Carry out a perspective projection, Computer Graphics

Assignment Help:

Consider the line segment AB in 3-Dimentional parallel to the z-axis along with end points A (- 5,4,2) and also B (5,-6,18). Carry out a perspective projection upon the X=0 plane; here the eye is placed at (10, 0,10).

Solution: Suppose here that P (x, y, z) be any point in the space.

The parametric equation of a line beginning from E and passing via P is: E + t. (P - E), o < t < 1.

= (10,0,10) + t. [(x, y, z) - (10, 0, 10)]

= (10, 0,10) + t [(x - 10)], y (z - 10)]

= (t. (x - 10) + 10, t. y, t (z - 10) + 10)

Suppose a point P' can be obtained, as t = t*

∴P' = (x', y', z') = (t* (x - 10) + 10, t*.y, t*. (z - 10) + 10)

 Because the point P' lies on x = 0 plane as:

1898_Carry out a perspective projection 1.png

          Figure: (j)

= t* (x - 10) + 10 = 0

= t* =(- 10)/ (x - 10)

= P' = (x',y',z') = (0,((-10.y)/(x - 10)),(((-10)(z - 10))/(x - 10)), + 10)

(0, ((-10.y)/(x - 10)),((10x - 10z)/(x - 10)))

In terms of Homogeneous coordinate system;

P' = (x', y', z', 1) = ( 0, ((-y )/((x - 10) - 1)) ,  (x -z)/((x/10) - 1)), 1)

= (0, -y, x-z, ((x/10) - 1))

In Matrix form there is:

2067_Carry out a perspective projection 2.png

-------------------------(1)

In above equation (1) is the needed perspective transformation, that gives a coordinates of a projected point P' (x', y', z') on the x = 0 plane, whereas a point p (x, y, z) is viewed from E (10, 0, 10)

Currently, for the specified points A (-5, 4, 2) and B (5, -6, 18), A' and B' are their projection upon the x = 0 plane.

So now from Equation (1) we get:

1289_Carry out a perspective projection 3.png

= (0,-4, -7, ((-5/10) - 1))

= (0 , -40, -70, -15)

(0, 40/15, 70/15, 1)

Thus x1' = 0;  y1' = 2.67 ;    z1' = 4.67

As the same in:

137_Carry out a perspective projection 4..png

= (0, 60, - 130, - 5)

= (0, - 12, 26, 1)

 Thus x2' = 0 ;  y2' = - 12 ;    z2' = 26

Hence the projected points A' and B' of specified points A and B are:

A' = (x1', y1'z1') = (0, 2.67, 4.67)    and     B' = (x2', y2', z2') = (0, - 12, 26, 1)


Related Discussions:- Carry out a perspective projection

Functioning of hardcopy devices and output primitives, Functioning of hardc...

Functioning of hardcopy devices and Output primitives 1.  Functioning of hardcopy devices-laser printers and dot matrix printers, plotters.  2.  Output primitives: Graphics

Define affine transformation, Define Affine transformation?  A coordina...

Define Affine transformation?  A coordinate transformation of the form X= axxx +axyy+bx, y 'ayxx+ayy y+by  is known as a two-dimensional affine transformation. Every of the tra

Image - based rendering, Explore and understand light field. Checking out o...

Explore and understand light field. Checking out one of the image libraries. 1. You can modify existing source code, or develop your own to achieve light field rendering; 2.

Categorization of light resources - point source, Categorization of Light r...

Categorization of Light resources - Point source This is the easiest model for a light emitter. Currently rays from source obey radically diverging ways from the source positi

File format-introduction to computer graphics, File format We want an i...

File format We want an image of a Fly. The wings are incompletely transparent and to present that in our presentation what be problematic if suitable file format is not there.

Discuss the overview of multimedia networks, Question 1 Discuss the overvi...

Question 1 Discuss the overview of multimedia networks Question 2 Discuss the types of synchronization in multimedia system >> Basic synchronization issues Content R

Image capture formats, Image Capture Formats: Video cameras appear in...

Image Capture Formats: Video cameras appear in two various image capture formats: progressive and interlaced scan. Interlaced Scan It is a technique of enhancing the

Text generation and character generation techniques, Write short notes on T...

Write short notes on Text generation.   OR Character Generation Techniques  Character Generation Techniques   Two different representations are used for storing computer fon

Event driven devices - polling, Event Driven Devices - Polling Pollin...

Event Driven Devices - Polling Polling: The status of all devices is periodically checked in a repetitive manner through a polling loop. While an event happens, the loop is

Application of sutherland hodgman polygon clipping, For good understanding ...

For good understanding of the application of the rules specified above see the following figure, where the shaded region demonstrates the clipped polygon. Fi

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