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

Exceptional cases - orthographic projection, Exceptional cases - Orthograph...

Exceptional cases - Orthographic Projection 1)   We have an Orthographic projection, if f=0, then cot (β) =0 that is β=90 0 . 2)   β =cot-1 (1)=450 and this Oblique projec

Briefly explain color profile, Question 1) Why are selection tools useful?...

Question 1) Why are selection tools useful? Describe them based on different categories Question 2) What are the different types of layers? Describe each type Quest

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

Define the term avatars- animation, Define the term Avatars- Animation ...

Define the term Avatars- Animation Avatars are another instance of animation. These are frequently used to represent people either in 3-D (as used in computer games) and in 2-D

Raster scan display processor, Draw the block diagram of raster scan displa...

Draw the block diagram of raster scan display processor.

Translate a triangle and scale it in coordinate direction, Translate a tria...

Translate a triangle and scale it in each coordinate direction Consider a triangle with vertices in 2D plane given by (0, 0), (1, 0) and (0,1) (called unit triangle).  Translat

Digital painting, Please guide if there is any easy steps tutorial availabl...

Please guide if there is any easy steps tutorial available for digital painting in adobe photoshop.

What is the minimum amount of video ram, Consider a raster system with the ...

Consider a raster system with the resolution of 1024 x 768 pixels and the color palette calls for 65,536 colors. What is the minimum amount of video RAM that the computer must have

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