RenderMan & RISpec, How to get first derivative value of a Bezier curve in C code.

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RenderMan & RISpec >> How to get first derivative value of a Bezier curve in C code.

by Ed » Fri, 19 Sep 2008 14:04:23 GMT

Hi, guys,
During the implementation of a Bezier curve, user want to get the
first derivative value at some position on the curve.
I know the Bezier equation, and using mathematic methods I can compute
the value easily.
But how did I put down the method into C code?

For example, I want to get the first derivative value at position t1
for a cubic Bezier curve (single float).
What I need to do is
1. Get the position value p1 at t1.
2. Get the position value p2 at (t1+0.000001).
3. Compute the derivative (p2-p1)/0.00001. Then normalize the value.
The value is the first derivative at position t1.

Right? Any problem? Precision is OK?

Thanks.

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RenderMan & RISpec >> How to get first derivative value of a Bezier curve in C code.

by Rick LaMont » Tue, 23 Sep 2008 09:43:20 GMT



Can't you just do the math on paper and implement the equation?

A cubic Bezier curve is defined by four control points: p0, p1, p2 and p3.

B(t) = (1 - t)^3 * p0 +
3t * (1 - t)^2 * p1 +
3t^2 * (1 - t) * p2 +
t^3 * p3

So the first derivative is:

B'(t) = -3 * (1 - 2t + t^2) * p0 -
3t * (4 - 3t) * p1 +
3t * (2 - 3t) * p2 +
3t^2 * p3

You better double-check my math. I just did it off the top of my head.
The point is if you can do the code for a Bezier curve, it should be
easy to implement the first derivative also.


Rick LaMont
Dot C Software, Inc.
http://www.dotcsw.com/
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1. How to get first derivative value of a Bezier curve in C code. 

Hi, guys,
During the implementation of a Bezier curve, user want to get the
first derivative value at some position on the curve.
I know the Bezier equation, and using mathematic methods I can compute
the value easily.
But how did I put down the method into C code?

For example, I want to get the first derivative value at position t1
for a cubic Bezier curve (single float).
What I need to do is
1. Get the position value p1 at t1.
2. Get the position value p2 at (t1+0.000001).
3. Compute the derivative (p2-p1)/0.00001. Then normalize the value.
The value is the first derivative at position t1.

Right? Any problem? Precision is OK?

Thanks.

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