libGDX - How can I draw polygon as a line (Miter join type)?

Question

If I have known vertices (RED) like this image:

• Drawing Lines is Hard
• Line Joins

How can I determine these below unknown vertices from above known vertices which join lines as a miter joining with each other?

Answer 1

First of all, look at this Q/A. Your task is the same, only a bit simpler, since line thickness is the same for all segments.

Basically, you need to calculate coordinates of D point, when coordinates of A, B, C and line thickness d are known.

1) Calculate angle α, using Law of Cosines, like here How to calculate an angle from three points?

2) Then you can find length L of vectors u and v:

L =|u| =|v| = d / sin α;

3) Calculate vector components for vectors u and v:

ux = L * (Ax – Bx) / |AB|;
uy = L * (Ay – By) / |AB|;

|AB| - length of vector AB, can easily be found from coordinates of points A and B.

vx = L * (Cx – Bx) / |BC|;
vy = L * (Cy – By) / |BC|;

4) Finally find coordinates of point D:

Dx = Bx + ux + vx;
Dy = By + uy + vy;

5) Do that for all points of you line.