shortest.c

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/*************************************************************************
 * Copyright (c) 2011 AT&T Intellectual Property 
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * https://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors: Details at https://graphviz.org
 *************************************************************************/
 
#include <stdbool.h>
#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <math.h>
#include <pathplan/pathutil.h>
#include <pathplan/tri.h>
#include <util/list.h>
#include <util/prisize_t.h>
 
#define DQ_FRONT 1
#define DQ_BACK  2
 
#define prerror(msg) \
        fprintf (stderr, "lib/pathplan/%s:%d: %s\n", __FILE__, __LINE__, (msg))
 
#define POINTSIZE sizeof (Ppoint_t)
 
typedef struct pointnlink_t {
    Ppoint_t *pp;
    struct pointnlink_t *link;
} pointnlink_t;
 
#define POINTNLINKSIZE sizeof (pointnlink_t)
#define POINTNLINKPSIZE sizeof (pointnlink_t *)
 
typedef struct {
    pointnlink_t *pnl0p;
    pointnlink_t *pnl1p;
    size_t right_index; 
} tedge_t;
 
typedef struct triangle_t {
    int mark;
    tedge_t e[3];
} triangle_t;
 
typedef struct deque_t {
    pointnlink_t **pnlps;
    size_t pnlpn, fpnlpi, lpnlpi, apex;
} deque_t;
 
static LIST(triangle_t) tris;
 
static Ppoint_t *ops;
static size_t opn;
 
static int triangulate(pointnlink_t **, size_t);
static int loadtriangle(pointnlink_t *, pointnlink_t *, pointnlink_t *);
static void connecttris(size_t, size_t);
static bool marktripath(size_t, size_t);
 
static void add2dq(deque_t *dq, int, pointnlink_t*);
static void splitdq(deque_t *dq, int, size_t);
static size_t finddqsplit(const deque_t *dq, pointnlink_t*);
 
static int pointintri(size_t, Ppoint_t *);
 
static int growops(size_t);
 
static Ppoint_t point_indexer(void *base, size_t index) {
  pointnlink_t **b = base;
  return *b[index]->pp;
}
 
/* Pshortestpath:
 * Find a shortest path contained in the polygon polyp going between the
 * points supplied in eps. The resulting polyline is stored in output.
 * Return 0 on success, -1 on bad input, -2 on memory allocation problem. 
 */
int Pshortestpath(Ppoly_t * polyp, Ppoint_t eps[2], Ppolyline_t * output)
{
    size_t pi, minpi;
    double minx;
    Ppoint_t p1, p2, p3;
    size_t trii, trij, ftrii, ltrii;
    int ei;
    pointnlink_t epnls[2], *lpnlp, *rpnlp, *pnlp;
    triangle_t *trip;
 
    /* make space */
    pointnlink_t *pnls = calloc(polyp->pn, sizeof(pnls[0]));
    if (polyp->pn > 0 && pnls == NULL) {
        prerror("cannot realloc pnls");
        return -2;
    }
    pointnlink_t **pnlps = calloc(polyp->pn, sizeof(pnlps[0]));
    if (polyp->pn > 0 && pnlps == NULL) {
        prerror("cannot realloc pnlps");
        free(pnls);
        return -2;
    }
    size_t pnll = 0;
    LIST_CLEAR(&tris);
 
    deque_t dq = {.pnlpn = polyp->pn * 2};
    dq.pnlps = calloc(dq.pnlpn, POINTNLINKPSIZE);
    if (dq.pnlps == NULL) {
        prerror("cannot realloc dq.pnls");
        free(pnlps);
        free(pnls);
        return -2;
    }
    dq.fpnlpi = dq.pnlpn / 2;
    dq.lpnlpi = dq.fpnlpi - 1;
 
    /* make sure polygon is CCW and load pnls array */
    for (pi = 0, minx = HUGE_VAL, minpi = SIZE_MAX; pi < polyp->pn; pi++) {
        if (minx > polyp->ps[pi].x)
            minx = polyp->ps[pi].x, minpi = pi;
    }
    p2 = polyp->ps[minpi];
    p1 = polyp->ps[minpi == 0 ? polyp->pn - 1 : minpi - 1];
    p3 = polyp->ps[(minpi == polyp->pn - 1) ? 0 : minpi + 1];
    if ((p1.x == p2.x && p2.x == p3.x && p3.y > p2.y) ||
        ccw(p1, p2, p3) != ISCCW) {
        for (pi = polyp->pn - 1; polyp->pn > 0 && pi != SIZE_MAX; pi--) {
            if (pi < polyp->pn - 1
                && polyp->ps[pi].x == polyp->ps[pi + 1].x
                && polyp->ps[pi].y == polyp->ps[pi + 1].y)
                continue;
            pnls[pnll].pp = &polyp->ps[pi];
            pnls[pnll].link = &pnls[pnll % polyp->pn];
            pnlps[pnll] = &pnls[pnll];
            pnll++;
        }
    } else {
        for (pi = 0; pi < polyp->pn; pi++) {
            if (pi > 0 && polyp->ps[pi].x == polyp->ps[pi - 1].x &&
                polyp->ps[pi].y == polyp->ps[pi - 1].y)
                continue;
            pnls[pnll].pp = &polyp->ps[pi];
            pnls[pnll].link = &pnls[pnll % polyp->pn];
            pnlps[pnll] = &pnls[pnll];
            pnll++;
        }
    }
 
#if defined(DEBUG) && DEBUG >= 1
    fprintf(stderr, "points\n%" PRISIZE_T "\n", pnll);
    for (size_t pnli = 0; pnli < pnll; pnli++)
        fprintf(stderr, "%f %f\n", pnls[pnli].pp->x, pnls[pnli].pp->y);
#endif
 
    /* generate list of triangles */
    if (triangulate(pnlps, pnll)) {
        free(dq.pnlps);
        free(pnlps);
        free(pnls);
        return -2;
    }
 
#if defined(DEBUG) && DEBUG >= 2
    fprintf(stderr, "triangles\n%" PRISIZE_T "\n", LIST_SIZE(&tris));
    for (trii = 0; trii < LIST_SIZE(&tris); trii++)
        for (ei = 0; ei < 3; ei++)
            fprintf(stderr, "%f %f\n", LIST_GET(&tris, trii).e[ei].pnl0p->pp->x,
                    LIST_GET(&tris, trii).e[ei].pnl0p->pp->y);
#endif
 
    /* connect all pairs of triangles that share an edge */
    for (trii = 0; trii < LIST_SIZE(&tris); trii++)
        for (trij = trii + 1; trij < LIST_SIZE(&tris); trij++)
            connecttris(trii, trij);
 
    /* find first and last triangles */
    for (trii = 0; trii < LIST_SIZE(&tris); trii++)
        if (pointintri(trii, &eps[0]))
            break;
    if (trii == LIST_SIZE(&tris)) {
        prerror("source point not in any triangle");
        free(dq.pnlps);
        free(pnlps);
        free(pnls);
        return -1;
    }
    ftrii = trii;
    for (trii = 0; trii < LIST_SIZE(&tris); trii++)
        if (pointintri(trii, &eps[1]))
            break;
    if (trii == LIST_SIZE(&tris)) {
        prerror("destination point not in any triangle");
        free(dq.pnlps);
        free(pnlps);
        free(pnls);
        return -1;
    }
    ltrii = trii;
 
    /* mark the strip of triangles from eps[0] to eps[1] */
    if (!marktripath(ftrii, ltrii)) {
        prerror("cannot find triangle path");
        free(dq.pnlps);
        free(pnlps);
        free(pnls);
        /* a straight line is better than failing */
        if (growops(2) != 0)
                return -2;
        output->pn = 2;
        ops[0] = eps[0], ops[1] = eps[1];
        output->ps = ops;
        return 0;
    }
 
    /* if endpoints in same triangle, use a single line */
    if (ftrii == ltrii) {
        free(dq.pnlps);
        free(pnlps);
        free(pnls);
        if (growops(2) != 0)
                return -2;
        output->pn = 2;
        ops[0] = eps[0], ops[1] = eps[1];
        output->ps = ops;
        return 0;
    }
 
    /* build funnel and shortest path linked list (in add2dq) */
    epnls[0].pp = &eps[0], epnls[0].link = NULL;
    epnls[1].pp = &eps[1], epnls[1].link = NULL;
    add2dq(&dq, DQ_FRONT, &epnls[0]);
    dq.apex = dq.fpnlpi;
    trii = ftrii;
    while (trii != SIZE_MAX) {
        trip = LIST_AT(&tris, trii);
        trip->mark = 2;
 
        /* find the left and right points of the exiting edge */
        for (ei = 0; ei < 3; ei++)
            if (trip->e[ei].right_index != SIZE_MAX && LIST_GET(&tris, trip->e[ei].right_index).mark == 1)
                break;
        if (ei == 3) {          /* in last triangle */
            if (ccw(eps[1], *dq.pnlps[dq.fpnlpi]->pp,
                    *dq.pnlps[dq.lpnlpi]->pp) == ISCCW)
                lpnlp = dq.pnlps[dq.lpnlpi], rpnlp = &epnls[1];
            else
                lpnlp = &epnls[1], rpnlp = dq.pnlps[dq.lpnlpi];
        } else {
            pnlp = trip->e[(ei + 1) % 3].pnl1p;
            if (ccw(*trip->e[ei].pnl0p->pp, *pnlp->pp,
                    *trip->e[ei].pnl1p->pp) == ISCCW)
                lpnlp = trip->e[ei].pnl1p, rpnlp = trip->e[ei].pnl0p;
            else
                lpnlp = trip->e[ei].pnl0p, rpnlp = trip->e[ei].pnl1p;
        }
 
        /* update deque */
        if (trii == ftrii) {
            add2dq(&dq, DQ_BACK, lpnlp);
            add2dq(&dq, DQ_FRONT, rpnlp);
        } else {
            if (dq.pnlps[dq.fpnlpi] != rpnlp
                && dq.pnlps[dq.lpnlpi] != rpnlp) {
                /* add right point to deque */
                size_t splitindex = finddqsplit(&dq, rpnlp);
                splitdq(&dq, DQ_BACK, splitindex);
                add2dq(&dq, DQ_FRONT, rpnlp);
                /* if the split is behind the apex, then reset apex */
                if (splitindex > dq.apex)
                    dq.apex = splitindex;
            } else {
                /* add left point to deque */
                size_t splitindex = finddqsplit(&dq, lpnlp);
                splitdq(&dq, DQ_FRONT, splitindex);
                add2dq(&dq, DQ_BACK, lpnlp);
                /* if the split is in front of the apex, then reset apex */
                if (splitindex < dq.apex)
                    dq.apex = splitindex;
            }
        }
        trii = SIZE_MAX;
        for (ei = 0; ei < 3; ei++)
            if (trip->e[ei].right_index != SIZE_MAX && LIST_GET(&tris, trip->e[ei].right_index).mark == 1) {
                trii = trip->e[ei].right_index;
                break;
            }
    }
 
#if defined(DEBUG) && DEBUG >= 1
    fprintf(stderr, "polypath");
    for (pnlp = &epnls[1]; pnlp; pnlp = pnlp->link)
        fprintf(stderr, " %f %f", pnlp->pp->x, pnlp->pp->y);
    fprintf(stderr, "\n");
#endif
 
    free(dq.pnlps);
    size_t i;
    for (i = 0, pnlp = &epnls[1]; pnlp; pnlp = pnlp->link)
        i++;
    if (growops(i) != 0) {
        free(pnlps);
        free(pnls);
        return -2;
    }
    output->pn = i;
    for (i = i - 1, pnlp = &epnls[1]; pnlp; i--, pnlp = pnlp->link)
        ops[i] = *pnlp->pp;
    output->ps = ops;
    free(pnlps);
    free(pnls);
 
    return 0;
}
 
/* triangulate polygon */
static int triangulate(pointnlink_t **points, size_t point_count) {
        if (point_count > 3)
        {
                for (size_t pnli = 0; pnli < point_count; pnli++)
                {
                        const size_t pnlip1 = (pnli + 1) % point_count;
                        const size_t pnlip2 = (pnli + 2) % point_count;
                        if (isdiagonal(pnli, pnlip2, points, point_count, point_indexer))
                        {
                                if (loadtriangle(points[pnli], points[pnlip1], points[pnlip2]) != 0)
                                        return -1;
                                for (pnli = pnlip1; pnli < point_count - 1; pnli++)
                                        points[pnli] = points[pnli + 1];
                                return triangulate(points, point_count - 1);
                        }
                }
                prerror("triangulation failed");
    } 
        else {
                if (loadtriangle(points[0], points[1], points[2]) != 0)
                        return -1;
        }
 
    return 0;
}
 
static int loadtriangle(pointnlink_t * pnlap, pointnlink_t * pnlbp,
                         pointnlink_t * pnlcp)
{
    triangle_t trip = {0};
    trip.e[0].pnl0p = pnlap, trip.e[0].pnl1p = pnlbp, trip.e[0].right_index = SIZE_MAX;
    trip.e[1].pnl0p = pnlbp, trip.e[1].pnl1p = pnlcp, trip.e[1].right_index = SIZE_MAX;
    trip.e[2].pnl0p = pnlcp, trip.e[2].pnl1p = pnlap, trip.e[2].right_index = SIZE_MAX;
 
    if (!LIST_TRY_APPEND(&tris, trip)) {
        prerror("cannot realloc tris");
        return -1;
    }
 
    return 0;
}
 
/* connect a pair of triangles at their common edge (if any) */
static void connecttris(size_t tri1, size_t tri2) {
    triangle_t *tri1p, *tri2p;
    int ei, ej;
 
    for (ei = 0; ei < 3; ei++) {
        for (ej = 0; ej < 3; ej++) {
            tri1p = LIST_AT(&tris, tri1);
            tri2p = LIST_AT(&tris, tri2);
            if ((tri1p->e[ei].pnl0p->pp == tri2p->e[ej].pnl0p->pp &&
                 tri1p->e[ei].pnl1p->pp == tri2p->e[ej].pnl1p->pp) ||
                (tri1p->e[ei].pnl0p->pp == tri2p->e[ej].pnl1p->pp &&
                 tri1p->e[ei].pnl1p->pp == tri2p->e[ej].pnl0p->pp))
                tri1p->e[ei].right_index = tri2, tri2p->e[ej].right_index = tri1;
        }
    }
}
 
/* find and mark path from trii, to trij */
static bool marktripath(size_t trii, size_t trij) {
    int ei;
 
    if (LIST_GET(&tris, trii).mark)
        return false;
    LIST_AT(&tris, trii)->mark = 1;
    if (trii == trij)
        return true;
    for (ei = 0; ei < 3; ei++)
        if (LIST_GET(&tris, trii).e[ei].right_index != SIZE_MAX &&
            marktripath(LIST_GET(&tris, trii).e[ei].right_index, trij))
            return true;
    LIST_AT(&tris, trii)->mark = 0;
    return false;
}
 
/* add a new point to the deque, either front or back */
static void add2dq(deque_t *dq, int side, pointnlink_t *pnlp) {
    if (side == DQ_FRONT) {
        if (dq->lpnlpi >= dq->fpnlpi)
            pnlp->link = dq->pnlps[dq->fpnlpi]; /* shortest path links */
        dq->fpnlpi--;
        dq->pnlps[dq->fpnlpi] = pnlp;
    } else {
        if (dq->lpnlpi >= dq->fpnlpi)
            pnlp->link = dq->pnlps[dq->lpnlpi]; /* shortest path links */
        dq->lpnlpi++;
        dq->pnlps[dq->lpnlpi] = pnlp;
    }
}
 
static void splitdq(deque_t *dq, int side, size_t index) {
    if (side == DQ_FRONT)
        dq->lpnlpi = index;
    else
        dq->fpnlpi = index;
}
 
static size_t finddqsplit(const deque_t *dq, pointnlink_t *pnlp) {
    for (size_t index = dq->fpnlpi; index < dq->apex; index++)
        if (ccw(*dq->pnlps[index + 1]->pp, *dq->pnlps[index]->pp, *pnlp->pp) == ISCCW)
            return index;
    for (size_t index = dq->lpnlpi; index > dq->apex; index--)
        if (ccw(*dq->pnlps[index - 1]->pp, *dq->pnlps[index]->pp, *pnlp->pp) == ISCW)
            return index;
    return dq->apex;
}
 
static int pointintri(size_t trii, Ppoint_t *pp) {
    int ei, sum;
 
    for (ei = 0, sum = 0; ei < 3; ei++)
        if (ccw(*LIST_GET(&tris, trii).e[ei].pnl0p->pp,
                *LIST_GET(&tris, trii).e[ei].pnl1p->pp, *pp) != ISCW)
            sum++;
    return sum == 3 || sum == 0;
}
 
static int growops(size_t newopn) {
    if (newopn <= opn)
        return 0;
    Ppoint_t *new_ops = realloc(ops, POINTSIZE * newopn);
    if (new_ops == NULL) {
        prerror("cannot realloc ops");
        return -1;
    }
    ops = new_ops;
    opn = newopn;
 
    return 0;
}