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

Fixed point scaling, what is fixed point scaling? how composit transformati...

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

Introduction to computer graphics, Introduction To Computer Graphics ...

Introduction To Computer Graphics Early man employed drawings to communicate even before he learnt to communicate, write or count. Incidentally, these earliest hierogly

Shading - polygon rendering and ray tracing methods, Shading - Polygon Rend...

Shading - Polygon Rendering and Ray Tracing Methods When one thing is under the exposure of light, so the rays of light are distributed over the surface and there the distribu

Explanation of light source by a luminance, Explanation of light source by ...

Explanation of light source by a luminance Explanation of any light source by a luminance the factors identified as: Light source explained by a luminance 1)   All color as

Notes for specular reflection - polygon rendering, Notes for Specular refl...

Notes for Specular reflection (1) In addition to diffuse reflection, light sources produce highlights or bright spots termed as specular reflection. Such highlighting is extre

Authoring tools in multimedia, Authoring Tools Authoring tools genera...

Authoring Tools Authoring tools generally refers to computer software that assists multimedia developers produce products. Authoring tools are various from computer programmi

Steps for clip a line segment-pq, Steps for clip a line segment-PQ ...

Steps for clip a line segment-PQ Initially, find all the points of intersections of the line segment PQ along with the edges of the polygonal window and describe them eith

Role in education and training, Role in Education and Training:- A multime...

Role in Education and Training:- A multimedia presentation is an important way to introduce new concepts or described a new technology. Individuals determine it easy to understand

Magnify a triangle with vertices, Magnify a triangle with vertices A = (1,1...

Magnify a triangle with vertices A = (1,1), B = (3,1) and C = (2,2) to twice its size in such a way that A remains in its original position.  Answer: You need to apply scaling b

Definitions of hypermedia, Definitions of Hypermedia It is a term ...

Definitions of Hypermedia It is a term created through Ted Nelson in the year 1970. It utilized as a logical extension of the term hypertext, wherein graphics, video, audi

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