Important point about the de casteljeau algorithm, Computer Graphics

Important point about the De casteljeau algorithm

1)     

1690_Important point about the De casteljeau algorithm.png

Bezier Curve: P (u) =

   ................     (1)

Here Bn,i (u) = nci ui (1 - u) n-i       ..............        (2)

C (n, i) = nCi = n!/i!(n - i)!      0 ≤ u ≤ 1

2)      Cubic Bezier curve has n = 3 as:

1691_Important point about the De casteljeau algorithm 1.png

------------------(3)

= p0 B3, 0 (u) + p1 B3, 1 (u) + p2 B3, 2 (u) + p3 B3, 3 (u)

Now, let's find B3, 0 (u), B3, 1 (u), B3, 2 (u) , B3, 3 (u) by using equation as in above:

Bn, i (u) = nci u (1 - u)

a)  B3, 0(u) = 3C0   u0   (1 - u)3 - 0

=          3!       . 1. (1 - u)3 = (1 - u)3

       0!(3 - 0)!

 

b)  B3, 1(u) = 3C1   u1   (1 - u)3 - 1

=          3!       . u. (1 - u)2 = 3u (1 - u)2

1!(3 - 1)!

c) B3,2(u) = 3C2   u2   (1 - u)3 - 2

=          3!       . u2. (1 - u) = 3u2(1 - u)

       2!(3 -2)!

B3,3(u) = 3C3   u3   (1 - u)3 - 3

=          3!       . u3. (1 - u) 

         3!(3 -3)!

By using (a), (b) , (c) and (d) in (5) we find here:

P (u) = p0 (1 - u)3 + 3p1u (1 - u)2 3p2u2 (1 - u) + p3 u3

Posted Date: 4/4/2013 5:13:58 AM | Location : United States







Related Discussions:- Important point about the de casteljeau algorithm, Assignment Help, Ask Question on Important point about the de casteljeau algorithm, Get Answer, Expert's Help, Important point about the de casteljeau algorithm Discussions

Write discussion on Important point about the de casteljeau algorithm
Your posts are moderated
Related Questions
Write short notes on active and passive transformations?  In the active transformation the points x and x represent different coordinates of the similar coordinate system. Here

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

Combination of Positive and Negative Accelerations Actually, it is not that a body once decelerated or accelerated will remain so, although the motion may include both speed-up

Define Octrees?  Hierarchical tree structures called octrees, are used to show solid objects in some graphics systems. Medical imaging and other applications that needs display

To find out average unit normal vector at each polygon vertex At each polygon vertex as demonstrated by point V in the figure above, the normal vector is acquired by averaging

explain vecgen algoritham

Constant intensity shading OR Flat shading  In this technique particular intensity is calculated for each polygon surface that is all points that lie upon the surface of the

Explain process of displaying objects in raster display and random display. Draw block diagrams of the architecture of both the display systems.


what is the numerical numbers