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
Persistence: How long they continue to emit light (that is, have excited electrons returning to the ground state) after the CRT beam is removed. Persistence is defined as the ti

Taxonomy of Projection - viewing transformation There are different types of projections as per to the view that is essential. The subsequent figure 3 demonstrates taxonomy o

What is the difference between odd-even rule and non-zero winding number rule to identify interior regions of an object? Develop an algorithm for a recursive method for filling a 4

what do you means by bresenham s him algorithm

Computer simulation - Computer Aided Design Computer simulation is the manner of designing a model of a real or theoretical physical system, not including the model on a digit

what is mean by virtual reality?

Types of Authoring Tools Authoring tools are grouped depends on metaphor used for sequencing or organizing multimedia components and events as: Page or Card Based Tools

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

Rotation about an arbitrary axis Rotation about an arbitrary axis is a composition of several rotations and translation operations. What you need to do is the following:  a)

how you doing the graphic?