Bezier cubic curves, Computer Graphics

Assignment Help:

Q. What are Bezier cubic curves? Derive their properties. OR  What are Bezier cubic curves? Derive these properties. Also show that the sum of the blending functions is identical to 1 for all values of t. Why is it important?

Ans. A Bezier curve section can be fitted to any no. of control points. The no. of control points to be approximated and their relative position determines the degree of the Bezier polynomial. These coordinates can be blended to produce the following position vector P (u), which describes the path of an approximating Bezier polynomial function between P0 and Pn. Thus the slope at the beginning of the curve is along the line joining the first two control points and the slope at the end of the curve is along the line joining the last two endpoints. Bezier curves are widely available in various CAD systems in graphics packages in painting packages since they are easy to implement and they are reasonably powerful in curve design. Many graphic packages provide only cubic spleen functions. This gives reasonable design flexibility while avoiding the increased calculation needed with higher order polynomials.  

 

 


Related Discussions:- Bezier cubic curves

Image editing tools in multimedia, Image Editing Tools These are specia...

Image Editing Tools These are specializing and influential tools for enhancing and re-touching existing bit-mapped images. Such applications also give several of the features a

What is aspect ratio, What is Aspect ratio?  The ratio of vertical poin...

What is Aspect ratio?  The ratio of vertical points to the horizontal points essential to produce length of lines in both directions of the screen is known as the Aspect ratio.

What are the steps to mapping artwork to an object, Question 1: (a) How...

Question 1: (a) How can you select and manipulate individual objects in a group? (b) How do you resize an object? Explain how you determine the point from which the object r

Light pen - input and output devices, Light Pen - input and output devices ...

Light Pen - input and output devices It is a pointing device. This has a light sensitive tip that is excited while the light is emitted and an illuminated point upon the disp

Explain briefly ancillary operations, Problem: a. Explain briefly six A...

Problem: a. Explain briefly six Ancillary Operations? b. When do ancillary operations take place? c. (i) What is flexography? (ii) Provide examples of finished produ

Objects - polygon rendering and ray tracing methods, Objects - polygon rend...

Objects - polygon rendering and ray tracing methods Objects could be any state of material as solid, liquid. Gas and plasma. Though ray tracers can merely assist objects whic

Remark for perspective projection - transformation, Remark for Perspective ...

Remark for Perspective projection - Transformation A Perspective projection can have at most three Principle Vanishing points and at any rate one Principle vanishing point. To

Interrupts - event driven devices, Interrupts - Event driven devices ...

Interrupts - Event driven devices Interrupts: An option to polling is the interrupt feature. The device sends an interrupt signal to the processor while an event happens. T

Web-based services, Web-based Services: Commonly utilized software is: ...

Web-based Services: Commonly utilized software is: Protected Area Archive characteristics: Image display, roam, zoom and Image enhancement. Simple image processing.

Dv encoder type 1, DV Encoder Type 1 : The video and audio streams are tog...

DV Encoder Type 1 : The video and audio streams are together interfaces by standard DV bit stream. Such format is fully supported through DirectShow which accepts this interleaved

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