ardupilot/libraries/AP_Math/polygon.cpp

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/*
* polygon.cpp
* Copyright (C) Andrew Tridgell 2011
*
* This file 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 3 of the License, or
* (at your option) any later version.
*
* This file is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
* See the GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "AP_Math.h"
#pragma GCC optimize("O3")
/*
* The point in polygon algorithm is based on:
* https://wrf.ecse.rpi.edu//Research/Short_Notes/pnpoly.html
*/
/*
* Polygon_outside(): test for a point in a polygon
* Input: P = a point,
* V[] = vertex points of a polygon V[n+1] with V[n]=V[0]
* Return: true if P is outside the polygon
*
* This does not take account of the curvature of the earth, but we
* expect that to be very small over the distances involved in the
* fence boundary
*/
template <typename T>
bool Polygon_outside(const Vector2<T> &P, const Vector2<T> *V, unsigned n)
{
const bool complete = Polygon_complete(V, n);
if (complete) {
// the last point is the same as the first point; treat as if
// the last point wasn't passed in
n--;
}
unsigned i, j;
// step through each edge pair-wise looking for crossings:
bool outside = true;
for (i=0; i<n; i++) {
j = i+1;
if (j >= n) {
j = 0;
}
if ((V[i].y > P.y) == (V[j].y > P.y)) {
continue;
}
const T dx1 = P.x - V[i].x;
const T dx2 = V[j].x - V[i].x;
const T dy1 = P.y - V[i].y;
const T dy2 = V[j].y - V[i].y;
const int8_t dx1s = (dx1 < 0) ? -1 : 1;
const int8_t dx2s = (dx2 < 0) ? -1 : 1;
const int8_t dy1s = (dy1 < 0) ? -1 : 1;
const int8_t dy2s = (dy2 < 0) ? -1 : 1;
const int8_t m1 = dx1s * dy2s;
const int8_t m2 = dx2s * dy1s;
2011-12-21 00:31:47 -04:00
// we avoid the 64 bit multiplies if we can based on sign checks.
if (dy2 < 0) {
if (m1 > m2) {
outside = !outside;
} else if (m1 < m2) {
continue;
} else {
if (std::is_floating_point<T>::value) {
if ( dx1 * dy2 > dx2 * dy1 ) {
outside = !outside;
}
} else {
if ( dx1 * (int64_t)dy2 > dx2 * (int64_t)dy1 ) {
outside = !outside;
}
}
}
} else {
if (m1 < m2) {
outside = !outside;
} else if (m1 > m2) {
continue;
} else {
if (std::is_floating_point<T>::value) {
if ( dx1 * dy2 < dx2 * dy1 ) {
outside = !outside;
}
} else {
if ( dx1 * (int64_t)dy2 < dx2 * (int64_t)dy1 ) {
outside = !outside;
}
}
}
}
}
return outside;
}
/*
* check if a polygon is complete.
*
* We consider a polygon to be complete if we have at least 4 points,
* and the first point is the same as the last point. That is the
* minimum requirement for the Polygon_outside function to work
*/
template <typename T>
bool Polygon_complete(const Vector2<T> *V, unsigned n)
{
return (n >= 4 && V[n-1] == V[0]);
}
// Necessary to avoid linker errors
template bool Polygon_outside<int32_t>(const Vector2l &P, const Vector2l *V, unsigned n);
template bool Polygon_complete<int32_t>(const Vector2l *V, unsigned n);
template bool Polygon_outside<float>(const Vector2f &P, const Vector2f *V, unsigned n);
template bool Polygon_complete<float>(const Vector2f *V, unsigned n);
/*
determine if the polygon of N verticies defined by points V is
intersected by a line from point p1 to point p2
intersection argument returns the intersection closest to p1
*/
bool Polygon_intersects(const Vector2f *V, unsigned N, const Vector2f &p1, const Vector2f &p2, Vector2f &intersection)
{
const bool complete = Polygon_complete(V, N);
if (complete) {
// if the last point is the same as the first point
// treat as if the last point wasn't passed in
N--;
}
float intersect_dist_sq = FLT_MAX;
for (uint8_t i=0; i<N; i++) {
uint8_t j = i+1;
if (j >= N) {
j = 0;
}
const Vector2f &v1 = V[i];
const Vector2f &v2 = V[j];
// optimisations for common cases
if (v1.x > p1.x && v2.x > p1.x && v1.x > p2.x && v2.x > p2.x) {
continue;
}
if (v1.y > p1.y && v2.y > p1.y && v1.y > p2.y && v2.y > p2.y) {
continue;
}
if (v1.x < p1.x && v2.x < p1.x && v1.x < p2.x && v2.x < p2.x) {
continue;
}
if (v1.y < p1.y && v2.y < p1.y && v1.y < p2.y && v2.y < p2.y) {
continue;
}
Vector2f intersect_tmp;
if (Vector2f::segment_intersection(v1,v2,p1,p2,intersect_tmp)) {
float dist_sq = sq(intersect_tmp.x - p1.x) + sq(intersect_tmp.y - p1.y);
if (dist_sq < intersect_dist_sq) {
intersect_dist_sq = dist_sq;
intersection = intersect_tmp;
}
}
}
return (intersect_dist_sq < FLT_MAX);
}
/*
return the closest distance that a line from p1 to p2 comes to an
edge of closed polygon V, defined by N points
negative numbers indicate the line cross into the polygon with the negative size being the distance from p2 to the intersection point closest to p1
*/
float Polygon_closest_distance_line(const Vector2f *V, unsigned N, const Vector2f &p1, const Vector2f &p2)
{
Vector2f intersection;
if (Polygon_intersects(V,N,p1,p2,intersection)) {
return -sqrtf(sq(intersection.x - p2.x) + sq(intersection.y - p2.y));
}
float closest_sq = FLT_MAX;
for (uint8_t i=0; i<N-1; i++) {
const Vector2f &v1 = V[i];
const Vector2f &v2 = V[i+1];
float dist_sq = Vector2f::closest_distance_between_lines_squared(v1, v2, p1, p2);
if (dist_sq < closest_sq) {
closest_sq = dist_sq;
}
}
return sqrtf(closest_sq);
}
/*
return the closest distance that point p comes to an edge of closed
polygon V, defined by N points
*/
float Polygon_closest_distance_point(const Vector2f *V, unsigned N, const Vector2f &p)
{
float closest_sq = FLT_MAX;
for (uint8_t i=0; i<N-1; i++) {
const Vector2f &v1 = V[i];
const Vector2f &v2 = V[i+1];
float dist_sq = Vector2f::closest_distance_between_line_and_point_squared(v1, v2, p);
if (dist_sq < closest_sq) {
closest_sq = dist_sq;
}
}
return sqrtf(closest_sq);
}