2D and 3D geometric transformations
Computer Graphics · Engineering
Study notes
Let us rotate a 2D point P(4, 2) by 90 degrees counter-clockwise around the center (0,0). Step 1: Identify the coordinates of the point. Here, x = 4 and y = 2. Step 2: Use the standard 2D Rotation Matrix for 90 degrees. The formula for rotation is: x' = x * cos(θ) - y * sin(θ) y' = x * sin(θ) + y * cos(θ) Step 3: For 90 degrees, cos(90) = 0 and sin(90) = 1. Step 4: Plug the numbers into the formula: New X (x') = (4 * 0) - (2 * 1) = 0 - 2 = -2 New Y (y') = (4 * 1) + (2 * 0) = 4 + 0 = 4 Step 5: The final position of the point after rotating is (-2, 4).