Proof of subsequent properties of bezier curves, Computer Graphics

Proof of subsequent properties of Bezier curves

Note: Proof of subsequent properties of Bezier curves is left as a work out for the students

P' (0) = n (p1 - p0)

P' (1) = n (pn - pn-1) = n (pn - pn - 1)

P" (0) = n (n - 1) (p0 - 2p1 + p2)

P" (1) = n (n - 1) (pn - 2 pn - 1 + pn - 2)

To ensure about the smooth transition from one part of a piecewise parametric curve or some Bezier curve to the subsequent we can impose different continuity circumstances at the connection point for parametric continuity we match parametric derivatives of adjacent curve section at their ordinary boundary.

Zero order parametric continuity illustrated by C0 continuity means curves are merely meeting as demonstrated in figure 14 whereas first order parametric continuity termed as C1 continuity, implies that tangent of successive curve sections are identical at their joining point. Second order parametric continuity or C2 continuity, implies that the parametric derivatives of the two curve sections are identical at the intersection. As demonstrated in figure 14 as given below; first order continuity have identical tangent vector but magnitude may not be the similar.

772_Proof of subsequent properties of Bezier curves.png

Along with the second order continuity, the rate of modification of tangent vectors for successive section is equivalent at intersection hence result in smooth tangent transition from one section to the other.Initial order continuity is often utilized in digitized drawing whereas second order continuity is utilized in CAD drawings.

Posted Date: 4/4/2013 5:42:52 AM | Location : United States







Related Discussions:- Proof of subsequent properties of bezier curves, Assignment Help, Ask Question on Proof of subsequent properties of bezier curves, Get Answer, Expert's Help, Proof of subsequent properties of bezier curves Discussions

Write discussion on Proof of subsequent properties of bezier curves
Your posts are moderated
Related Questions
Polygon representation methods - Boundary representations Boundary representations: now the 3-D object is shown as a set of surfaces which separate the object interior from

Scenes - polygon rendering and ray tracing methods In the context of ray tracing, a scene is a set of objects and light sources which will be viewed through a camera. All of

QUESTION 1: a) Draw a Bezier curve showing the following components i. hull ii. curve CV iii. span iv. start and end point b) Maya provides highly effective tools for all t


write digital differntial analyzers(DDA) Algorithm

Geometric continuity - Properties of Bezier Curves Geometric continuity is the other process to join two successive curve sections. G 0 continuity is the similar as parametri

deffrent between vecgen algorithm and bresenham line algorithm in computer graphic

Flat Panel Displays - Hardware Primitives 1.  Flat panel displays have now become more common. These include liquid crystal displays (LCD) and thin film electroluminescent disp

Determine the advantages of raster-scan systems (i)  Rasterisation is now performed faster since a special purpose processor is used. (ii)  The CPU is not slowed down by the

1. Use the outline method to plot the following font boundaries (style should remain the same). Implement your method in C language.    ANswer: Here letter G is produced