CODEWITHSUNDEEP
c++algorithmgeometry
jmasterx
jmasterx

Reputation: 54113

Point in OBB (Oriented Bounding Box) algorithm?

Given a center point, width, height and angle forming an OBB, how can I find if a given point P is inside the OBB?

Thanks

Upvotes: 6

Views: 8317

Answers (2)

acjay
acjay

Reputation: 36511

I take it that the wrinkle in your problem is that the bounding box can be rotated? If so, the easiest solution to me seems to be to do all calculations in the rotated coordinate plane, centered on the center of the bounding box.

To calculate the coordinates of the point relative to these axes:

newy = sin(angle) * (oldy - centery) + cos(angle) * (oldx - centerx);
newx = cos(angle) * (oldx - centerx) - sin(angle) * (oldy - centery);

(you may need to adjust this depending on how angle is supposed to be measured, I'll leave that to you, since you didn't specify)

Then hit test, the normal way:

return (newy > centery - height / 2) && (newy < centery + height / 2) 
    && (newx > centerx - width / 2) && (newx < centerx + width / 2);

Upvotes: 9

Darren Engwirda
Darren Engwirda

Reputation: 7015

You could transform the coordinates of your test point (via a transformation matrix) into a rotated coordinate system based on the angle of the bounding box.

At this stage it should just be an axis-aligned point-in-rectangle test, i.e. compare against xmin, xmax, ymin, ymax. In the rotated coordinate system xmin, xmax = xmid -+ width/2 and ymin, ymax = ymid -+ height/2.

Hope this helps.

Upvotes: 1

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