X-shear regarding the origin - 2-d and 3-d transformations, Computer Graphics

X-shear Regarding 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, via the given scale parameter 'a',that is, P'(x'y') be the outcome of x-shear of point P(x,y) through scale factor a regarding the origin, that is demonstrated in Figure 4.

1873_X-shear Regarding the Origin - 2-d and 3-d Transformations.png

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

x' = x + ay

y' = y         

= Shx(a)                                                    ------(11a)

Here 'a' is a constant (termed as shear parameter) which measures the degree of shearing.  The shearing is in the opposite direction, if a is negative.

Remember that P(0,H) is taken into P'(aH,H).  This obeys that the shearing angle A which is the angle by that the vertical edge was sheared; is specified by:

tan(A) = aH/H = a.

Consequently the parameter a is simply the tan of the shearing angle. Within matrix form of 2-D Euclidean system, we contain:

1131_X-shear Regarding the Origin - 2-d and 3-d Transformations 1.png

(12)

In terms of Homogeneous Coordinates, above equation (12) is:

456_X-shear Regarding the Origin - 2-d and 3-d Transformations 2.png

-----------------------(13)

That is, P'h = Ph Shx(a)   --(14)

Here Ph and P'h represent object points, before and after needed transformation, in Homogeneous Coordinates and Shx(a) is termed as homogeneous transformation matrix for x-shear along with scale parameter 'a' in the x-direction.

Posted Date: 4/3/2013 5:27:11 AM | Location : United States







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

Write discussion on X-shear regarding the origin - 2-d and 3-d transformations
Your posts are moderated
Related Questions
Rotation - 2-D and 3-D transformations Within 2-D rotation, an object is rotated via an angle θ along w.r.t. the origin. This angle is assumed to be +ive for anticlockwise rot

Question: (a) Some adverts are set up only with facts and with no use on concepts/emotions. Name and explain two strengths and two weaknesses of "no use of emotions in

Use DDA algorithm to get the output of your program as shown in Figure ANs: Use DDA( ) function to plot line segments that have end points on diametrically opposite points

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

Amiga - Hardware for computer animation Originally owned through Commodore, Amiga computers have conduct a position in the computer animation industry for many years. This is

The table as given below demonstrates possible values of such parameters for classic applications of digital video. Application                  Frame rate                  Dime

Question 1: a. List respectively ten main technical and human components necessary to ensure a studio-based one-plus-one interview? b. How does each component contribute in


Axis of Rotation - Construction of a solid with a translational sweep Figure:  (a)                                                                          Figure  (b)

The subsequent are also considered graphics applications as: • Paint Programs: Permit you to create rough freehand drawings. The images are saved as bit maps and can simply be