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

xy-Shear about the Origin - 2-d and 3-d transformations

Suppose an object point P(x,y) be moved to P'(x',y') as a outcome of shear transformation in both x- and y-directions along with shearing factors a and b, respectively, as demonstrated in

323_xy-Shear about the Origin - 2-d and 3-d transformations.png

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

x' = x +ay

 

y' = y+bx

= Shxy(a,b)

 

(19)

Here ′ay′ and ′bx′ are shear factors in x and y directions, respectively. The xy-shear is also termed as shearing for short or simultaneous shearing.

In matrix form, we contain:

541_xy-Shear about the Origin - 2-d and 3-d transformations 1.png

-------------(20)

In terms of Homogeneous Coordinates, we contain:

397_xy-Shear about the Origin - 2-d and 3-d transformations 2.png

---------(21)

It is, P'h = Ph.Shxy(a,b)  ----------(22)

Here Ph   and P'h represent object points, before and after needed transformation, in Homogeneous Coordinates and Shxy(a,b) is termed as homogeneous transformation matrix for xy-shear in both x- and y-directions along with shearing factors a and b, respectively, particular case: while we put b=0 in above equation (21), we contain shearing in x-direction, and while a=0, we have Shearing in the y-direction, correspondingly.

Posted Date: 4/3/2013 5:39:49 AM | Location : United States







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

Write discussion on Xy-shear about the origin - 2-d and 3-d transformations
Your posts are moderated
Related Questions
Cases of clip a line segment-pq Case 1: As we determine a new value of t E that is value of parameter t for any potentially entering (PE) point we select t max as:  t max

Exceptional cases - Orthographic Projection 1)   We have an Orthographic projection, if f=0, then cot (β) =0 that is β=90 0 . 2)   β =cot-1 (1)=450 and this Oblique projec

Write a polygon clipping algorithm to clip a polygon against rectangular clipping are. Read the vertices of polygon to be clipped. 2. Read the coordinates of the rectangular cl


Role in Education and Training:- A multimedia presentation is an important way to introduce new concepts or described a new technology. Individuals determine it easy to understand

Summary of Graphic Primitives In this all section, we have illustrated the basic graphic primitives that are line, point and circle; we have also illustrated both practical an

How avar values generate to get realistic movement There are numerous ways of generating avar values to get realistic movement. One way is to use markers on a real person (or w

Line Clipping Algorithm - Cohen Sutherland Algorithm Line is a series of endless number of points; here no two points contain space in among them. Hence, the above said inequa

interactive picture-construction techniques

Question 1: (a) Explain the term ‘Corporate Identity'. (b) Give four examples of what a Corporate Identity comprises of and briefly explain their uses. (c) You are an employe