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Geometric Transformation Algorithm/Shear Transformation/README.md
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# README for 2D Shear Transformation | ||
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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. | ||
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## Process | ||
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### 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. | ||
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### 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. | ||
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### Output: | ||
The program prints the new coordinates after applying the shear transformation. | ||
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## Example Run | ||
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**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 | ||
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**Output:** | ||
Sheared Coordinates: (1, 2) -> (3, 2) (3, 4) -> (5, 5) | ||
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## Complexity Analysis | ||
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### Time Complexity: | ||
- **O(n)**, where **n** is the number of points. Each point is processed once. | ||
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### Space Complexity: | ||
- **O(1)**, as the program only uses input arrays and basic variables. | ||
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## 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. |