Important points about the curve segment, Computer Graphics

Important Points about the Curve segment - properties of bezier curves

Note: if P (u) → = Bezier curve of sequence n and Q (u) → Bezier curve of sequence m.

After that Continuities in between P(u) and Q(u) are as:

1)      Positional continuity of 2 curves

892_Important Points about the Curve Segment.png

That is pn = q0

2)       C1 continuity of 2 curve P (u) and Q (u) as that point pn - 1, pn on curve P(u) and q0, q1 points upon curve Q(u) are collinear that is:

n( pn  - pn-1 ) = m(q1 - q0 )

n q1  = q0  +( pn  - pn -1 ).(n/m)

 ⇒ (d p/du)u=1         =  (d q/dv)v=0

G(1)  continuity of two curves P(u) and Q(u) at the joining that are the end of P(u) along with the beginning of q(u) as:

pn  = q0n( pn  - pn -1 ) = kn(q1  - q0 ),

Here k is a constant and k > 0

⇒ pn -1 , p­  = q0 , q1  are collinear

3)  c2 continuity is:

a)   C(1) continuity

b)   m (m - 1) (q0 - 2q1 + q2)

= n (n - 1) (pn - 2pn - 1 + pn - 2)

That points are as: pn - 2, pn - 1, pn of P(u) and points q0 , q1, q2 of Q(u) should  be collinear further we can verify whether both second and first order derivatives of two curve sections are similar at the intersection or not  that is:

(d p)/( d u) u=1  =   (d q) /(d v )v=0

And (d2 p)/( d u2) u=1  =   (d2 q) /(d v2 )v=0

Whether they are similar we can as we have C2 continuity   

 Note: as the same we can explain higher order parametric continuities

Posted Date: 4/4/2013 5:57:14 AM | Location : United States







Related Discussions:- Important points about the curve segment, Assignment Help, Ask Question on Important points about the curve segment, Get Answer, Expert's Help, Important points about the curve segment Discussions

Write discussion on Important points about the curve segment
Your posts are moderated
Related Questions
what are the advertising effects of scan conversion

Computer Aided Design and Drafting CADD or CAD stands for Computer Aided Design and Drafting. This is different from both "draw" and "paint" programs in which measurement is c

File Formats that are used for Vector Data This data can be saved in a wide variety of file formats are as: •EPS: the most well-accepted file format to exchange vector dra

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

MPEG-2 : MPEG-2 that is Moving Picture Experts Group format 2 is the standard used through DVD and is of a much higher quality than MPEG- 1. This format gives for 720 x 480 resolu

Scale a sphere cantered on the point (1, 2, and 3) with radius 1, so that the new sphere has the same centre with radius 2.    Solution: Translate the sphere so that its centre

What is the advantages of electrostatic plotters? Advantages of electrostatic plotters: They have very high quality printers and faster than pen plotters. Recent electros

Question 1 Explain any ten types of artistic filters Question 2 What is Freehand Tool? Explain the procedure of drawing lines and curves with freehand tool Question 3 Ho

Cohen Sutherland Line Clippings Algorithm The clipping problem is identified by dividing the region surrounding the window area into four segments Up as U, Down as D, Left as

Polygon Representation Methods - Modeling and Rendering Any scene to be created by computer graphics may include a variety of objects, a few of them natural and manmade. Hence