Rotation - 2-d and 3-d transformations, Computer Graphics

Assignment Help:

Rotation - 2-d and 3-d transformations

Given a 2-D point P(x,y), that we want to rotate, along with respect to an arbitrary point A(h,k). Suppose P'(x'y') be the effect of anticlockwise rotation of point P via angle q about A, that is demonstrated in Figure 6.

1722_Rotation - 2-d and 3-d transformations.png

Because, the rotation matrix Rq is explained only with respect to the origin, we have a set of fundamental transformations, that constitutes the composite transformation to calculate the rotation regarding a given arbitrary point A, signified by Rq,A. We can find out the transformation Rq,A in three steps:

Translate the point A(h,k) to the origin O, hence the center of rotation A is at the origin.

Execute the necessary rotation of q degrees about the origin, and also

Translate the origin back to the original position A(h,k).     

Using v=hI+kJ as the translation vector, we have the following sequence of  three transformations:

Rq,A =T-v. Rq. Tv

465_Rotation - 2-d and 3-d transformations 2.png


Related Discussions:- Rotation - 2-d and 3-d transformations

Categories of line segments - 2d clipping algorithms, Categories of Line Se...

Categories of Line Segments It categorizes line segments into three categories (i) trivially rejected (ii) trivially selected (iii) may be partially visible or totally invisibl

Is cad only helpful for design drawings, Question: Is CAD only helpful for ...

Question: Is CAD only helpful for design drawings? No. When true-scale, structurally valid drawings are the purpose for CAD's existence; it utilizes is as diverse as imagination

Devi, Explain the 3d transformations

Explain the 3d transformations

Education and training systems multimedia in education, Education and train...

Education and training systems are making with three major objectives as: a) The learning objectives and purpose of the training. b)  Assessment or testing of the students to

Image processing, Image Processing New digital technology has made this...

Image Processing New digital technology has made this possible for the manipulation of multi- dimensional signals along with systems which range from easy digital circuits to

Explain the acoustic properties of sound, Problem: (a) What is meant b...

Problem: (a) What is meant by ‘Time - Stretching ‘in relation to a sound data file? (b) Calculate the size of a 5 minutes mono sound file of CD quality and with a 16 -bit

Removing polygons hidden through a surrounding polygon, Removing Polygons H...

Removing Polygons Hidden through a Surrounding Polygon: The key to capable visibility calculation lies actually a polygon is not visible whether it is in back of a surrounding

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd