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

Example of bezier curves - modeling and rendering, To prove: P (u = 0) = p0...

To prove: P (u = 0) = p0 Solution : = p 0 B n,0 (u) + p 1 B n, 1 (u) +...... + p n B n, n (u)...............(1)  B n,i (u) = n c i u i (1 - u) n-i B n,0

Introduction, how can we write the introduction matter for graphicaluser in...

how can we write the introduction matter for graphicaluser interface

Interpolation of surface - polygon rendering, Interpolation of surface - Po...

Interpolation of surface - Polygon Rendering Interpolation of surface normals beside the polygonedge between two vertices is demonstrated above in the figure 15. Here the norm

Specular reflection - polygon rendering & ray tracing method, Specular Refl...

Specular Reflection - Polygon Rendering & Ray Tracing Methods Specular reflection is while the reflection is stronger in one viewing direction that is a bright spot, termed

Scientific visualization, Scientific Visualization This is complex for...

Scientific Visualization This is complex for the human brain to create sense out of the large volume of numbers produced through a scientific computation. Statistical and nume

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

What is riged body transformation matrix, What is riged body transformation...

What is riged body transformation matrix? Show that the composition lf two rotation is additive by concatenating the matrix representation of r (theta 2 ) = R (theta1 + theta 2 ) t

Explain the advantage and disadvantage of raster crt, Explain the advantage...

Explain the advantage and disadvantage of Raster CRT Advantages Allows solids, not just wireframes Leverages low-cost CRT technology (i.e., TVs) Bright, i.e.

Touch panels - input and output devices, Touch Panels - Input and output de...

Touch Panels - Input and output devices It allows displayed screen or object positions to be selected along with the touch of the finger and is also termed as Touch Sensitive

Types of animation systems - computer animation, Types of Animation Systems...

Types of Animation Systems - Computer Animation We have discussed above about the sequencing of animation is helpful in developing any animation. Such sequencing is more or le

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