distance from point to line

[Darkmaster]

I'm having problems with the calculation of the distance from a point to a line in a two dimensional space. It's something wrong with the math in this code, but i just can't find the problem. Maybe you can help me with this or have some working functions.

double Detection::distance_to_Line(cv::Point line_start, cv::Point line_end, cv::Point point)
{
	cv::Point line; //direction of the line
	line.x = line_end.x - line_start.x;
	line.y = line_end.y - line_start.y;
	cv::Point point_to_start; //vector from the point to the start of the line
	point_to_start.x = line_start.x - point.x;
	point_to_start.y = line_start.y - point.y;
	int dot = point_to_start.x * line.x + point_to_start.y * line.y; //dot product of point_to_start * line
	cv::Point distance; //shortest distance vector from point to line
	distance.x = point_to_start.x - dot * line.x; 
	distance.y = point_to_start.y - dot * line.y;
	double output = sqrt((double)(distance.x * distance.x + distance.y * distance.y));
	return output;
}

cv:Point is from the OpenCV library. You can just use a 2d instead and post your code, if you don't have the library.

[ne555]

double distance_to_line( point begin, point end, point x ){
   //translate the begin to the origin
   end -= begin;
   x -= begin;

   //¿do you see the triangle?
   double area = cross_product(x, end);
   return area / norm(end);
}

As a bonus it would tell you if the point is at the right or the left of the line.

[mik2718]

I make it something like this (not tested)

double Detection::distance_to_Line(cv::Point line_start, cv::Point line_end, cv::Point point)
{
	cv::Point line; //direction of the line
	line.x = line_end.x - line_start.x;
	line.y = line_end.y - line_start.y;
	cv::Point point_to_start; //vector from the point to the start of the line
	point_to_start.x = line_start.x - point.x;
	point_to_start.y = line_start.y - point.y;
	int dot = point_to_start.x * line.x + point_to_start.y * line.y; //dot product of point_to_start * line
	cv::Point distance; //shortest distance vector from point to line

        int linelength2 = line.x*line.x+line.y*line.y;//length of line squared
        distance.x = double(dot * line.x) / linelength2 + line_start.x;
        distance.y = double(dot * line.y) / linelength2 + line_start.y

	double output = sqrt((double)(distance.x * distance.x + distance.y * distance.y));
	return output;
}

[Darkmaster]

finally got it to work

double Detection::distance_to_Line(cv::Point line_start, cv::Point line_end, cv::Point point)
{
	double normalLength = _hypot(line_end.x - line_start.x, line_end.y - line_start.y);
	double distance = (double)((point.x - line_start.x) * (line_end.y - line_start.y) - (point.y - line_start.y) * (line_end.x - line_start.x)) / normalLength;
	return distance;
}

return abs(distance), if you don't want a vector.

[ne555]

double distance = -line_direction.x * diff.x + line_direction.y * diff.y; ¿what are you doing here?

If you intend to use my code

double cross_product( point a, point b ){
   return a.x*b.y - a.y*b.x;
}

[Darkmaster]

think that was the dot product and the minus is neccessary to create the normal vector from the direction vector