General perspective transformation, Computer Graphics

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

Posted Date: 4/4/2013 3:32:21 AM | Location : United States







Related Discussions:- General perspective transformation, Assignment Help, Ask Question on General perspective transformation, Get Answer, Expert's Help, General perspective transformation Discussions

Write discussion on General perspective transformation
Your posts are moderated
Related Questions

Combination of Positive and Negative Accelerations Actually, it is not that a body once decelerated or accelerated will remain so, although the motion may include both speed-up

Important Points for Designing the Animation Sequence There are several applications which do not follow this sequence as, real time computer animations generated by vehicle dr

Write a C program to create a window of specified size and position and draw the following objects with dimensions of your choice, to fit within the window.   (a) A point  (b) A

Gourand shading OR Intensity interpolation scheme Now there polygon is rendered through linearly interpolating intensity values across the surface. Intensity values for all po

pagemaker is a image editor

Numerical Analysis Packages: generally utilized software is: MatLab. Characteristics: Focus generally on numeric processing. Programming with mathematical skills usuall

Cases of clip a line segment-pq Case 1: As we determine a new value of t E that is value of parameter t for any potentially entering (PE) point we select t max as:  t max

Put the system of a geometric data table for a 3d rectangle. Solution : Vertex Table Edge Table Polygon Surface Table

Points and Lines - Graphic primitives In the previous section, we have seen to draw primitive objects; one has to firstly scan convert the objects. This concern to the operat