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
Write a program that allows interactive manipulation of the position and orientation of a camera. Draw a teapot at the global origin 0,0,0. You can find a shaded teapot model and

DV Encoder Types: While DV is captured in a computer this is stored in an AVI file, that is Microsoft's standard file format used for video files. Video support in Windows is prov

Objectives After completing this section, you must be familiar with: explain computer graphics, its characteristics and features; Conversations about applicat

Cases for Subdivisions of Polygon No additional subdivisions of a particular area are desired, if one of the subsequent conditions is true as: Case 1: All the polygons ar

Introduction of Curves and Surfaces This section has covered the methods of generating polygons, closed and curves surfaces. Under those methods we have discussed different ty

What are the various representation schemes used in three dimensional objects?  Boundary representation (B-res) - explain the 3 dimensional objects as a set of surfaces that se

Question: (a) A statistical encoding algorithm is being considered for the transmission of a large number of long text files over a public network. Part of the file content i

Objectives of Curves and surfaces - modeling and rendering After going through the section, you should be capable to: Implement the methods utilized to represent a pol

all details of Graphical User interface and interactive input methods

Horizontal Retrace - Hardware Primitives Horizontal retrace refers to the time an electron beam takes to traverse a scan line.Vertical retrace means the time taken by the elect