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


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

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


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
Suggest a method to draw an object as in figure using four Bézier curves of suitable degree Answer: Employ four quartic Bézier curves with the endpoint of one as the initial poi

Animation and Games - CAD and CAM In our childhood, we all have seen that the flip books of cricketers that came free with some soft drink and where some pictures of similar p

LCD - Liquid Crystal Display A liquid crystal display consists of two glass plates each containing a light polarizer. One glass plate contains vertical polarizer and the ot

Assignment Task Your task is to review and compare the current cad/cam software systems available with the intention to make a recommendation in the form of a written report f

Assume here are three polygon surfaces P,Q, R along with vertices specified by as: P: P1(1,1,1), P2(4,5,2), P3(5,2,5) And as Q: Q1(2,2,0.5), Q2(3,3,1.75), Q3(6,1,0.5) R: R1(0.5,

2D Shape Primitives You have already learnt to plot a point or a pixel on any display device. In this unit, we shall introduce you to various devices available for data input o

Assumptions for Polygon or Area Clipping Algorithm Assumption: The viewport and window are rectangular. So only, by identifying the maximum and the minimum coordinates t

Example1: Translate a square ABCD along with the coordinates as: A(0,0),B(5,0),C(5,5),D(0,5) via 2 units in x-direction and 3 units in y-direction. Solution: We can show the

Question: (a) Explain the importance of knowing and understanding your target market before doing a design work. Use example(s) to enhance your answer. (b) Describe the

Parameterized Systems - Computer Animation Parameterized Systems is the systems which permit objects motion features to be given as part of the object descriptions. The adjus