Matrix Multiplication To Rotate An Image In C#?

Question

I need to write a program that uses matrix multiplication to rotate an image (a simple square), based on the center of the square, a certain amount of degree based on what I need. Any help on this would be greatly appreciated?

Answer 1

using System;

public readonly struct Point2D

{

public double X { get; }

public double Y { get; }

public Point2D(double x, double y) { X = x; Y = y; }

public override string ToString() => $"({X:F2}, {Y:F2})";

}

public static class Rotation

{

public static Point2D[] RotateSquare(Point2D[] corners, double degrees)

{

if (corners.Length != 4)

throw new ArgumentException("Expected 4 corners.", nameof(corners));

// 1. Find the center (average of the four corners)

double centerX = (corners[0].X + corners[1].X + corners[2].X + corners[3].X) / 4.0;

double centerY = (corners[0].Y + corners[1].Y + corners[2].Y + corners[3].Y) / 4.0;

// 2. Convert degrees to radians, precompute sin and cos

double radians = degrees * Math.PI / 180.0;

double cos = Math.Cos(radians);

double sin = Math.Sin(radians);

// 3. Translate -> rotate -> translate back, for each corner

var rotated = new Point2D[4];

for (int i = 0; i < 4; i++)

{

double dx = corners[i].X - centerX;

double dy = corners[i].Y - centerY;

double newX = dx * cos - dy * sin + centerX;

double newY = dx * sin + dy * cos + centerY;

rotated[i] = new Point2D(newX, newY);

}

return rotated;

}

}

class Program

{

static void Main()

{

// A square with corners at (2,2), (6,2), (6,6), (2,6) — center at (4,4)

var square = new[]

{

new Point2D(2, 2),

new Point2D(6, 2),

new Point2D(6, 6),

new Point2D(2, 6),

};

var rotated = Rotation.RotateSquare(square, 45);

Console.WriteLine("Original:");

foreach (var p in square) Console.WriteLine(" " + p);

Console.WriteLine("Rotated 45°:");

foreach (var p in rotated) Console.WriteLine(" " + p);

}

}