Example of bezier curves - modeling and rendering, Computer Graphics

Assignment Help:

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


Related Discussions:- Example of bezier curves - modeling and rendering

Whether cavalier projection is a parallel projection, State whether the fol...

State whether the following statements are true or false. Give reasons/examples to justify your answer.  a)  Cavalier projection is a parallel projection. b)  Angles are not

Lossless audio formats, Lossless Audio Formats: Lossless audio formats as ...

Lossless Audio Formats: Lossless audio formats as TTA and FLAC give a compression ratio of around 2:1, sometimes extra. During exchange, for their lower compression ratio, such co

Drawing, how can I draw a flower.

how can I draw a flower.

Geometric tables - polygon tables, Geometric tables - Polygon Tables ...

Geometric tables - Polygon Tables 1) Vertex table: Keep vertices' coordinates values in the object. 2) Edge table: Keep pointers back in to the vertex table for identif

Interactive 3d computer graphics, Describe interactive model of computer gr...

Describe interactive model of computer graphics and application areas of interactive computer graphics.

Military-applications for computer animation, Military: In order to enter ...

Military: In order to enter the military, one has to go by various training. Depending upon whether you want to be in the army, navy or the marines, you may be working along with

Translation and shifting in spatial domain, Translation and shifting in Spa...

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

Vertices of bezier curve find out 3 points on bezier curve, Specified p 0 ...

Specified p 0 (1, 1): p 1 (2, 3); p 2 (4, 3); p 3 (3, 1) as vertices of Bezier curve find out 3 points on Bezier curve? Solution : We consider Cubic Bezier curve as: P (

Define the term multimedia, Question (a) Define the term Multimedia. ...

Question (a) Define the term Multimedia. (b) Describe any four important tools you know about for a virtual campus. (c) Following our discussion in our lecture list an

Stochastic animation - computer animation, Stochastic Animation - Computer ...

Stochastic Animation - Computer Animation This utilizes stochastic processes that are a stochastic process can be identified as a random function. Such randomness could be in

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd