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

What is fixed point scaling, What is fixed point scaling?  The location...

What is fixed point scaling?  The location of a scaled object can be controlled by a position known as the fixed point that is to remain unchanged after the scaling transformat

Interactive computer animation, Interactive Computer Animation Interac...

Interactive Computer Animation Interactive Computer Animation that is interactively utilized by users for example: games. Sprite animation is interactive and utilized broadly

Algorithms for basic line segment plotting, Algorithms for Basic Line Segme...

Algorithms for Basic Line Segment Plotting There are two important algorithms for basic line segment plotting-DDA algorithm and Bresenham algorithm.  Both the algorithms use th

Reflection and shear - output primitives, Reflection and Shear There ar...

Reflection and Shear There are a few important transformations which are not primitive in the sense that they can be expressed as compositions of translation, rotation and scal

Projections - viewing transformation, Projections - Viewing Transformation ...

Projections - Viewing Transformation Specified 3-D object in a space, Projection can be explained as a mapping of 3-D object into 2-D viewing screen. Now, 2-D screen is termed

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

Transformation, Explain window to view port transformation

Explain window to view port transformation

Boundary fill algorithm - output primitives, Boundary Fill Algorithm Bo...

Boundary Fill Algorithm Boundary fill algorithm is suitable when the boundary has single color while flood fill algorithm is more suitable for filling regions which are defined

Soft image and strata studio - computer animation, Soft Image and Strata ...

Soft Image and Strata Studio - Computer Animation SoftImage It is the one of most well known computer animation software packages. It is used in several top production

Transformation for 3-d reflection, Transformation for 3-D Reflection F...

Transformation for 3-D Reflection For 3-Dimensions reflections, we should to know the reference plane, which is a plane about that reflection is to be considered. Remember tha

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