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

Explain about the Computer-Aided Design CAD is used in the design and development of new products in a several of applications both at home and on a commercial/industrial basis

when dda line drawing algorithm is more efficient than bresenhem line drawing algorithm?

Determine the advantages of raster-scan systems (i)  Rasterisation is now performed faster since a special purpose processor is used. (ii)  The CPU is not slowed down by the

What is persistence? The time it takes the emitted light from the screen to decompose one tenth of its original intensity is known as persistence.

Translation and shifting in Spatial Domain A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le

Pen Tablet and Plotter Pen Tablet: It is a digitizer tablet which is specialized for handwriting and hand marking. LCD-based tablets imitate the flow of ink as the tip tou

Three Dimensional Concepts and Display Methods   Imagine yourself taking a picture by a camera.  What do you normally do?  You specify a viewpoint and view direction and then s

Given two triangles P along with vertices as P1(100,100,50), P2(50,50,50), P3(150,50,50) and q along with vertices as Q1(40,80,60), q2(70,70,50), Q3( 10,75,70), determine that tria

Macintosh - Hardware for computer animation It was originally designed to be graphic and desktop publishing machines. Macs did not turn into which widely known till recently, a