Important point about the de casteljeau algorithm, Computer Graphics

Important point about the De casteljeau algorithm


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


= 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
State the technology used in LCD Some passive matrix (Pixels are illuminated in scanline order like a raster display but  the lack of phospherescence causes flicker) LCDs have

Assumption regarding to the Digital Differential Analyzer Algorithm The line generation by DDA is discussed merely for the first Quadrant, whether the line lies in the other q

What is translation?  Translation is the process of changing the position of an object in a straight-line path from one coordinate location to another. Each point (x, y) in the

What is Polygon mesh?  Polygon mesh is a method to show the polygon, when the object surfaces are tiled, it is more convenient to state the surface facets with a mesh function.

Q. Define Advanced Graphics Port? AGP signify Advanced (or Accelerated) Graphics Port. It's a connector standard defining a high speed bus connection between the microprocessor

Ask questionkms eey frame syst #Minimum 100 words accepted#

Question 1: (a) How can you select and manipulate individual objects in a group? (b) How do you resize an object? Explain how you determine the point from which the object r

Explain the working of Animators Animators want to create a human image that moves and interacts with its background in such a way that viewers can't tell if a specific scene i

3D Primitive and Composite Transformations Previously you have studied and implemented 2D geometric transformations for object definitions in two dimensions. These transformati

The hand-held pointer and tablet in the form of a stylus i.e. pen or puck can function one or more of these three functions: (i)  For choosing positions on a drawing or on a men