/*    superman.c

    Compute Superman's flight path -- geometry example 
*/

/* Copyright 2003-2020 by Steven S. Skiena; all rights reserved.
Permission is granted for use in non-commerical applications
provided this copyright notice remains intact and unchanged.

These programs appear in my books:

"The Algorithm Design Manual" by Steven Skiena, second edition, Springer,
London 2008.  See out website www.algorist.com for additional information
or https://www.amazon.com/exec/obidos/ASIN/1848000693/thealgorith01-20

"Programming Challenges: The Programming Contest Training Manual"
by Steven Skiena and Miguel Revilla, Springer-Verlag, New York 2003.
See our website www.programming-challenges.com for additional information,
or https://www.amazon.com/exec/obidos/ASIN/0387001638/thealgorithmrepo/
*/



#define MAXN 100    /* maximum number of circles */

#include <math.h>
#include <stdio.h>
#include <stdbool.h>

#include "geometry.h"

point s;         /* Superman's initial position */
point t;         /* target position */
int ncircles;    /* number of circles */
circle c[MAXN];  /* circles data structure */

void superman(void) {
    line l;               /* line from start to target position */
    point close;          /* closest point */
    double d;             /* distance from circle-center */
    double xray = 0.0;    /* length of intersection with circles */
    double around = 0.0;  /* length around circular arcs */
    double angle;         /* angle subtended by arc */
    double travel;        /* total travel distance */
    int i;                /* counter */

    points_to_line(s, t, &l);

    for (i = 1; i <= ncircles; i++) {
        closest_point(c[i].c,l, close);
        d = distance(c[i].c, close);
        if ((d >= 0) && (d < c[i].r) && point_in_box(close, s, t)) {
            xray += 2 * sqrt(c[i].r * c[i].r - d * d);
            angle = acos(d/c[i].r);
            around += ((2 * angle) / (2 * PI)) * (2 * PI * c[i].r);
            printf("circle %d (%7.3lf,%7.3lf,%7.3lf) is %7.3lf away from l, xray=%7.3lf around=%7.3lf angle=%7.3lf.\n",
                    i, c[i].c[X], c[i].c[Y], c[i].r, d, xray, around, angle);
        }
    }

    travel = distance(s, t) - xray + around;
    printf("Superman sees through %7.3lf units, and flies %7.3lf units\n",
    xray, travel);
}

int main(void) {
    int i;    /* counter */

    scanf("%lf %lf", &s[X], &s[Y]);
    scanf("%lf %lf", &t[X], &t[Y]);
    scanf("%d", &ncircles);
    for (i = 1; i <= ncircles; i++) {
        scanf("%lf %lf %lf", &c[i].c[X], &c[i].c[Y], &c[i].r);
    }

    printf("%7.3lf %7.3lf\n",s[X],s[Y]);
    printf("%7.3lf %7.3lf\n",t[X],t[Y]);
    printf("%d\n",ncircles);
    for (i = 1; i <= ncircles; i++) {
        printf("%7.3lf %7.3lf %7.3lf\n", c[i].c[X], c[i].c[Y], c[i].r);
    }

    superman();

    return 0;
}