Calculate Bezier AABB

Question

I'd like to calculate the AABB (axis aligned bounding box) for a quadratic or bezier curve.

The only way I know how to do this is evaluating a high number of points on the bezier curve, and then use those points to calculate the AABB.

Is there a better way?

score 2 · Answer 1 · answered Jul 22 '15 at 22:12

2

Great resource on Bezier curves, and working example of AABB http://pomax.github.io/bezierinfo/#boundingbox For quadratic curve if you need it, also calculate this using derivatives.

Always avoid iterative methods when closed form is available.

answered Jul 22 '15 at 22:12

Evil

score 1 · Answer 2 · edited Jul 22 '15 at 22:55

1

It should be possible by looking for minimum and maximum thanks to the derivative of the curve in parametric form. have a look at this article: http://nishiohirokazu.blogspot.jp/2009/06/how-to-calculate-bezier-curves-bounding.html

edited Jul 22 '15 at 22:55

Peter O.

answered Mar 27 '11 at 09:22

Felice Pollano

score 0 · Answer 3 · answered Nov 10 '17 at 11:31

The quadratic bezier curve consists of 2 coordinate functions — x(t) and y(t) where.

These functions may have maximum or minimum (the points where x'(t) = 0 and y'(t) = 0) and these points are the boundary points of the aabb.

So the algorithm is:

Imagine x0, y0, x1, y1, x2, y2 are known and calculate the values t(x0, x1, x2) and t(y0, y1, y2) when x'(t) = 0 and y'(t) = 0 respectively.
Calculate both values and check whether they are >= 0 and <= 1. If they are evaluate the points of the quadratic bezier.
Take the first and the last points.
Now you have 4 points (or maybe less), use them to calculate AABB.

By the way:

t(x0, x1, x2) = (x0 - x1) / (x2 - 2 * x1 + x0)

t(y0, y1, y2) = (y0 - y1) / (y2 - 2 * y1 + y0)

3 Answers3