Important points about the curve segment, Computer Graphics

Assignment Help:

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


Related Discussions:- Important points about the curve segment

Bresenham line generation algorithm, Bresenham Line Generation Algorithm ...

Bresenham Line Generation Algorithm This algorithm is exact and efficient raster line generation algorithm. Such algorithm scan converts lines utilizing only incremental integ

Define refresh rate and refresh buffer, Refresh Rate: refreshing on raster...

Refresh Rate: refreshing on raster - scan displays is carried out at the rate of 60 to 80 frames per second, although some system are designed for higher refresh rates. Sometimes,

Important points about the diffuse reflection, Important Points About the D...

Important Points About the Diffuse Reflection An extremely rough surface appears uniformly bright from each viewing direction Q the intensity of reflected light is identical i

Algorithms for identification of observable objects, Algorithms for Identif...

Algorithms for Identification of Observable Objects There are various algorithms for identification of observable objects for various types of applications. Several methods ne

Features for good 3-dimentional modeling , Features for good 3-Dimentional ...

Features for good 3-Dimentional modeling software are as: Multiple windows which permit you to view your model in each dimension. Capability to drag and drop primitive

Objectives of viewing ttransformation, Objectives of Viewing transformation...

Objectives of Viewing transformation After going through this section, you should be capable to: - Explain the projection; - Classify different types of Perspective and

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd