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

Principle vanishing point - perspective projections, Principle Vanishing po...

Principle Vanishing point - Perspective Projections Assume that line 1 and l2 be two straight lines parallel to each other that are also parallel to x-axis. If the projection

Describe transformation, What is Transformation?  Transformation is the...

What is Transformation?  Transformation is the process of introducing changes in the shape size and orientation of the object using scaling rotation reflection shearing & trans

Flash - software to generate computer animations, Flash - software to gener...

Flash - software to generate computer animations Flash: Learning Macro-Media's Flash can quite complicated, although you can do almost anything along with it. You can devel

Reflection, What is the advantages and disadvantages of reflection ?

What is the advantages and disadvantages of reflection ?

Archeology-applications for computer animation, Archeology: along with the...

Archeology: along with the advent of the computer, the archeologist has obtained a new tool, computer animation. An object-model can be made comparatively quick and without any we

What are the important properties of bezier curve, What are the important p...

What are the important properties of Bezier Curve?  It requires only four control points It always passes by the first and last control points The curve lies enti

Multimedia applications, what are activities to be undertaken or executed a...

what are activities to be undertaken or executed and the expected output of each activity for a plan creation of a movie?

What are the advantages of the boundary representation, Advantages of the B...

Advantages of the Boundary Representation (i) This format gives efficient picture generation and easy access to other geometric information. (ii) The changes produced by mos

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