Uniform b - spline curve, Computer Graphics

Uniform B - spline curve: When the spacing between Knot values is constant, the resulting curve is called a uniform B- spline. Blending function for B- spline curves are defined by cox- deboor recursion formulas: Where each blending, function is defined over d subintervals of the total range of u. the selected set of subinterval end points uj is referred to as a Knot vector. B- spline curves have the following properties:

1.the polynomial curve has degree d - 1 and Cd-2 continuity over the range of u.  

2. For n + 1 control points, the curve is described with n + 1 blending functions.  

3. Each blending function B is defined over subintervals of the total range of u starting at knot value u.  

4. The range of parameter u is divided into n + d subintervals by the n + d + 1 values specified in knot vector. 

5. With knot values lableled as the resulting B-spline curve is defined only in the interval from knot value upto knot value.  

6. Each section of the spline curve is influenced by d control points.  

7. Any one central point can affect the shap of at most d curve section.  

8. In addition B-spline curve lies within the convex hull of at must d + 1 control points so that B-spline are lightly bound to the positions. 

9. For any values of u in the interval from knot value the sum over all basis functions is 1.  

 

 

Posted Date: 7/12/2012 6:58:01 AM | Location : United States







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