Merge pull request #1464 from Arushi2S/Arushi2S-patch-3

Geometric Transformation Algorithms

Author: pankaj-bind

Geometric Transformation Algorithm/3D Rotation (About X, Y, or Z Axis)/README.md

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+# README for 3D Rotation (User-Specified Axis)
+
+This project implements a 3D Rotation algorithm in C, where the user specifies the axis of rotation (X, Y, or Z) along with the rotation angle. It transforms a 3D point to new coordinates after rotation.
+
+## Process
+
+### User Input:
+1. The user is prompted to enter the coordinates of the point in 3D: (x, y, z).
+2. The user chooses the axis of rotation: X, Y, or Z.
+3. The user specifies the rotation angle in degrees.
+
+### Rotation Calculation:
+The program rotates the input point about the chosen axis using trigonometric transformations:
+
+#### X-axis Rotation:
+-  newY = y * cos(angle) - z * sin(angle)  
+-  newZ = y * sin(angle) + z * cos(angle)
+
+#### Y-axis Rotation:
+-   newX = x * cos(angle) + z * sin(angle)
+-   newZ = -x * sin(angle) + z * cos(angle)
+
+#### Z-axis Rotation:
+-   newX = x * cos(angle) - y * sin(angle)  
+-   newY = x * sin(angle) + y * cos(angle)
+
+### Output:
+The program prints the new coordinates of the point after rotation.
+
+## Example Run
+
+### Input:
+Enter the coordinates of the point (x y z): 1 2 3  
+Enter the axis of rotation (X, Y, or Z): Z  
+Enter the rotation angle (in degrees): 90
+
+
+### Output:
+After rotation about Z-axis: (1, 2, 3) -> (-2, 1, 3)
+
+# Complexity Analysis
+### Time Complexity:𝑂(1) 
+O(1) since the program performs a constant number of operations regardless of input size.
+
+### Space Complexity:𝑂(1) 
+O(1) as no extra memory is allocated beyond the basic variables for coordinates and calculations.
+
+# Assumptions
+The program assumes the angle is entered in degrees and converts it to radians internally.
+It only rotates about one axis at a time.
+The axis input is case-insensitive (X, Y, or Z)." format this file 

Geometric Transformation Algorithm/3D Rotation (About X, Y, or Z Axis)/program.c

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+#include <stdio.h>
+#include <math.h>
+#include <ctype.h>
+
+void rotate(int *x, int *y, int *z, float angle, char axis) {
+    float rad = angle * (M_PI / 180);  // Convert angle to radians
+    int newX = *x, newY = *y, newZ = *z;
+
+    if (axis == 'X') {  // Rotate about the X-axis
+        newY = round(*y * cos(rad) - *z * sin(rad));
+        newZ = round(*y * sin(rad) + *z * cos(rad));
+    } else if (axis == 'Y') {  // Rotate about the Y-axis
+        newX = round(*x * cos(rad) + *z * sin(rad));
+        newZ = round(-*x * sin(rad) + *z * cos(rad));
+    } else if (axis == 'Z') {  // Rotate about the Z-axis
+        newX = round(*x * cos(rad) - *y * sin(rad));
+        newY = round(*x * sin(rad) + *y * cos(rad));
+    }
+
+    printf("\nAfter rotation about %c-axis:\n", axis);
+    printf("(%d, %d, %d) -> (%d, %d, %d)\n", *x, *y, *z, newX, newY, newZ);
+}
+
+int main() {
+    int x, y, z;
+    float angle;
+    char axis;
+
+    printf("Enter the coordinates of the point (x y z): ");
+    scanf("%d %d %d", &x, &y, &z);
+
+    printf("Enter the axis of rotation (X, Y, or Z): ");
+    scanf(" %c", &axis);  // Space before %c to avoid newline issue
+    axis = toupper(axis); // Ensure consistency with uppercase
+
+    printf("Enter the rotation angle (in degrees): ");
+    scanf("%f", &angle);
+
+    rotate(&x, &y, &z, angle, axis);
+    return 0;
+}

Geometric Transformation Algorithm/Shear Transformation/README.md

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+# README for 2D Shear Transformation
+
+This project contains a 2D Shear Transformation program in C, which allows users to shear a set of points along both the X-axis and Y-axis based on user-specified shear factors.
+
+## Process
+
+### User Input:
+1. The user inputs the number of points.
+2. They enter the coordinates for each point as **(x, y)**.
+3. They specify the shear factors: **shearX** for the X-axis and **shearY** for the Y-axis.
+
+### Shear Calculation:
+The coordinates are transformed using the following equations:  
+newX = x[i] + shearX * y[i]   
+newY = y[i] + shearY * x[i]  
+Each point is updated independently based on the given shear factors.
+
+### Output:
+The program prints the new coordinates after applying the shear transformation.
+
+## Example Run
+
+**Input:**
+Enter the number of points: 2   
+Enter the coordinates of the points (x y): 1 2 3 4  
+Enter the shear factors (shearX shearY): 1.0 0.5
+
+**Output:**
+Sheared Coordinates: (1, 2) -> (3, 2) (3, 4) -> (5, 5)
+
+## Complexity Analysis
+
+### Time Complexity:
+- **O(n)**, where **n** is the number of points. Each point is processed once.
+
+### Space Complexity:
+- **O(1)**, as the program only uses input arrays and basic variables.
+
+## Assumptions
+- The shear factors are real numbers (floating-point values).
+- The program does not validate whether the shear factors result in visually meaningful transformations.
+- Input coordinates are assumed to be integers.

Geometric Transformation Algorithm/Shear Transformation/program.c

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+#include <stdio.h>
+
+void shear2D(int x[], int y[], int n, float shearX, float shearY) {
+    printf("\nSheared Coordinates:\n");
+    for (int i = 0; i < n; i++) {
+        int newX = x[i] + shearX * y[i];
+        int newY = y[i] + shearY * x[i];
+        printf("(%d, %d) -> (%d, %d)\n", x[i], y[i], newX, newY);
+    }
+}
+
+int main() {
+    int n;
+    printf("Enter the number of points: ");
+    scanf("%d", &n);
+    
+    int x[n], y[n];
+    printf("Enter the coordinates of the points (x y):\n");
+    for (int i = 0; i < n; i++) {
+        scanf("%d %d", &x[i], &y[i]);
+    }
+    
+    float shearX, shearY;
+    printf("Enter the shear factors (shearX shearY): ");
+    scanf("%f %f", &shearX, &shearY);
+
+    shear2D(x, y, n, shearX, shearY);
+    return 0;
+}