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
Cohen Sutherland algorithm Point clipping is very simple.  All you need to check is whether a point is inside the window extremes in x- and y-directions.  For line clipping sev

what is fixed point scaling? how composit transformation techniques works on it

Question: Adobe InDesign software is used to create works such as posters, flyers, brochures, magazines and books. Designers and graphics production artists are the principa

Write a program that allows interactive manipulation of the position and orientation of a camera. Draw a teapot at the global origin 0,0,0. You can find a shaded teapot model and

QUESTION (a) Draw and explain the block diagram of a Digital Signal Processing System for an analog signal. (b) Draw the pictorial representation of the signals at each leve

Single Point Perspective Transformation - Viewing Transformations In order to derive the particular point perspective transformations beside the x and y-axes, we construct fi

De Casteljau Algorithm For computation of Bézier curves an iterative algorithm known as de Casteljau algorithm is used.  The algorithm uses repeated linear interpolation.

Explain the utility and purpose of display processor in the graphic system.  The purpose of the display processor is to free the CPU from the graphics chores. A major task of the d

Program of PERT in c language

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)