Example of bezier curves - modeling and rendering, Computer Graphics

To prove: P (u = 0) = p0

Solution:

1848_Example of Bezier Curves - Modeling and Rendering.png

= p0 Bn,0 (u) + p1 Bn, 1 (u) +...... + pn Bn, n(u)...............(1)

 Bn,i (u) = nci ui (1 - u)n-i

Bn,0 (u) = nc0 u0 (1 -u)n -0 = n!/(0!(n-0)!).1.(1 - u)n = (1 - u)n

Bn,1 (u) = nc1 u1 (1 -u)n -1 = n!/(1!(n-1)!).u.(1 - u)n-1

We observe that all terms expect Bn,0  (u) have various of ui  (i = 0 to n) by using these terms along with u = 0 in (1) we find:

P (u = 0) = p0 (1 - 0)n + p1. 0. (1 - 0)n - 1 . n + 0 + 0 + ......+ 0

P (u = 0) = p0 Proved

Posted Date: 4/4/2013 5:31:01 AM | Location : United States







Related Discussions:- Example of bezier curves - modeling and rendering, Assignment Help, Ask Question on Example of bezier curves - modeling and rendering, Get Answer, Expert's Help, Example of bezier curves - modeling and rendering Discussions

Write discussion on Example of bezier curves - modeling and rendering
Your posts are moderated
Related Questions
What is uniform rational splines

a__________of a scene is apart of a scene by which relate one part of the scene with the other parts of the scene

Line Drawing Display - Random Scan Display Device The display through this system is termed as Line Drawing Display. The sequence controls the subsequent stages, demonstrated

Historical and traditional methods for production of animation                                              Definition: Computer animation is a time depends phenome

Write short notes on active and passive transformations?  In the active transformation the points x and x| show different coordinates of the similar coordinate system. Here all

what is curve clipping

Resolution Graphic demonstrations are utilized in presentations to assist convey a concept or express a mood, two kinds of demonstrations graphics are: Vector, and B

QUESTION (a) Give some ways you can change the magnification of a document? (b) Give three ways to display a panel? (c) Identify the differences between Selection tool an

Polygon Clipping - Raster Graphics and Clipping After considerate the idea of line clipping and its algorithms, we can currently extend the idea of line clipping to polygon cl

Definitions of Hypertext A manner of presenting information online along with links among one piece of information and the other. These links are termed as hypertext links