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
QUESTION You are employed as a graphics designer in an advertising agency and recently completed a brochure artwork for a client. You need to send the file for printing before

What is a Blobby object?  Some objects do not handle a fixed shape, but change their surface characteristics in sure motions or when in proximity to other objects. That is call

Polygon or Area Clipping Algorithm - Sutherland-Hodgman Algorithm There are different algorithms as Liang-Barsky, Line clipping, Weiler-Atherton Polygon Clipping,

Write the Liang B arsky line clipping algorithm. Why is Liang Barsky algorithm more efficient than the Cohen Sutherland algorithm?  Liang Barsky Line Clipping: Faster line cl

What are the advantages of Bresenham's line drawing algorithm over DDA line drawing algorithm? DDA and Bresenham algorithms both are efficient line drawing algorithm. Breaenham

Disadvantages with the Boundary Representation (i) It requires more storage than the corresponding half-space method. (ii) There is no guarantee that the object created is v

what is mean by virtual reality?

What is Graphics It is a term that refers to any computer device or program which makes a computer able of displaying and manipulating pictures. The name also refers to the im


(a)  Voltage or Electro-Magnetic Field Tablet and Pointer: This has a grid of wires, embedded in the tablet surface along with various voltages or magnetic fields consequent to va