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// Begin License:
// Copyright (C) 2006-2011 Tobias Sargeant (tobias.sargeant@gmail.com).
// All rights reserved.
//
// This file is part of the Carve CSG Library (http://carve-csg.com/)
//
// This file may be used under the terms of the GNU General Public
// License version 2.0 as published by the Free Software Foundation
// and appearing in the file LICENSE.GPL2 included in the packaging of
// this file.
//
// This file is provided "AS IS" with NO WARRANTY OF ANY KIND,
// INCLUDING THE WARRANTIES OF DESIGN, MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE.
// End:
#pragma once
#include <carve/carve.hpp>
#include <carve/math.hpp>
#include <carve/math_constants.hpp>
#include <carve/geom.hpp>
#include <vector>
#include <algorithm>
#include <math.h>
#if defined(CARVE_DEBUG)
# include <iostream>
#endif
#if defined CARVE_USE_EXACT_PREDICATES
# include <carve/shewchuk_predicates.hpp>
#endif
namespace carve {
namespace geom2d {
typedef carve::geom::vector<2> P2;
typedef carve::geom::ray<2> Ray2;
typedef carve::geom::linesegment<2> LineSegment2;
struct p2_adapt_ident {
P2 &operator()(P2 &p) const { return p; }
const P2 &operator()(const P2 &p) const { return p; }
};
typedef std::vector<P2> P2Vector;
/**
* \brief Return the orientation of c with respect to the ray defined by a->b.
*
* (Can be implemented exactly)
*
* @param[in] a
* @param[in] b
* @param[in] c
*
* @return positive, if c to the left of a->b.
* zero, if c is colinear with a->b.
* negative, if c to the right of a->b.
*/
#if defined CARVE_USE_EXACT_PREDICATES
inline double orient2d(const P2 &a, const P2 &b, const P2 &c) {
return shewchuk::orient2d(a.v, b.v, c.v);
}
#else
inline double orient2d(const P2 &a, const P2 &b, const P2 &c) {
double acx = a.x - c.x;
double bcx = b.x - c.x;
double acy = a.y - c.y;
double bcy = b.y - c.y;
return acx * bcy - acy * bcx;
}
#endif
/**
* \brief Determine whether p is internal to the anticlockwise
* angle abc, where b is the apex of the angle.
*
* @param[in] a
* @param[in] b
* @param[in] c
* @param[in] p
*
* @return true, if p is contained in the anticlockwise angle from
* b->a to b->c. Reflex angles contain p if p lies
* on b->a or on b->c. Acute angles do not contain p
* if p lies on b->a or on b->c. This is so that
* internalToAngle(a,b,c,p) = !internalToAngle(c,b,a,p)
*/
inline bool internalToAngle(const P2 &a,
const P2 &b,
const P2 &c,
const P2 &p) {
bool reflex = (a < c) ? orient2d(b, a, c) <= 0.0 : orient2d(b, c, a) > 0.0;
double d1 = orient2d(b, a, p);
double d2 = orient2d(b, c, p);
if (reflex) {
return d1 >= 0.0 || d2 <= 0.0;
} else {
return d1 > 0.0 && d2 < 0.0;
}
}
/**
* \brief Determine whether p is internal to the anticlockwise
* angle ac, with apex at (0,0).
*
* @param[in] a
* @param[in] c
* @param[in] p
*
* @return true, if p is contained in a0c.
*/
inline bool internalToAngle(const P2 &a,
const P2 &c,
const P2 &p) {
return internalToAngle(a, P2::ZERO(), c, p);
}
template<typename P2vec>
bool isAnticlockwise(const P2vec &tri) {
return orient2d(tri[0], tri[1], tri[2]) > 0.0;
}
template<typename P2vec>
bool pointIntersectsTriangle(const P2 &p, const P2vec &tri) {
int orient = isAnticlockwise(tri) ? +1 : -1;
if (orient2d(tri[0], tri[1], p) * orient < 0) return false;
if (orient2d(tri[1], tri[2], p) * orient < 0) return false;
if (orient2d(tri[2], tri[0], p) * orient < 0) return false;
return true;
}
template<typename P2vec>
bool lineIntersectsTriangle(const P2 &p1, const P2 &p2, const P2vec &tri) {
double s[3];
// does tri lie on one side or the other of p1-p2?
s[0] = orient2d(p1, p2, tri[0]);
s[1] = orient2d(p1, p2, tri[1]);
s[2] = orient2d(p1, p2, tri[2]);
if (*std::max_element(s, s+3) < 0) return false;
if (*std::min_element(s, s+3) > 0) return false;
// does line lie entirely to the right of a triangle edge?
int orient = isAnticlockwise(tri) ? +1 : -1;
if (orient2d(tri[0], tri[1], p1) * orient < 0 && orient2d(tri[0], tri[1], p2) * orient < 0) return false;
if (orient2d(tri[1], tri[2], p1) * orient < 0 && orient2d(tri[1], tri[2], p2) * orient < 0) return false;
if (orient2d(tri[2], tri[0], p1) * orient < 0 && orient2d(tri[2], tri[0], p2) * orient < 0) return false;
return true;
}
template<typename P2vec>
int triangleLineOrientation(const P2 &p1, const P2 &p2, const P2vec &tri) {
double lo, hi, tmp;
lo = hi = orient2d(p1, p2, tri[0]);
tmp = orient2d(p1, p2, tri[1]); lo = std::min(lo, tmp); hi = std::max(hi, tmp);
tmp = orient2d(p1, p2, tri[2]); lo = std::min(lo, tmp); hi = std::max(hi, tmp);
if (hi < 0.0) return -1;
if (lo > 0.0) return +1;
return 0;
}
template<typename P2vec>
bool triangleIntersectsTriangle(const P2vec &tri_b, const P2vec &tri_a) {
int orient_a = isAnticlockwise(tri_a) ? +1 : -1;
if (triangleLineOrientation(tri_a[0], tri_a[1], tri_b) * orient_a < 0) return false;
if (triangleLineOrientation(tri_a[1], tri_a[2], tri_b) * orient_a < 0) return false;
if (triangleLineOrientation(tri_a[2], tri_a[0], tri_b) * orient_a < 0) return false;
int orient_b = isAnticlockwise(tri_b) ? +1 : -1;
if (triangleLineOrientation(tri_b[0], tri_b[1], tri_a) * orient_b < 0) return false;
if (triangleLineOrientation(tri_b[1], tri_b[2], tri_a) * orient_b < 0) return false;
if (triangleLineOrientation(tri_b[2], tri_b[0], tri_a) * orient_b < 0) return false;
return true;
}
static inline double atan2(const P2 &p) {
return ::atan2(p.y, p.x);
}
struct LineIntersectionInfo {
LineIntersectionClass iclass;
P2 ipoint;
int p1, p2;
LineIntersectionInfo(LineIntersectionClass _iclass,
P2 _ipoint = P2::ZERO(),
int _p1 = -1,
int _p2 = -1) :
iclass(_iclass), ipoint(_ipoint), p1(_p1), p2(_p2) {
}
};
struct PolyInclusionInfo {
PointClass iclass;
int iobjnum;
PolyInclusionInfo(PointClass _iclass,
int _iobjnum = -1) :
iclass(_iclass), iobjnum(_iobjnum) {
}
};
struct PolyIntersectionInfo {
IntersectionClass iclass;
P2 ipoint;
size_t iobjnum;
PolyIntersectionInfo(IntersectionClass _iclass,
const P2 &_ipoint,
size_t _iobjnum) :
iclass(_iclass), ipoint(_ipoint), iobjnum(_iobjnum) {
}
};
bool lineSegmentIntersection_simple(const P2 &l1v1, const P2 &l1v2,
const P2 &l2v1, const P2 &l2v2);
bool lineSegmentIntersection_simple(const LineSegment2 &l1,
const LineSegment2 &l2);
LineIntersectionInfo lineSegmentIntersection(const P2 &l1v1, const P2 &l1v2,
const P2 &l2v1, const P2 &l2v2);
LineIntersectionInfo lineSegmentIntersection(const LineSegment2 &l1,
const LineSegment2 &l2);
int lineSegmentPolyIntersections(const std::vector<P2> &points,
LineSegment2 line,
std::vector<PolyInclusionInfo> &out);
int sortedLineSegmentPolyIntersections(const std::vector<P2> &points,
LineSegment2 line,
std::vector<PolyInclusionInfo> &out);
static inline bool quadIsConvex(const P2 &a, const P2 &b, const P2 &c, const P2 &d) {
double s_1, s_2;
s_1 = carve::geom2d::orient2d(a, c, b);
s_2 = carve::geom2d::orient2d(a, c, d);
if ((s_1 < 0.0 && s_2 < 0.0) || (s_1 > 0.0 && s_2 > 0.0)) return false;
s_1 = carve::geom2d::orient2d(b, d, a);
s_2 = carve::geom2d::orient2d(b, d, c);
if ((s_1 < 0.0 && s_2 < 0.0) || (s_1 > 0.0 && s_2 > 0.0)) return false;
return true;
}
template<typename T, typename adapt_t>
inline bool quadIsConvex(const T &a, const T &b, const T &c, const T &d, adapt_t adapt) {
return quadIsConvex(adapt(a), adapt(b), adapt(c), adapt(d));
}
double signedArea(const std::vector<P2> &points);
static inline double signedArea(const P2 &a, const P2 &b, const P2 &c) {
return ((b.y + a.y) * (b.x - a.x) + (c.y + b.y) * (c.x - b.x) + (a.y + c.y) * (a.x - c.x)) / 2.0;
}
template<typename T, typename adapt_t>
double signedArea(const std::vector<T> &points, adapt_t adapt) {
P2Vector::size_type l = points.size();
double A = 0.0;
for (P2Vector::size_type i = 0; i < l - 1; i++) {
A += (adapt(points[i + 1]).y + adapt(points[i]).y) * (adapt(points[i + 1]).x - adapt(points[i]).x);
}
A += (adapt(points[0]).y + adapt(points[l - 1]).y) * (adapt(points[0]).x - adapt(points[l - 1]).x);
return A / 2.0;
}
template<typename iter_t, typename adapt_t>
double signedArea(iter_t begin, iter_t end, adapt_t adapt) {
double A = 0.0;
P2 p, n;
if (begin == end) return 0.0;
p = adapt(*begin);
for (iter_t c = begin; ++c != end; ) {
P2 n = adapt(*c);
A += (n.y + p.y) * (n.x - p.x);
p = n;
}
n = adapt(*begin);
A += (n.y + p.y) * (n.x - p.x);
return A / 2.0;
}
bool pointInPolySimple(const std::vector<P2> &points, const P2 &p);
template<typename T, typename adapt_t>
bool pointInPolySimple(const std::vector<T> &points, adapt_t adapt, const P2 &p) {
CARVE_ASSERT(points.size() > 0);
P2Vector::size_type l = points.size();
double s = 0.0;
double rp, r0, d;
rp = r0 = atan2(adapt(points[0]) - p);
for (P2Vector::size_type i = 1; i < l; i++) {
double r = atan2(adapt(points[i]) - p);
d = r - rp;
if (d > M_PI) d -= M_TWOPI;
if (d < -M_PI) d += M_TWOPI;
s = s + d;
rp = r;
}
d = r0 - rp;
if (d > M_PI) d -= M_TWOPI;
if (d < -M_PI) d += M_TWOPI;
s = s + d;
return !carve::math::ZERO(s);
}
PolyInclusionInfo pointInPoly(const std::vector<P2> &points, const P2 &p);
template<typename T, typename adapt_t>
PolyInclusionInfo pointInPoly(const std::vector<T> &points, adapt_t adapt, const P2 &p) {
P2Vector::size_type l = points.size();
for (unsigned i = 0; i < l; i++) {
if (equal(adapt(points[i]), p)) return PolyInclusionInfo(POINT_VERTEX, i);
}
for (unsigned i = 0; i < l; i++) {
unsigned j = (i + 1) % l;
if (std::min(adapt(points[i]).x, adapt(points[j]).x) - EPSILON < p.x &&
std::max(adapt(points[i]).x, adapt(points[j]).x) + EPSILON > p.x &&
std::min(adapt(points[i]).y, adapt(points[j]).y) - EPSILON < p.y &&
std::max(adapt(points[i]).y, adapt(points[j]).y) + EPSILON > p.y &&
distance2(carve::geom::rayThrough(adapt(points[i]), adapt(points[j])), p) < EPSILON2) {
return PolyInclusionInfo(POINT_EDGE, i);
}
}
if (pointInPolySimple(points, adapt, p)) {
return PolyInclusionInfo(POINT_IN);
}
return PolyInclusionInfo(POINT_OUT);
}
bool pickContainedPoint(const std::vector<P2> &poly, P2 &result);
template<typename T, typename adapt_t>
bool pickContainedPoint(const std::vector<T> &poly, adapt_t adapt, P2 &result) {
#if defined(CARVE_DEBUG)
std::cerr << "pickContainedPoint ";
for (unsigned i = 0; i < poly.size(); ++i) std::cerr << " " << adapt(poly[i]);
std::cerr << std::endl;
#endif
const size_t S = poly.size();
P2 a, b, c;
for (unsigned i = 0; i < S; ++i) {
a = adapt(poly[i]);
b = adapt(poly[(i + 1) % S]);
c = adapt(poly[(i + 2) % S]);
if (cross(a - b, c - b) < 0) {
P2 p = (a + b + c) / 3;
if (pointInPolySimple(poly, adapt, p)) {
result = p;
return true;
}
}
}
return false;
}
}
}
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