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
What is orthographic parallel projection?  When the direction of the projection is normal (perpendicular) to the view plane then the projection is called as orthographic paral

Graphics Tablet - CAD and CAM We need to know what we mean via tablet in computer terminology, before going into details on the graphic tablet, since in the other disciplines

Question 1 Briefly explain the twelve principles of animation Question 2 Explain the methods to set-up pre and post-infinity curves Question 3 What is a model sheet? Exp

Describe briefly Sutherland Cohen line clipping algorithm.   OR   Describe Cohen Sutherland line clipping algorithm. Cohen Sutherland line clipping algorithm In this algorith

Question 1: (a) Describe the term Mask Path and give brief steps how you could change a rectangle into a triangle with respect to time in AE CS3. (b) Expressions are ve

What happens while two polygons have similar z value and the z-buffer algorithm is utilized? Solution : z-buffer algorithms, varies colors at a pixel if z(x,y)

How avar values generate to get realistic movement There are numerous ways of generating avar values to get realistic movement. One way is to use markers on a real person (or w

Compression methods utilized for digital video can be categorized in three major groups: General reason compression techniques can be utilized for any type of data. Intr

Illustration: Find the normalization transformation N that uses the rectangle W (1, 1), X (5, 3), Y (4, 5) and Z (0, 3) as a window and also the normalized device screen like the

Explore and understand light field. Checking out one of the image libraries. 1. You can modify existing source code, or develop your own to achieve light field rendering; 2.