Translation of objects in computer graphics

19 Jun, 2022
In computer graphics, we have seen how to draw some basic figures like line and circles. In this post we will discuss on basics of an important operation in computer graphics as well as 2-D geometry, which is transformation. In computer graphics, transformation of the coordinates consists of three major processes:  
Translation
Rotation
Scaling
In this post we will discuss about translation only.  
What is translation?
A translation process moves every point a constant distance in a specified direction. It can be described as a rigid motion. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. Suppose, If point (X, Y) is to be translated by amount Dx and Dy to a new location (X’, Y’) then new coordinates can be obtained by adding Dx to X and Dy to Y as:  
X' = Dx + X
Y' = Dy + Y

or P' = T + P where

P' = (X', Y'),
T = (Dx, Dy ),
P = (X, Y)
Here, P(X, Y) is the original point. T(Dx, Dy) is the translation factor, i.e. the amount by which the point will be translated. P'(X’, Y’) is the coordinates of point P after translation. Examples:  
Chapters
descriptions off, selected
captions settings, opens captions settings dialog
captions off, selected
English
This is a modal window.
Beginning of dialog window. Escape will cancel and close the window.
End of dialog window.
Input : P[] = {5, 6}, T = {1, 1}
Output : P'[] = {6, 7}

Input : P[] = {8, 6}, T = {-1, -1}
Output : P'[] = {7, 5}
Whenever we perform translation of any object we simply translate its each and every point. Some of basic objects along with their translation can be drawn as:  
Point Translation P(X, Y) : Here we only translate the x and y coordinates of given point as per given translation factor dx and dy respectively. Below is the C++ program to translate a point:  
Point Translation P(X, Y) : Here we only translate the x and y coordinates of given point as per given translation factor dx and dy respectively. Below is the C++ program to translate a point:  
CPP
// C++ program for translation// of a single coordinate#include<bits/stdc++.h>#include<graphics.h>  using namespace std;  // function to translate pointvoid translatePoint ( int P[], int T[]){    /* init graph and putpixel are used for        representing coordinates through graphical        functions     */    int gd = DETECT, gm, errorcode;    initgraph (&gd, &gm, "c:\\tc\\bgi");           cout<<"Original Coordinates :"<<P[0]<<","<<P[1];      putpixel (P[0], P[1], 1);      // calculating translated coordinates    P[0] = P[0] + T[0];    P[1] = P[1] + T[1];      cout<<"\nTranslated Coordinates :"<< P[0]<<","<< P[1];         // Draw new coordinates    putpixel (P[0], P[1], 3);    closegraph();}  // driver programint main(){    int P[2] = {5, 8}; // coordinates of point    int T[] = {2, 1}; // translation factor    translatePoint (P, T);    return 0;} 
Output:  
Output:  
Original Coordinates : 5, 8
Translated Coordinates : 7, 9
 Line Translation: The idea to translate a line is to translate both of the end points of the line by the given translation factor(dx, dy) and then draw a new line with inbuilt graphics function. Below is the C++ implementation of above idea:  
 
Line Translation: The idea to translate a line is to translate both of the end points of the line by the given translation factor(dx, dy) and then draw a new line with inbuilt graphics function. Below is the C++ implementation of above idea:  
CPP
// cpp program for translation// of a single line#include<bits/stdc++.h>#include<graphics.h>  using namespace std;  // function to translate linevoid translateLine ( int P[][2], int T[]){    /* init graph and line() are used for        representing line through graphical       functions     */    int gd = DETECT, gm, errorcode;    initgraph (&gd, &gm, "c:\\tc\\bgi");           // drawing original line using graphics functions    setcolor (2);    line(P[0][0], P[0][1], P[1][0], P[1][1]);      // calculating translated coordinates    P[0][0] = P[0][0] + T[0];    P[0][1] = P[0][1] + T[1];    P[1][0] = P[1][0] + T[0];    P[1][1] = P[1][1] + T[1];      // drawing translated line using graphics functions    setcolor(3);    line(P[0][0], P[0][1], P[1][0], P[1][1]);    closegraph();}  // driver programint main(){    int P[2][2] = {5, 8, 12, 18}; // coordinates of point    int T[] = {2, 1}; // translation factor    translateLine (P, T);    return 0;} 
Output:  
Output:  
 Rectangle Translation : Here we translate the x and y coordinates of both given points A(top left ) and B(bottom right) as per given translation factor dx and dy respectively and then draw a rectangle with inbuilt graphics function  
 
Rectangle Translation : Here we translate the x and y coordinates of both given points A(top left ) and B(bottom right) as per given translation factor dx and dy respectively and then draw a rectangle with inbuilt graphics function  
CPP
// C++ program for translation// of a rectangle#include<bits/stdc++.h>#include<graphics.h>using namespace std;  // function to translate rectanglevoid translateRectangle ( int P[][2], int T[]){    /* init graph and rectangle() are used for     representing rectangle through graphical functions */    int gd = DETECT, gm, errorcode;    initgraph (&gd, &gm, "c:\\tc\\bgi");     setcolor (2);    // rectangle (Xmin, Ymin, Xmax, Ymax)    // original rectangle    rectangle (P[0][0], P[0][1], P[1][0], P[1][1]);      // calculating translated coordinates    P[0][0] = P[0][0] + T[0];    P[0][1] = P[0][1] + T[1];    P[1][0] = P[1][0] + T[0];    P[1][1] = P[1][1] + T[1];      // translated rectangle (Xmin, Ymin, Xmax, Ymax)    // setcolor(3);    rectangle (P[0][0], P[0][1], P[1][0], P[1][1]);    // closegraph();}  // driver programint main(){    // Xmin, Ymin, Xmax, Ymax as rectangle    // coordinates of top left and bottom right points    int P[2][2] = {5, 8, 12, 18};    int T[] = {2, 1}; // translation factor    translateRectangle (P, T);    return 0;} 
Output:  
Output:  
 
 
References : http://math.hws.edu/graphicsbook/.This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
arorakashish0911
computer-graphics
Algorithms
Algorithms
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.