Linear algebra

Prompt

Act as a Computer Vision and Linear Algebra expert. I am working on an academic university project titled "Warps and Morphs" for my Linear Algebra course using Python. Please write a complete, bug-free, and fully-documented Python script using OpenCV, NumPy, and Matplotlib that demonstrates both Image Warping and Image Morphing. Key Requirements: 1. Linear Algebra Core: - Explicitly compute and print the 2x3 Affine Transformation Matrix. - Include detailed comments explaining how system of linear equations and matrix multiplications ($A \mathbf{x} + \mathbf{b}$) map pixel coordinates from source to destination. 2. Image Warping: - Define source control vectors and destination control vectors. - Calculate transformation matrices using `cv2.getAffineTransform` or custom matrix solver. - Apply geometric distortion to the source image. 3. Image Morphing: - Implement an iterative cross-dissolve/blending function across time steps $t \in [0, 1]$ (e.g., $t = 0.0, 0.25, 0.5, 0.75, 1.0$). - Ensure linear interpolation of both shape/coordinates and pixel color intensities. 4. Robust Code Architecture: - Provide clean, modular functions (`compute_matrix`, `warp_frame`, `morph_sequence`). - Include auto-generated synthetic shapes (so the script runs standalone without external image files), along with clear instructions on how to swap in custom local image paths. - Generate side-by-side Matplotlib subplots for output visualization, perfectly formatted for saving and pasting into a formal Word/PDF report.