route.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 <assert.h>
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <pathplan/pathutil.h>
#include <pathplan/solvers.h>
 
#define EPSILON1 1E-3
#define EPSILON2 1E-6
 
typedef struct tna_t {
    double t;
    Ppoint_t a[2];
} tna_t;
 
#define DISTSQ(a, b) ( \
    (((a).x - (b).x) * ((a).x - (b).x)) + (((a).y - (b).y) * ((a).y - (b).y)) \
)
 
#define POINTSIZE sizeof (Ppoint_t)
 
static Ppoint_t *ops;
static size_t opn, opl;
 
static int reallyroutespline(Pedge_t *, size_t,
                             Ppoint_t *, int, Ppoint_t, Ppoint_t);
static int mkspline(Ppoint_t *, int, const tna_t *, Ppoint_t, Ppoint_t,
                    Ppoint_t *, Ppoint_t *, Ppoint_t *, Ppoint_t *);
static int splinefits(Pedge_t *, size_t, Ppoint_t, Pvector_t, Ppoint_t,
                      Pvector_t, Ppoint_t *, int);
static int splineisinside(Pedge_t *, size_t, Ppoint_t *);
static int splineintersectsline(Ppoint_t *, Ppoint_t *, double *);
static void points2coeff(double, double, double, double, double *);
static void addroot(double, double *, int *);
 
static Pvector_t normv(Pvector_t);
 
static int growops(size_t);
 
static Ppoint_t add(Ppoint_t, Ppoint_t);
static Ppoint_t sub(Ppoint_t, Ppoint_t);
static double dist(Ppoint_t, Ppoint_t);
static Ppoint_t scale(Ppoint_t, double);
static double dot(Ppoint_t, Ppoint_t);
static double B0(double t);
static double B1(double t);
static double B2(double t);
static double B3(double t);
static double B01(double t);
static double B23(double t);
 
/* Given a set of barrier line segments edges as obstacles, a template
 * path input_route, and endpoint vectors endpoint_slopes, construct a spline
 * fitting the input and endpoint vectors, and return in output_route.
 * Return 0 on success and -1 on failure, including no memory.
 */
int Proutespline(Pedge_t *barriers, size_t n_barriers, Ppolyline_t input_route,
                 Ppoint_t endpoint_slopes[2], Ppolyline_t *output_route) {
    Ppoint_t *inps;
    int inpn;
 
    /* unpack into previous format rather than modify legacy code */
    inps = input_route.ps;
    assert(input_route.pn <= INT_MAX);
    inpn = (int)input_route.pn;
 
    /* generate the splines */
    endpoint_slopes[0] = normv(endpoint_slopes[0]);
    endpoint_slopes[1] = normv(endpoint_slopes[1]);
    opl = 0;
    if (growops(4) < 0) {
        return -1;
    }
    ops[opl++] = inps[0];
    if (reallyroutespline(barriers, n_barriers, inps, inpn, endpoint_slopes[0],
                          endpoint_slopes[1]) == -1)
        return -1;
    output_route->pn = opl;
    output_route->ps = ops;
 
    return 0;
}
 
static int reallyroutespline(Pedge_t *edges, size_t edgen, Ppoint_t *inps,
                             int inpn, Ppoint_t ev0, Ppoint_t ev1) {
    Ppoint_t p1, p2;
    Pvector_t v1, v2;
    double d;
 
    assert(inpn > 0);
    tna_t *const tnas = calloc((size_t)inpn, sizeof(tna_t));
    if (tnas == NULL) {
        return -1;
    }
    tnas[0].t = 0;
    for (int i = 1; i < inpn; i++)
        tnas[i].t = tnas[i - 1].t + dist(inps[i], inps[i - 1]);
    for (int i = 1; i < inpn; i++)
        tnas[i].t /= tnas[inpn - 1].t;
    for (int i = 0; i < inpn; i++) {
        tnas[i].a[0] = scale(ev0, B1(tnas[i].t));
        tnas[i].a[1] = scale(ev1, B2(tnas[i].t));
    }
    if (mkspline(inps, inpn, tnas, ev0, ev1, &p1, &v1, &p2, &v2) == -1) {
        free(tnas);
        return -1;
    }
    int fit = splinefits(edges, edgen, p1, v1, p2, v2, inps, inpn);
    if (fit > 0) {
        free(tnas);
        return 0;
    }
    if (fit < 0) {
        free(tnas);
        return -1;
    }
    const Ppoint_t cp1 = add(p1, scale(v1, 1 / 3.0));
    const Ppoint_t cp2 = sub(p2, scale(v2, 1 / 3.0));
    int maxi = -1;
    double maxd = -1;
    for (int i = 1; i < inpn - 1; i++) {
        const double t = tnas[i].t;
        const Ppoint_t p = {
          .x = B0(t) * p1.x + B1(t) * cp1.x + B2(t) * cp2.x + B3(t) * p2.x,
          .y = B0(t) * p1.y + B1(t) * cp1.y + B2(t) * cp2.y + B3(t) * p2.y};
        if ((d = dist(p, inps[i])) > maxd) {
            maxd = d;
            maxi = i;
        }
    }
    free(tnas);
    const int spliti = maxi;
    const Pvector_t splitv1 = normv(sub(inps[spliti], inps[spliti - 1]));
    const Pvector_t splitv2 = normv(sub(inps[spliti + 1], inps[spliti]));
    const Pvector_t splitv = normv(add(splitv1, splitv2));
    if (reallyroutespline(edges, edgen, inps, spliti + 1, ev0, splitv) < 0) {
        return -1;
    }
    if (reallyroutespline(edges, edgen, &inps[spliti], inpn - spliti, splitv,
                          ev1) < 0) {
        return -1;
    }
    return 0;
}
 
static int mkspline(Ppoint_t * inps, int inpn, const tna_t *tnas, Ppoint_t ev0,
                    Ppoint_t ev1, Ppoint_t * sp0, Ppoint_t * sv0,
                    Ppoint_t * sp1, Ppoint_t * sv1)
{
    Ppoint_t tmp;
    double c[2][2], x[2], det01, det0X, detX1;
    double d01, scale0, scale3;
    int i;
 
    scale0 = scale3 = 0.0;
    c[0][0] = c[0][1] = c[1][0] = c[1][1] = 0.0;
    x[0] = x[1] = 0.0;
    for (i = 0; i < inpn; i++) {
        c[0][0] += dot(tnas[i].a[0], tnas[i].a[0]);
        c[0][1] += dot(tnas[i].a[0], tnas[i].a[1]);
        c[1][0] = c[0][1];
        c[1][1] += dot(tnas[i].a[1], tnas[i].a[1]);
        tmp = sub(inps[i], add(scale(inps[0], B01(tnas[i].t)),
                               scale(inps[inpn - 1], B23(tnas[i].t))));
        x[0] += dot(tnas[i].a[0], tmp);
        x[1] += dot(tnas[i].a[1], tmp);
    }
    det01 = c[0][0] * c[1][1] - c[1][0] * c[0][1];
    det0X = c[0][0] * x[1] - c[0][1] * x[0];
    detX1 = x[0] * c[1][1] - x[1] * c[0][1];
    if (fabs(det01) >= 1e-6) {
        scale0 = detX1 / det01;
        scale3 = det0X / det01;
    }
    if (fabs(det01) < 1e-6 || scale0 <= 0.0 || scale3 <= 0.0) {
        d01 = dist(inps[0], inps[inpn - 1]) / 3.0;
        scale0 = d01;
        scale3 = d01;
    }
    *sp0 = inps[0];
    *sv0 = scale(ev0, scale0);
    *sp1 = inps[inpn - 1];
    *sv1 = scale(ev1, scale3);
    return 0;
}
 
static double dist_n(Ppoint_t * p, int n)
{
    int i;
    double rv;
 
    rv = 0.0;
    for (i = 1; i < n; i++) {
        rv += hypot(p[i].x - p[i - 1].x, p[i].y - p[i - 1].y);
    }
    return rv;
}
 
static int splinefits(Pedge_t *edges, size_t edgen, Ppoint_t pa, Pvector_t va,
                      Ppoint_t pb, Pvector_t vb, Ppoint_t *inps, int inpn) {
    Ppoint_t sps[4];
    double a;
    int pi;
    int forceflag;
    int first = 1;
 
    forceflag = (inpn == 2 ? 1 : 0);
 
    a = 4;
    for (;;) {
        sps[0].x = pa.x;
        sps[0].y = pa.y;
        sps[1].x = pa.x + a * va.x / 3.0;
        sps[1].y = pa.y + a * va.y / 3.0;
        sps[2].x = pb.x - a * vb.x / 3.0;
        sps[2].y = pb.y - a * vb.y / 3.0;
        sps[3].x = pb.x;
        sps[3].y = pb.y;
 
        /* shortcuts (paths shorter than the shortest path) not allowed -
         * they must be outside the constraint polygon.  this can happen
         * if the candidate spline intersects the constraint polygon exactly
         * on sides or vertices.  maybe this could be more elegant, but
         * it solves the immediate problem. we could also try jittering the
         * constraint polygon, or computing the candidate spline more carefully,
         * for example using the path. SCN */
 
        if (first && (dist_n(sps, 4) < (dist_n(inps, inpn) - EPSILON1)))
            return 0;
        first = 0;
 
        if (splineisinside(edges, edgen, &sps[0])) {
            if (growops(opl + 4) < 0) {
                return -1;
            }
            for (pi = 1; pi < 4; pi++)
                ops[opl].x = sps[pi].x, ops[opl++].y = sps[pi].y;
#if defined(DEBUG) && DEBUG >= 1
            fprintf(stderr, "success: %f %f\n", a, a);
#endif
            return 1;
        }
        // is `a` 0, accounting for the precision with which it was computed (on the
        // last loop iteration) below?
        if (a < 0.005) {
            if (forceflag) {
                if (growops(opl + 4) < 0) {
                    return -1;
                }
                for (pi = 1; pi < 4; pi++)
                    ops[opl].x = sps[pi].x, ops[opl++].y = sps[pi].y;
#if defined(DEBUG) && DEBUG >= 1
                fprintf(stderr, "forced straight line: %f %f\n", a, a);
#endif
                return 1;
            }
            break;
        }
        if (a > .01)
            a /= 2;
        else
            a = 0;
    }
#if defined(DEBUG) && DEBUG >= 1
    fprintf(stderr, "failure\n");
#endif
    return 0;
}
 
static int splineisinside(Pedge_t *edges, size_t edgen, Ppoint_t *sps) {
    double roots[4];
    int rooti, rootn;
    Ppoint_t lps[2], ip;
    double t, ta, tb, tc, td;
 
    for (size_t ei = 0; ei < edgen; ei++) {
        lps[0] = edges[ei].a, lps[1] = edges[ei].b;
        if ((rootn = splineintersectsline(sps, lps, roots)) == 4)
            continue;
        for (rooti = 0; rooti < rootn; rooti++) {
            if (roots[rooti] < EPSILON2 || roots[rooti] > 1 - EPSILON2)
                continue;
            t = roots[rooti];
            td = t * t * t;
            tc = 3 * t * t * (1 - t);
            tb = 3 * t * (1 - t) * (1 - t);
            ta = (1 - t) * (1 - t) * (1 - t);
            ip.x = ta * sps[0].x + tb * sps[1].x +
                tc * sps[2].x + td * sps[3].x;
            ip.y = ta * sps[0].y + tb * sps[1].y +
                tc * sps[2].y + td * sps[3].y;
            if (DISTSQ(ip, lps[0]) < EPSILON1 ||
                DISTSQ(ip, lps[1]) < EPSILON1)
                continue;
            return 0;
        }
    }
    return 1;
}
 
static int splineintersectsline(Ppoint_t * sps, Ppoint_t * lps,
                                double *roots)
{
    double scoeff[4], xcoeff[2], ycoeff[2];
    double xroots[3], yroots[3], tv, sv, rat;
    int rootn, xrootn, yrootn, i, j;
 
    xcoeff[0] = lps[0].x;
    xcoeff[1] = lps[1].x - lps[0].x;
    ycoeff[0] = lps[0].y;
    ycoeff[1] = lps[1].y - lps[0].y;
    rootn = 0;
    if (xcoeff[1] == 0) {
        if (ycoeff[1] == 0) {
            points2coeff(sps[0].x, sps[1].x, sps[2].x, sps[3].x, scoeff);
            scoeff[0] -= xcoeff[0];
            xrootn = solve3(scoeff, xroots);
            points2coeff(sps[0].y, sps[1].y, sps[2].y, sps[3].y, scoeff);
            scoeff[0] -= ycoeff[0];
            yrootn = solve3(scoeff, yroots);
            if (xrootn == 4)
                if (yrootn == 4)
                    return 4;
                else
                    for (j = 0; j < yrootn; j++)
                        addroot(yroots[j], roots, &rootn);
            else if (yrootn == 4)
                for (i = 0; i < xrootn; i++)
                    addroot(xroots[i], roots, &rootn);
            else
                for (i = 0; i < xrootn; i++)
                    for (j = 0; j < yrootn; j++)
                        if (xroots[i] == yroots[j])
                            addroot(xroots[i], roots, &rootn);
            return rootn;
        } else {
            points2coeff(sps[0].x, sps[1].x, sps[2].x, sps[3].x, scoeff);
            scoeff[0] -= xcoeff[0];
            xrootn = solve3(scoeff, xroots);
            if (xrootn == 4)
                return 4;
            for (i = 0; i < xrootn; i++) {
                tv = xroots[i];
                if (tv >= 0 && tv <= 1) {
                    points2coeff(sps[0].y, sps[1].y, sps[2].y, sps[3].y,
                                 scoeff);
                    sv = scoeff[0] + tv * (scoeff[1] + tv *
                                           (scoeff[2] + tv * scoeff[3]));
                    sv = (sv - ycoeff[0]) / ycoeff[1];
                    if ((0 <= sv) && (sv <= 1))
                        addroot(tv, roots, &rootn);
                }
            }
            return rootn;
        }
    } else {
        rat = ycoeff[1] / xcoeff[1];
        points2coeff(sps[0].y - rat * sps[0].x, sps[1].y - rat * sps[1].x,
                     sps[2].y - rat * sps[2].x, sps[3].y - rat * sps[3].x,
                     scoeff);
        scoeff[0] += rat * xcoeff[0] - ycoeff[0];
        xrootn = solve3(scoeff, xroots);
        if (xrootn == 4)
            return 4;
        for (i = 0; i < xrootn; i++) {
            tv = xroots[i];
            if (tv >= 0 && tv <= 1) {
                points2coeff(sps[0].x, sps[1].x, sps[2].x, sps[3].x,
                             scoeff);
                sv = scoeff[0] + tv * (scoeff[1] +
                                       tv * (scoeff[2] + tv * scoeff[3]));
                sv = (sv - xcoeff[0]) / xcoeff[1];
                if ((0 <= sv) && (sv <= 1))
                    addroot(tv, roots, &rootn);
            }
        }
        return rootn;
    }
}
 
static void points2coeff(double v0, double v1, double v2, double v3,
                         double *coeff)
{
    coeff[3] = v3 + 3 * v1 - (v0 + 3 * v2);
    coeff[2] = 3 * v0 + 3 * v2 - 6 * v1;
    coeff[1] = 3 * (v1 - v0);
    coeff[0] = v0;
}
 
static void addroot(double root, double *roots, int *rootnp)
{
    if (root >= 0 && root <= 1)
        roots[*rootnp] = root, (*rootnp)++;
}
 
static Pvector_t normv(Pvector_t v)
{
    double d;
 
    d = v.x * v.x + v.y * v.y;
    if (d > 1e-6) {
        d = sqrt(d);
        v.x /= d, v.y /= d;
    }
    return v;
}
 
static int growops(size_t newopn) {
    if (newopn <= opn)
        return 0;
    if (!(ops = realloc(ops, POINTSIZE * newopn))) {
        return -1;
    }
    opn = newopn;
    return 0;
}
 
static Ppoint_t add(Ppoint_t p1, Ppoint_t p2)
{
    p1.x += p2.x, p1.y += p2.y;
    return p1;
}
 
static Ppoint_t sub(Ppoint_t p1, Ppoint_t p2)
{
    p1.x -= p2.x, p1.y -= p2.y;
    return p1;
}
 
static double dist(Ppoint_t p1, Ppoint_t p2)
{
    double dx, dy;
 
    dx = p2.x - p1.x, dy = p2.y - p1.y;
    return hypot(dx, dy);
}
 
static Ppoint_t scale(Ppoint_t p, double c)
{
    p.x *= c, p.y *= c;
    return p;
}
 
static double dot(Ppoint_t p1, Ppoint_t p2)
{
    return p1.x * p2.x + p1.y * p2.y;
}
 
static double B0(double t)
{
    double tmp = 1.0 - t;
    return tmp * tmp * tmp;
}
 
static double B1(double t)
{
    double tmp = 1.0 - t;
    return 3 * t * tmp * tmp;
}
 
static double B2(double t)
{
    double tmp = 1.0 - t;
    return 3 * t * t * tmp;
}
 
static double B3(double t)
{
    return t * t * t;
}
 
static double B01(double t)
{
    double tmp = 1.0 - t;
    return tmp * tmp * (tmp + 3 * t);
}
 
static double B23(double t)
{
    double tmp = 1.0 - t;
    return t * t * (3 * tmp + t);
}