is not completely inside
if (pointInsideTriangle(t1.getA(), t2) == OUTSIDE)
{
return false;
}
if (pointInsideTriangle(t1.getB(), t2) == OUTSIDE)
{
return false;
}
if (pointInsideTriangle(t1.getC(), t2) == OUTSIDE)
{
return false;
}
return true;
}
/* 2D */
bool almostEqual(const SimplePoint2d& p1, const SimplePoint2d& p2)
{
return AlmostEqual(p1.getX(), p2.getX())
&& AlmostEqual(p1.getY(), p2.getY());
}
double distance(const SimplePoint2d& p1, const SimplePoint2d& p2)
{
return sqrt(distance_square(p1, p2));
}
double distance_square(const SimplePoint2d& p1, const SimplePoint2d& p2)
{
double lx = p1.getX() - p2.getX();
double ly = p1.getY() - p2.getY();
return lx * lx + ly * ly;
}
double getPolarAngle(const SimplePoint2d& point)
{
return atan2(point.getY(), point.getX());
}
// Positiv: Rechtsknick; Negativ: Linksknick
double clockwise(const SimplePoint2d& p1,
const SimplePoint2d& p2,
const SimplePoint2d& p3)
{
return (p3.getX() - p1.getX()) * (p2.getY() - p1.getY()) -
(p2.getX() - p1.getX()) * (p3.getY() - p1.getY());
}
// never true for parallel segments
bool doSegmentsIntersect(const SimplePoint2d& a1, const SimplePoint2d& a2,
const SimplePoint2d& b1, const SimplePoint2d& b2)
{
SimplePoint2d ip;
bool r = lineIntersectionPoint(a1, a2, b1, b2, ip);
if (r)
{
// Lines are not parallel, so we have an intersection point.
// Just check whether the intersection is inside the segments.
if (!AlmostLte(min(a1.getX(), a2.getX()), ip.getX()))
return false;
if (!AlmostLte(min(b1.getX(), b2.getX()), ip.getX()))
return false;
if (!AlmostLte(min(a1.getY(), a2.getY()), ip.getY()))
return false;
if (!AlmostLte(min(b1.getY(), b2.getY()), ip.getY()))
return false;
if (!AlmostLte(ip.getX(), max(a1.getX(), a2.getX())))
return false;
if (!AlmostLte(ip.getX(), max(b1.getX(), b2.getX())))
return false;
if (!AlmostLte(ip.getY(), max(a1.getY(), a2.getY())))
return false;
if (!AlmostLte(ip.getY(), max(b1.getY(), b2.getY())))
return false;
return true;
}
else
{
return false;
}
}
bool lineIntersectionPoint(const SimplePoint2d& a1, const SimplePoint2d& a2,
const SimplePoint2d& b1, const SimplePoint2d& b2,
SimplePoint2d& out_intersection)
{
double denominator = (a1.getX() - a2.getX()) * (b1.getY() - b2.getY())
- (a1.getY() - a2.getY()) * (b1.getX() - b2.getX());
if (AlmostEqual(denominator, 0))
return false;
double X = (a1.getX() * a2.getY() - a1.getY() * a2.getX())
* (b1.getX() - b2.getX()) -
(a1.getX() - a2.getX())
* (b1.getX() * b2.getY() - b1.getY() * b2.getX());
double Y = (a1.getX() * a2.getY() - a1.getY() * a2.getX())
* (b1.getY() - b2.getY()) -
(a1.getY() - a2.getY())
* (b1.getX() * b2.getY() - b1.getY() * b2.getX());
out_intersection.set(X / denominator, Y / denominator);
return true;
}
InsideResult pointInsideTriangle(const SimplePoint2d& pointToTest,
const SimplePoint2d& pointA,
const SimplePoint2d& pointB,
const SimplePoint2d& pointC)
{
double cw0 = clockwise(pointA, pointB, pointToTest);
double cw1 = clockwise(pointB, pointC, pointToTest);
double cw2 = clockwise(pointC, pointA, pointToTest);
if ( !(AlmostLte(cw0, 0) && AlmostLte(cw1, 0) && AlmostLte(cw2, 0))
&& !(AlmostLte(0, cw0) && AlmostLte(0, cw1) && AlmostLte(0, cw2)))
{
return OUTSIDE;
}
int numberOfSegmentsThePointIsIn = 0;
if (AlmostEqual(cw0, 0)) {
++ numberOfSegmentsThePointIsIn;
}
if (AlmostEqual(cw1, 0)) {
++ numberOfSegmentsThePointIsIn;
}
if (AlmostEqual(cw2, 0)) {
++ numberOfSegmentsThePointIsIn;
}
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;
}
}