What are the utilizations of inverse transformation, Computer Graphics

What are the utilizations of Inverse transformation? Provide the Inverse transformation for translation, shearing, reflection, scaling and rotation.

Solution: We have observed the basic matrix transformations for translation, reflection; shearing, scaling and rotation are the origin of the coordinate system. Via multiplying these fundamental matrix transformations, we can build complicated transformations, as rotation regarding to an arbitrary point, mirror reflection regarding a line etc. This process is termed as concatenation of matrices and the consequential matrix is frequently referred to as the composite transformation matrix.  Inverse transformations play a significant role when you are dealing with a composite transformation. They appear to the rescue of fundamental transformations through making them applicable throughout the construction of composite transformation. You can seen that the Inverse transformations for shearing, reflection, scaling, rotation and translation have the subsequent relations, and v, θ, a, b, sx, sy, sz are each parameter concerned in the transformations.

1)  Tv -1 =T-v

2)  Rθ -1 = R

3) (i)  Shx-1(a) =Shx(-a)

(ii) Shy-1(b) = Shx(-b)

(iii) Shxy-1(a,b) Shx(-a,-b)

4) S-1sx,sy,sz =S1/sx,1/sy,1/sz

5) The transformation for mirror reflection regarding the principal axes does not change after inversion.

(i) Mx-1 =M-x= Mx

(ii) My-1 =M-y= My

(iii) Mz-1 =M-z= Mz

6) The transformation for rotations made regarding to x,y,z axes have the subsequent inverse:

 (i)  R-1 x,θ = Rx,-θ = RTx,θ

 (ii)  R-1y,θ  = Ry,-θ = RTy,θ

(iii) R-1z,θ  = Rz,-θ = RTz,θ

Posted Date: 4/3/2013 5:41:19 AM | Location : United States







Related Discussions:- What are the utilizations of inverse transformation, Assignment Help, Ask Question on What are the utilizations of inverse transformation, Get Answer, Expert's Help, What are the utilizations of inverse transformation Discussions

Write discussion on What are the utilizations of inverse transformation
Your posts are moderated
Related Questions
Entertainment - Applications For Computer Animation Advertising, Games, Film, Video, Television, Multimedia are various of the entertainment fields wherein computer animation h


What is Transformation?  Transformation is the method of introducing changes in the shape size and orientation of the object using scaling rotation reflection shearing & transl

Area-Subdivision method This method is a type of an image-space method although uses object-space operations re-ordering or sorting of surfaces as per to depth. Area sub-div

Plasma Panel - Raster Graphics and Clipping This is an inherent memory device. Images can be written into the surface point by point and they keep stable, without flicked for

Transformation for 3-D Reflection For 3-Dimensions reflections, we should to know the reference plane, which is a plane about that reflection is to be considered. Remember tha

Implement displacement mapping and bump mapping on a sphere. The displacement can be whatever your choice. The bump map can be whatever your choice as well.

What are the advantages of rendering polygons by scan line method?  i. The max and min values of the scan were simply found.  ii. The intersection of scan lines with edges i

Construction of an Isometric Projection - Transformation In this projection, the direction of projection i.e. d = (d 1 ,d 2 ,d 3 ) makes an identical angles with all the 3-pr

explain about gks