Vector Cross Product

text only
 
progress indicator progress indicator progress indicator progress indicator

Finding Derivatives of B-Spline Curves

Finding the derivative of a point on a B-spline is conceptually the same as finding the derivative on a Bezier curve. You must first find the derivatives of the basis functions. Finding the derivative of Equation 4.1 is slightly more involved and requires more calculus than what I have given you in Appendix A. If you do apply a little more calculus, you get the derivative shown in Equation 4.9.

(4.9) Recursive equation for the derivative of a basis function. 

Using this new equation, you can solve for the derivatives of a curve the same way you solve for points along the curve. The derivatives of the first-order basis functions are zero for all values of t, so you can use that to begin the recursive calculations at the second-order functions. The code needed to visualize the slope of the curve is included with all of the sample applications.

Up to this point, I have talked about this mathematically or in the abstract. It now seems like a great time to talk about the actual implementation.

progress indicator progress indicator progress indicator progress indicator


Focus on Curves and Surfaces
Focus On Curves and Surfaces (Focus on Game Development)
ISBN: 159200007X
EAN: 2147483647
Year: 2003
Pages: 104
Authors: Kelly Dempski

flylib.com © 2008-2017.
If you may any questions please contact us: flylib@qtcs.net