Determine a bounding rectangle around a diagonal line

问题

A user will define a line on screen which will have, when drawn, a given thickness (or width).

I now need to be able to determine the coordinates of a bounding rectangle around this.

I have the coordinates A and B, along with the line thickness (W).

How can I calculate the coordinates A1, A2, B1 and B2.

I searched but was unable to find a question corresponding to this already asked.

回答1:

Dx= Xb - Xa
Dy= Yb - Ya
D= sqrt(Dx * Dx + Dy * Dy)
Dx= 0.5 * W * Dx / D
Dy= 0.5 * W * Dy / D

This computes (Dx, Dy) a vector of length W/2 in the direction of AB. Then (-Dy, Dx) is the perpendicular vector.

Xmin = min(Xa, Xb) - abs(Dy) 
Xmax = max(Xa, Xb) + abs(Dy)
Ymin = min(Ya, Yb) - abs(Dx)
Ymax = max(Ya, Yb) + abs(Dx)

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Update:

I answered for the AABB by mistake.

For the four corners of the stroke

Xa - Dy, Ya + Dx
Xa + Dy, Ya - Dx
Xb - Dy, Yb + Dx
Xb + Dy, Yb - Dx

来源：https://stackoverflow.com/questions/38807203/determine-a-bounding-rectangle-around-a-diagonal-line