Y-shear about the origin - 2-d and 3-d transformations, Computer Graphics

y-shear about the origin - 2-d and 3-d transformations

Suppose an object point P(x,y) be moved to P'(x',y') in the x-direction, through the specified scale parameter 'b'. that is, P'(x'y') be the result of y-shear of point P(x,y) through scale factor 'b' regarding the origin, that is demonstrated in Figure 5(a).

1739_y-shear about the origin - 2-d and 3-d transformations.png

Figure: 5(a)

Hence, the points P(x,y) and P'(x',y') have the subsequent relationship :

x' = x

 

y' = y+bx

= Shy(b)

 

 

Here 'b' is a constant (termed as shear parameter) which measures the degree of shearing. In matrix form, we contain:

2465_y-shear about the origin - 2-d and 3-d transformations 1.png

In terms of Homogeneous Coordinates, above equation (16) is:

479_y-shear about the origin - 2-d and 3-d transformations 2.png

There is, P'h = Ph.Shy(b)

Here Ph  and P'h  represents object points, before and after needed transformation, in Homogeneous Coordinates and Shy(b) is termed as homogeneous transformation matrix for y-shear along with scale factor 'b' in the y-direction.

Posted Date: 4/3/2013 5:33:17 AM | Location : United States







Related Discussions:- Y-shear about the origin - 2-d and 3-d transformations, Assignment Help, Ask Question on Y-shear about the origin - 2-d and 3-d transformations, Get Answer, Expert's Help, Y-shear about the origin - 2-d and 3-d transformations Discussions

Write discussion on Y-shear about the origin - 2-d and 3-d transformations
Your posts are moderated
Related Questions
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

Advertising: One of the most well known uses for computer animation is in television advertising. Many of the models which the commercials would call for would be extremely compli

Question 1: (a)Using your awareness of typography and design, make a new logo manually for one of the following. The logo should compulsorily consist of the name and may or may

Web Design and Editing To edit and make a website, the big three softwares are use: 1)   DreamWeaver (MacroMedia) 2)   Frontpage (MicroSoft) 3)   Go Live (Adobe) 4)


Panning and zooming Components (such as your Polybounce or Animation) is simply a matter of reFrameing the world window. To pan right or left horizontally, one shifts it in the pos

JAS: The JAS file formats were implemented to form the smallest possible picture files for 24bits per pixel image and 8 bit per pixel gray scaled pictures. This uses a discrete co

Adavantage and disadvantages of DDA and Bresenhams line drawing algorithm

1. Design a bitmap for the English vowels A, E, I, O, U for two different sizes and then implement the bitmaps to plot these vowels on the display. Keep in mind that baseline of al

Area subdivision Method - Visible Surface Detection What are the circumstances to be fulfilled, in Area-subdivision method, thus a surface not to be divided in addition? S