## Derive the common transformation of parallel projection, Computer Graphics

Assignment Help:

Derive the common transformation of parallel projection into the xy-plane in the direction of projection d=aI+bJ+cK.

Solution: The common transformation of parallel projection into the xy-plane towards the projection d=aI+bJ+cK, is derived as follows in the figure a:

Assume here that P(x,y,z) be an object point, projected to P'(x',y',z') into the z'=0 plane. By figure (a) we observe that the vectors d and PP' have the similar direction. It implies that:

PP'=k.d , comparing part, we find that:

x'-x=k.a

y'-y=k.b

z'-z=k.c

As like z'=0 on the projection plane, we obtain k=-z/c. As,

x'=x-a.z/c

y'=y-b.z/c

z'=0

Figure: (a)

In terms of coordinates of homogeneous, so this equation can be become as:

It is,  P'h =Ph.Ppar,z , here Ppar,z  is the parallel projection along with the direction of projection d along the unit vector k.

#### What is shearing, What is shearing?  The shearing transformation actua...

What is shearing?  The shearing transformation actually slants the object with the X direction or the Y direction as needed.ie; this transformation slants the shape of an obje

#### 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

#### Scaling, Scaling, shear, reflection and Viewing coordinates 1) Scaling,...

Scaling, shear, reflection and Viewing coordinates 1) Scaling, shear and reflection operations have natural extensions to 3D.    2)  Viewing coordinates are the coordinates

#### Calculate the gray level value for all the pixels, An 8x8 image f[i,j] has ...

An 8x8 image f[i,j] has gray levels given by the following equation: f [i , j]= ? i-j ? ; i,j=0,1,2,3,4,5,6,7. a. Calculate the gray level value for all the pixels in the 8x8

#### Video games, why do video game characters look better today?

why do video game characters look better today?

#### Important points about the surface of revolution, Important points about th...

Important points about the Surface of Revolution a) if a point on base curve is given by parametric form, that are: (x(u), y(u), z(u)) so surface of revolution regarding to th

#### What is aspect ratio, What is Aspect ratio?  The ratio of vertical poin...

What is Aspect ratio?  The ratio of vertical points to the horizontal points essential to produce length of lines in both directions of the screen is known as the Aspect ratio.

#### Implement cohen sutherland and liang barsky algorithm, Implement Cohen Suth...

Implement Cohen Sutherland and Liang Barsky line clipping algorithms in C-language.  Test your code for line segments with end points falling in various regions.

#### Differentiate images and graphics, Question 1 Discuss the general properti...

Question 1 Discuss the general properties of analog signal Question 2 Differentiate images and graphics Question 3 Explain the video compression standard H.263

#### Scan line polygon fill algorithm - raster graphics, Scan Line Polygon Fill ...

Scan Line Polygon Fill Algorithm - Raster Graphics In such algorithm, the information for a solid body is stored in the frame buffer and utilizing that information each pixel