Example of bezier curves - modeling and rendering, Computer Graphics

To prove: P (u = 0) = p0


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
2-dimensional xy-shearing transformation, as explained in equation (19), can also be simply extended to 3-dimensional case. All coordinates are translated as a function of displace

side-effect of scan-conversion

What is the use of control points?  Spline curve can be specified by giving a set of coordinate positions known as control points, which shows the general shape of the curve, c

Derive the common transformation of parallel projection into the xy-plane in the direction of projection d=aI+bJ+cK. Solution: The common transformation of parallel projection

Three Dimensional Transformations A 3D geometric transformation is used extensively in object modelling and rendering.2D transformations are naturally extended to 3D situations

Applications that can handle Bitmap Data Hundreds of applications are there in the market which can be used to modify or make bitmap data. For illustration: Adobe Photo Shop, C

Notes for Specular reflection (1) In addition to diffuse reflection, light sources produce highlights or bright spots termed as specular reflection. Such highlighting is extre

Bresenham Line Generation Algorithm This algorithm is exact and efficient raster line generation algorithm. Such algorithm scan converts lines utilizing only incremental integ

Low level techniques (motion specific) Techniques utilized to fully control the motion of any graphic object in any type of animation scene, these techniques are also considere

Improving GIF Compression: Features of LZW compression can be used to enhance its efficiency and thereby decrease the size of your graphic interchange format graphics. The strateg