Question

I develop in .NET an application that draws some lines.
In the middle of a line I need to draw the line direction array.

Have:
(xA, yA, xB, yB) or (pA, pB) – segment AB points
arrWidth, arrHeight – arrow dimensions;
> B – arrow direction.

Need:
3 new points pArr1, pArr2, pArr3 – points of the directional arrow, that should be situated in the middle of the segment AB.

Answer 1

First I’ll make some definitions.

let:

• p = position vector to tail of line
• v = the line vector
• h = the arrow height
• w = the arrow width
• L = the anti-clockwise rotation by 90 degrees

Then your three points are:

1. p + (|v|/2 – h/2 + w/2 L) v/|v|
2. p + (|v|/2 – h/2 – w/2 L) v/|v|
3. p + (|v|/2 + h/2) v/|v|

Where v/|v| is the unit vector along your line.

In 2 dimensions L is just the mapping (x, y) => (-y, x)

To be more explicit, using the variables in the question, the points above could be written in C# as:

// assuming xA, yA, xB, yB, arrWidth, arrHeight are initialised
var xV = xB - xA;
var yV = yB - yA;
var v = Math.Sqrt(xV*xV + yV*yV);
var pArr1 = new[] {
    xA + xV / 2 - xV * arrHeight / (2 * v) - yV * arrWidth / (2 * v),
    yA + yV / 2 - yV * arrHeight / (2 * v) + xV * arrWidth / (2 * v) };
var pArr2 = new[] {
    xA + xV / 2 - xV * arrHeight / (2 * v) + yV * arrWidth / (2 * v),
    yA + yV / 2 - yV * arrHeight / (2 * v) - xV * arrWidth / (2 * v) };
var pArr3 = new[] {
    xA + xV / 2 + xV * arrHeight / (2 * v),
    yA + yV / 2 + yV * arrHeight / (2 * v) };