Path: utzoo!attcan!uunet!samsung!gem.mps.ohio-state.edu!apple!sun-barr!newstop!sun!looney!dopey
From: dopey%looney@Sun.COM (Can't ya tell by the name)
Newsgroups: comp.misc
Subject: Re: Trig question
Message-ID: <128175@sun.Eng.Sun.COM>
Date: 21 Nov 89 02:53:10 GMT
References: <RON.89Nov17110506@clarity.Princeton.EDU> <4881@cbnewsc.ATT.COM>
Sender: news@sun.Eng.Sun.COM
Reply-To: dopey@sun.UUCP (Can't ya tell by the name)
Distribution: comp
Organization: Sun Microsystems, Mountain View
Lines: 87

In article <4881@cbnewsc.ATT.COM> ajaym@cbnewsc.ATT.COM (alton.jay.mitchell) writes:
>>    " What is the shortest distance between coordinate (a3, b3) and the line
>>      through coordinates (a1, b1) and (a2, b2)? "
>
>I didn't take the time to compute a formula, but it seems somewhat
>obvious that the answer can be presented in 3 parts:
>
>			(a1,b1)------------------(a2,b2)
>
>If (a3,b3) is "within" the area bounded by the perpendicular
>lines through (a1,b1) and (a2,b2), then the shortest distance
>is the perpendicular line from (a3,b3) to the line shown.
>
>Otherwise, the shortest distance is the line to one of the
>2 points, depending on which "side" of the above mentioned
>area (a3,b3) exists on.

In nitty gritty detail (this works but may not be the BEST way):
I stole this from some code I had written before and checked it
over but I have not run THIS version but I hope it helps. It
only computes the SQUARE of the distance because I was only 
looking for relative distances and finding the square root
was to much over head.

/* This routine computes the SQUARE of the 
 * distance from point x,y to line l
 */

struct line                     /* format of line overlay */
{
        short label;            /* indecates type */
        long x1;                /* start x */
        long y1;                /* start y */
        long x2;                /* end x */
        long y2;                /* end y */
};

#define SIGN(x)         (((x) >= 0)? 1: -1)

double  hypot();

double
point_line(x, y, l)
int     x;
int     y;
struct  line    *l;
{
        double  a;	/* slop of the line */
        double  b;	/* -1 in double form */
        double  c;	/* y intercept */
        double  d0;	/* distance from x,y to "infinite" line */
        double  d1;	/* length of line */
        double  d2;	/* worst case of point to line */
        double  d3;	/* distance from x,y to line endpoint 1 */
        double  d4;	/* distance from x,y to line endpoint 2 */
        double  d;	/* distance from x,y to line */

        if((l->x2 - l->x1) == 0)
        {
                d0 = MIN(ABS(l->y2 - y), ABS(l->y1 - y));
        }
        else
        {   
                a = (double)(l->y2 - l->y1)/(double)(l->x2 - l->x1);
                b = -1;
                c = l->y1 - a*l->x1;
                d0 = (double)(a*x + b*y + c)/(double)(-1*SIGN(c)*hypot(a,b));
                d0 = ABS(d0);
        }

        d1 = hypot((double)ABS(l->x2 - l->x1), (double)ABS(l->y2 - l->y1));

        d2 = hypot(d0, d1);

        d3 = hypot((double)ABS(l->x1 - x), (double)ABS(l->y1 - y));

        d4 = hypot((double)ABS(l->x2 - x), (double)ABS(l->y2 - y));

        d = d0;

        if (d3 > d2 || d4 > d2)
        {
                d = MIN(d3,d4);
        }

        return(ABS(d));
}