Page 150 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Lab on Computer Graphics

Notes So a 4×4 matrix implements a frame to frame transformation for translated frames, and any
matrix of this type (for arbitrary a, b, c) will translate the frame F. We call any matrix

È 1 000˘
Í 01 00 ˙
T a,b,c = Í ˙
Í 00 10˙
Í ˙
Î ab c 1 ˚
A translation matrix and utilize matrices of this type to implement translations.
Transformation Directly to the Coordinates of Point
 
, )
Given a frame F = (, ,uv wo and a point P that has coordinates (u, v, w) in F, if we apply the
transformation to the coordinates of the point we obtain
È 1 000˘
Í 01 00 ˙
[u v w 1] Í ˙ = [u + a v + b w + c 1]
Í 00 10˙
Í ˙
Î ab c 1 ˚
That is, we can translate the point within the frame F. An illustration of this is shown in Figure 9.1

Figure 9.1: Translating a Point

Translation is a simple transformation that is calculated directly from the conversion matrix for
two frames, one a translate of the other. The translation matrix is most frequently applied to
all points of an object in a local coordinate system resulting in an action that moves the object
within this system.
#include<stdio.h>
#include<string.h>
#include<alloc.h>
#include<graphics.h>
#include<stdlib.h>
#include<conio.h>
#include<bios.h>
#include<math.h>
#include<dos.h>
#defineLTARROW0x4B
#defineRTARROW0x4D
#defineUPARROW0x48
#defineDNARROW0x50
#defineCR0x0d

144 LOVELY PROFESSIONAL UNIVERSITY