Re: Does cocoa just leak?
Re: Does cocoa just leak?
- Subject: Re: Does cocoa just leak?
- From: Rob Rix <email@hidden>
- Date: Sun, 30 Sep 2001 17:36:58 -0400
Could any one point me in the direction for the documentation / reference
on the mathematics behind bezier paths?
I do google searches for bezier path/cubic spline math quite frequently.
Basically, you use the handy-dandy bezier curve equation:
(1t^1(1 - t)^0) + (1t^0(1 - t)^1) = 1
That's the basic bezier equation (it's just a straight line, since there
are only two points involved). In order to get anything useful out of it,
you have to multiply each section by a point:
P1(1t^1(1 - t)^0) + P2(1t^0(1 - t)^1) = 1
Again, this is a straight line: only two points (it's called a first
degree bezier curve). To get an actual curve, you need at least three
points:
P1(1t^2(1 - t)^0) + P2(2t^1(1 - t)^1) + P3(1t^0(1 - t)^2) = 1
For more points it becomes more complex, but that should do for a bezier
path (unless its implemented using third-degree curves, which are a bit
more complex).
Oh, and for all of these, let t = position along the curve. Note that this
isn't an x or y position, this is a position along the length of the curve.
-- Rob
For this is summer--we spin slowly on the edge of song. - Kira Byers