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

Graphic interchange format (gif), Graphic Interchange Format (GIF): The Gr...

Graphic Interchange Format (GIF): The Graphic Interchange Format is an efficient implies to transmit images across data networks. In the early 1990 year the original designers of

Shading , short note on shading

short note on shading

Non trivial case of cohen sutherland line clippings, Non Trivial Case of co...

Non Trivial Case of cohen sutherland line clippings Case: assume for the line segment PQ, both the trivial rejection and acceptance tests failed (that is, Case 1 and Case 2

Boundary fill algorithm - output primitives, Boundary Fill Algorithm Bo...

Boundary Fill Algorithm Boundary fill algorithm is suitable when the boundary has single color while flood fill algorithm is more suitable for filling regions which are defined

Translation and shifting in spatial domain, Translation and shifting in Spa...

Translation and shifting in Spatial Domain A) The three images shown below were blurred using square masks of sizes n=23, 25, and 45, respectively. The vertical bars on the le

Improving gif compression, Improving GIF Compression: Features of LZW comp...

Improving GIF Compression: Features of LZW compression can be used to enhance its efficiency and thereby decrease the size of your graphic interchange format graphics. The strateg

Production of animation , Historical and traditional methods for productio...

Historical and traditional methods for production of animation                                              Definition: Computer animation is a time depends phenome

Describe digital printing and prepress, Question 1: (a) Describe Digita...

Question 1: (a) Describe Digital Printing and Prepress? Also state the advantages and disadvantages of Digital printing? Question 2: (a) What are the three most import

Student, hi I need help with photoshop

hi I need help with photoshop

What happens while two polygons have similar z value , What happens while t...

What happens while two polygons have similar z value and the z-buffer algorithm is utilized? Solution : z-buffer algorithms, varies colors at a pixel if z(x,y)

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