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
what is fixed point scaling? how composit transformation techniques works on it

Optical Character Recognition Software (OCR) Frequently, you will have printed matter and the other text to incorporate in your project although no electronic text file. Along

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

Suppose P be the point object along with the coordinate (x,y,z). We want to translate such object point to the new position as, P'(x',y',z') through the translation Vector as V=t x

Numerically-Controlled Machines: Prior to the development of Computer-aided design, the manufacturing world adopted elements controlled through numbers and letters to fi

Find the normalization transformation N, which uses the rectangle W(1, 1); X(5, 3); Y(4, 5) and Z(0, 3) as a window and the normalized deice screen as viewpoint.

Computer Animation Tools  To create various types of animation discussed above, we want to have particular software and hardware as well. Here, the fundamental constraint is re

Introduction To Computer Graphics Early man employed drawings to communicate even before he learnt to communicate, write or count. Incidentally, these earliest hierogly

Other Video File Formats: There are several the other formats for storing video in the digital formats. Such formats are usually used for the storage and viewing of video through

determine the tranformation matrix for reflection,computer graphics