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







Related Discussions:- Uniform b - spline curve, Assignment Help, Ask Question on Uniform b - spline curve, Get Answer, Expert's Help, Uniform b - spline curve Discussions

Write discussion on Uniform b - spline curve
Your posts are moderated
Related Questions
QUESTION (a) Median filters do not cater for a dynamic range of pixels in a given area, S. Thus to ensure that no loss of image details occur in S, adaptive median filters coul

Phong shading OR Normal Vector Interpolation Shading In Gouraud shading we were doing direct interpolation of intensities although a more exact method for rendering a polygon

#BLA for slope greater and equal to 1

Question: (a) Differentiate between lossy and lossless compression. (b) State the uses of the two compression standards MPEG-1 and MPEG-2. (c) State three areas where

Curve Clipping and Character Clipping As you proceed further, you would see that the methods for curve clipping and character clipping have also been developed based on boundin

"Random Painter" uses an array to store a collection of randomly coloured shapes, either squares or circles as filled shapes or outlines.  Using an array imposes severe limitati

What are the advantages of laser printer  High speed, precision and economy. Quality printers. .Cheap to handle Lasts for longer time.

Important points for Bresenham Line Generation Algorithm Note: Bresenhams algorithm is generalised to lines along with arbitrary slopes with identifying the symmetry

Essentialily of Computer Simulation You may want to understand why to do simulation? Is there any one way to perform the tasks? To converse these matters lets briefly discuss