Adrián Deccico

Hi, below there is a little snippet that calculates the closest point to a segment. It is written in C++ but could be easily translated to any other language. Disclaimer: given its age, it use hungarian notation, and some names are in spanish, but it was deeply tested and works ok.

//--------------------------------------------------------------------------------------------------------
//author: Adrián Deccico - http://adrian.org.ar
/*
Description: calculate the closest point belonging to a given segment.
Parameters:
nSx1, nSy1 =  First point of the segment
nSx2, int nSy2 = Second point of the segment
nPx, int nPy = The point to analize
*nCercaX,  *nCercaY = The closest point to the given point (nPx,nPy) that belongs to the segment
Returns: The distance between the given point and the point found of the segment
*/
double ElPuntoMasCercanoAUnSegmento(double nSx1, double nSy1, double nSx2,
double nSy2, double nPx, double nPy,
double *nCercaX,  double *nCercaY)
{

//caracterizo la recta del segmento dado Y=m*X + b
double m, b;

bool bEsHorizontalOVertical = false;

//el segmento es vertical
if (nSx2 == nSx1){
    *nCercaX = nSx1;
    *nCercaY = nPy;
    bEsHorizontalOVertical = true;
}

//el segmento es horizontal
if (nSy2 == nSy1){
    *nCercaY = nSy1;
    *nCercaX = nPx;
    bEsHorizontalOVertical = true;
}

//el segmento está caracterizado por una recta \"AX + BY + C = 0\" con
// A y B distintos de cero
if (!bEsHorizontalOVertical)
{
    m= (nSy2 - nSy1) / (nSx2 - nSx1);
    b = nSy1 - (nSx1 * m);

    //caracterizo la recta que une al punto dado con el punto más
    // cercano dentro del segmento Y=m1*X + b1
    double m1, b1;

    m1 = -1 / m;
    b1 = -m1 * nPx + nPy;

    //encuentro el punto de intersección
    *nCercaX =  (b1 - b) / (m - m1);
    *nCercaY =  m * *nCercaX + b;
}

//verificar que el punto encontrado está dentro del segmento
if (*nCercaX < min(nSx1,nSx2)
||  *nCercaX > max(nSx1,nSx2)
||  *nCercaY < min(nSy1,nSy2)
||  *nCercaY > max(nSy1,nSy2) )
{
    //el punto más cercano será uno de los dos extremos (el más cercano al punto)
    if (dDistanciaEntrePuntos(nSx1, nSy1, nPx, nPy) <= dDistanciaEntrePuntos(nSx2, nSy2, nPx, nPy))
    {
        *nCercaX = nSx1;
        *nCercaY = nSy1;
    }
    else
    {
        *nCercaX = nSx2;
        *nCercaY = nSy2;
    }
}

return dDistanciaEntrePuntos(nPx, nPy, *nCercaX , *nCercaY);

}
//--------------------------------------------------------------------------------------------

//------------------------------------------------------------------------
//return the distance between thwo points in a x,y plane.
double dDistanciaEntrePuntos(double lOldX, double lOldY,
double lNewX, double lNewY)
{
    double x = lNewX - lOldX;
    double y = lNewY - lOldY;

    return sqrt(pow(x,2) + pow(y,2));
}
//------------------------------------------------------------------------