Translation of objects in computer graphics
Last Updated :
03 May, 2024
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:
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:
CPP
#include <iostream>
#include <vector>
using namespace std;
// Function to translate a point
void translatePoint(vector<int>& P, const vector<int>& T) {
// Original point
cout << "Original Coordinates: (" << P[0] << ", " << P[1] << ")" << endl;
// Calculate translated coordinates
P[0] += T[0];
P[1] += T[1];
// Translated point
cout << "Translated Coordinates: (" << P[0] << ", " << P[1] << ")" << endl;
}
int main() {
vector<int> P = {5, 8}; // coordinates of point
vector<int> T = {2, 1}; // translation factor
translatePoint(P, T);
return 0;
}
public class Translation {
public static void main(String[] args) {
int[] P = {5, 8}; // coordinates of point
int[] T = {2, 1}; // translation factor
translatePoint(P, T);
}
// function to translate point
static void translatePoint(int[] P, int[] T) {
// Original point
System.out.println("Original Coordinates: (" + P[0] + ", " + P[1] + ")");
// Calculate translated coordinates
P[0] += T[0];
P[1] += T[1];
// Translated point
System.out.println("Translated Coordinates: (" + P[0] + ", " + P[1] + ")");
}
}
# Function to translate point
def translate_point(P, T):
# Original point
print("Original Coordinates: ({}, {})".format(P[0], P[1]))
# Calculate translated coordinates
P[0] += T[0]
P[1] += T[1]
# Translated point
print("Translated Coordinates: ({}, {})".format(P[0], P[1]))
# Main function
def main():
# Coordinates of point
P = [5, 8]
# Translation factor
T = [2, 1]
# Call the function to translate the point
translate_point(P, T)
# Execute the main function
if __name__ == "__main__":
main()
// Function to translate a point
function translatePoint(P, T) {
// Original point
console.log("Original Coordinates: (" + P[0] + ", " + P[1] + ")");
// Calculate translated coordinates
P[0] += T[0];
P[1] += T[1];
// Translated point
console.log("Translated Coordinates: (" + P[0] + ", " + P[1] + ")");
}
// Main function
function main() {
let P = [5, 8]; // coordinates of point
let T = [2, 1]; // translation factor
translatePoint(P, T);
}
// Calling the main function
main();
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:
CPP
#include <iostream>
#include <graphics.h>
// function to translate line
void 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 program
int main() {
int P[2][2] = {{5, 8}, {12, 18}}; // coordinates of points
int T[] = {2, 1}; // translation factor
translateLine(P, T);
return 0;
}
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
CPP
#include <graphics.h>
#include <iostream>
// Function to translate rectangle
void translateRectangle(int P[][2], int T[])
{
int gd = DETECT, gm, errorcode;
initgraph(&gd, &gm,
"c:\\tc\\bgi"); // Initialize graphics
// Original rectangle
setcolor(2);
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
setcolor(3);
rectangle(P[0][0], P[0][1], P[1][0], P[1][1]);
delay(5000); // Delay to show the result
closegraph(); // Close graphics
}
// Driver program
int main()
{
// 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;
}
import java.util.Arrays;
public class Main {
// Function to translate rectangle
public static void translateRectangle(int[][] P,
int[] T)
{
// Original rectangle
System.out.println("Original rectangle: (" + P[0][0]
+ ", " + P[0][1] + ") - ("
+ P[1][0] + ", " + P[1][1]
+ ")");
// Calculating translated coordinates
P[0][0] += T[0];
P[0][1] += T[1];
P[1][0] += T[0];
P[1][1] += T[1];
// Translated rectangle
System.out.println("Translated rectangle: ("
+ P[0][0] + ", " + P[0][1]
+ ") - (" + P[1][0] + ", "
+ P[1][1] + ")");
}
// Driver program
public static void main(String[] args)
{
// Rectangle coordinates of top left and bottom
// right points
int[][] P = { { 5, 8 }, { 12, 18 } };
int[] T = { 2, 1 }; // Translation factor
translateRectangle(P, T);
}
}
# Importing required libraries
from matplotlib import pyplot as plt
from matplotlib.patches import Rectangle
# Function to translate rectangle
def translate_rectangle(P, T):
# Create a figure and a set of subplots
fig, ax = plt.subplots()
# Original rectangle
# Rectangle((xmin, ymin), width, height)
original_rectangle = Rectangle(
(P[0][0], P[0][1]), P[1][0] - P[0][0], P[1][1] - P[0][1], fill=None, edgecolor='r')
ax.add_patch(original_rectangle)
# 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
translated_rectangle = Rectangle(
(P[0][0], P[0][1]), P[1][0] - P[0][0], P[1][1] - P[0][1], fill=None, edgecolor='b')
ax.add_patch(translated_rectangle)
# Set limits for x and y axis
ax.set_xlim([0, 20])
ax.set_ylim([0, 20])
# Show the plot with the original and translated rectangle
plt.show()
# Driver program
if __name__ == "__main__":
# Coordinates of top left and bottom right points
P = [[5, 8], [12, 18]]
# Translation factor
T = [2, 1]
translate_rectangle(P, T)
// Function to translate rectangle
function translateRectangle(P, T) {
// Original rectangle
console.log(`Original rectangle: (${P[0][0]}, ${P[0][1]}) - (${P[1][0]}, ${P[1][1]})`);
// Calculating translated coordinates
P[0][0] += T[0];
P[0][1] += T[1];
P[1][0] += T[0];
P[1][1] += T[1];
// Translated rectangle
console.log(`Translated rectangle: (${P[0][0]}, ${P[0][1]}) - (${P[1][0]}, ${P[1][1]})`);
}
// Driver program
function main() {
// Rectangle coordinates of top left and bottom right points
var P = [[5, 8], [12, 18]];
var T = [2, 1]; // Translation factor
translateRectangle(P, T);
}
// Call the main function
main();
Output:
References : https://math.hws.edu/graphicsbook/
2D Translation in Computer Graphics
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