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
1. Using a time Delay Method The delay required between issuing each character to the LCD is about 5-10ms (it's simply known as DELAY). When programming an LCD, a long delay is

how to develop bresenham''s line drawing algorithm?

State the purpose of scan conversion , along with the side effects

explain cohen sutherland line clipping algorithm

explain the working procedure of crt digram

Question 1 What is 2D? Explain method of converting 2D patterns into 3D images Question 2 Write about the following tools to create dart Create dart Multiply dar


Illustration 1: How does the z-buffer algorithm find out which surfaces are hidden? Solution : Depth or Z-buffer algorithm employs a two buffer area each of two-dimensional ar

Problems at Shared Vertices - Modeling and Rendering Shading discontinuities can arise while two adjacent polygons fail to share a vertex which lies along their common edge.

Graphic Interchange Format (GIF): The Graphic Interchange Format is an efficient implies to transmit images across data networks. In the early 1990 year the original designers of