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mathvectorcoordinates

Find distance to middle of line

So I have a line, connecting two points, and I want to give this line a visual name in my canvas. I want this name to be positioned right at the middle of the line but with an offset so that the text doesn't go through the line. Determining the middle of the line isn't that hard you can just find it out like that:

formula of middle point

And the line equation of the normal to the line can be determined pretty easy too:

line equation

Where you can find out n just by inserting P into the equation.

Now to the problem: For a given distance to the line, I want to find a point P(xn, yn) that is on that normal to the line through the middle of the line. After inserting the linear function into the distance formula I end up with this:

formula for P(xn, yn)

Not only am I not able to transform this equation to get a valid value for xn, I believe there has to be an mathematically easier way to achieve this.

Solution

  • Line middle is

    mx = (x1 + x2)/2
my = (y1 + y2)/2

    Line length is

    len = sqrt((x1 - x2)^2 + (y1 - y2)^2)

    Normalized direction vector of the line is

    dx = (x2-x1) / len
dy = (y2-y1) / len

    Perpendicular vector is

    nx = -dy
ny = dx

    Point at offset d from middle is

    px = mx + d * nx
py = mx + d * ny

    or for other side

    px = mx - d * nx
py = mx - d * ny