General perspective transformation, Computer Graphics

Assignment Help:

General Perspective transformation w.r.t. an arbitrary center of projection

Suppose here that the COP is at C(a,b,c), as demonstrated in Figure.

By Figure, the vectors CP and CP' have the simila direction. The vector CP' is a factor of CP, which is CP'=α. CP

Hence, (x'-a)= α.(x-a)                                  z

(y'-b)= α.(y-b)

(z'-c)= α.(z-c)

1163_General Perspective Transformation.png

We know about the projection plane passing via a reference point R0(x0,y0,z0) and consisting a normal vector N= n1I+n2J+n3K, satisfies the subsequent equation:

n1.(x-x0)+n2.(y-y0)+n3.(z-z0)=0

When P'(x',y',z') lies upon this plane then we have:

n1.(x'-x0)+n2.(y'-y0)+n3.(z'-z0)=0

now substitute the value of x', y' and z' then we have:

α= (n1.(x0-a)+n2.(y0-b)+n3.(z0-c))/( n1.(x-a)+n2.(y-b)+n3.(z-c))

=((n1.x0+n2.y0+n3.z0)-(n1.a+n2.b+n3.c))/(n1.(x-a)+n2.(y-b)+n3.(z-c))

=(d0-d1)/(n1.(x-a)+n2.(y-b)+n3.(z-c))

=d/(n1.(x-a)+n2.(y-b)+n3.(z-c))

Currently,  d=d0-d1=  (n1.x0+n2.y0+n3.z0) - (n1.a+n2.b+n3.c)  shows  perpendicular distance from center of projection, C to the projection plane.

In order to determine the general perspective transformation matrix so we have to proceed as given here:

Translate COP, C (a, b, c) to the origin.  Now, R'0=(x0-a, y0-b, z0-c) turn sinto the reference point of the translated plane which is normal vector will remain similar.

By applying the general perspective transformation as Pper,N,R'o

Now translate the origin back to C as.

116_General Perspective Transformation 2.png

Here d = N.CR' 0 = d0 - d1 = (n1. x0 + n2. Y0 + n3.z0) - (n1.a+n2.b +n3.c)

= n1. (x0 - a) + n2. (y0 - b) + n3. (z0 - c)

And also d1 = n1.a + n2.b + n3.c


Related Discussions:- General perspective transformation

C++ programming, self test exercise 17 asked you to overload the operator >...

self test exercise 17 asked you to overload the operator >> and the operator Overload biinary operator + to add pairs according to the rule (a, b) + (c, d) = (a + c, b, + d) overl

Difference, difference between vecgen algoritham and bresenham''s algori

difference between vecgen algoritham and bresenham''s algori

Alias wavefront - softwares for computer animation, Alias Wavefront - Softw...

Alias Wavefront - Softwares for Computer Animation Alias is one of the highest computer animation packages out there. Alias was formed by the company which used to be Alias, a

Multimedia tool features, Multimedia Tool Features General to nearly a...

Multimedia Tool Features General to nearly all multimedia tool platforms are various features for encapsulating the content, presenting the data, acquiring user input and cont

View volumes and general projection transformations, View Volumes and Gener...

View Volumes and General Projection Transformations You have to remember that the view volume is the volume which sets up near and far extents, top and bottom extents and left

Ray tracing - polygon rendering and ray tracing methods, Ray Tracing - poly...

Ray Tracing - polygon rendering and ray tracing methods "Ray tracing" is a technique of following the light by the eye to the light source. While ray casting only relates its

What are the utilizations of inverse transformation, What are the utilizati...

What are the utilizations of Inverse transformation? Provide the Inverse transformation for translation, shearing, reflection, scaling and rotation. Solution: We have observed

Display devices - graphics hardware, Display Devices - Graphics Hardware ...

Display Devices - Graphics Hardware Since the importance of output and input devices has been discussed over, so let us now focus our discussion particularly on display dev

Cohen sutherland line clippings algorithm, Cohen Sutherland Line Clippings ...

Cohen Sutherland Line Clippings Algorithm The clipping problem is identified by dividing the region surrounding the window area into four segments Up as U, Down as D, Left as

Where the video controller is used, Where the video controller is used?  ...

Where the video controller is used?  A special purpose processor, which is used to control the operation of the display device, is called as display controller or video control

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