B-spline curves - uniform b-splines and de boor algorithm, Computer Graphics

Assignment Help:

B-spline curves are piecewise smooth polynomial curves. 

  • B-spline curves are defined over an interval which has been partitioned into sub-intervals. On each subinterval B-spline curve reduces to a polynomial curve. The curve pieces are joined in such a way that the composite curve satisfies certain smoothness conditions specified in terms of matching of derivatives of certain orders. Points defining the partition of the interval are called knots or knot points. This is because at this common domain point of the interval, two polynomial curve segments are joined to make the composite curve.
  • B-spline curves as well as blending functions are computed using the iterative de Boor algorithm.
  • B-splines satisfy the important properties suitable for geometric modellling in computer Graphics. Some of these include (i) local control (ii) smoothness (iii) degree of spline curve does not depend on the number of control points (iv) convex hull property (v) convenient blending functions.
  • Uniform B-splines are B-spline curves with uniform spacing between the knots.
  • Uniform B-splines give periodic blending functions. This means all blending functions are translated versions of a single B-spline.

Related Discussions:- B-spline curves - uniform b-splines and de boor algorithm

De casteljeau algorithm - bezier curves, De Casteljeau algorithm: The cont...

De Casteljeau algorithm: The control points P 0 , P 1 , P 2 and P 3 are combined with line segments termed as 'control polygon', even if they are not actually a polygon although

Math, what is the numerical numbers

what is the numerical numbers

Distinguish between uniform scaling and differential scaling, Distinguish b...

Distinguish between uniform scaling and differential scaling?  When the scaling factors sx and sy are assigned to the similar value, a uniform scaling is produced that maintain

Accessories, Accessories : A Screen Grabber is a necessary accessory. Bitm...

Accessories : A Screen Grabber is a necessary accessory. Bitmap images are so common in multimedia, that it is important to have a tool for grabbing all or part of the screen disp

Explain the merits and demerits of penetration techniques, Explain the meri...

Explain the merits and demerits of Penetration techniques. The merits and demerits of the Penetration techniques are as follows:     It is an inexpensive method.     It h

Consider shiny surface with diffused reflection coefficient, Consider a Shi...

Consider a Shiny Surface Along With Diffused Reflection coefficient Consider a shiny surface along with diffused reflection coefficient of 0.8 and ambient reflection coeffici

Z- buffer algorithm, Q.   Describe the z- Buffer algorithm for hidden surfa...

Q.   Describe the z- Buffer algorithm for hidden surface removal. Ans. Z- buffer method: This method compares surface depths at each pixel position on the projection plane. T

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