MATLAB Implementation of Affine Transformations with 2D Graphics Programming

Affine transformation is a fundamental technique in 2D graphics programming that enables various geometric manipulations of graphical images. Through MATLAB's graphical user interface, users can efficiently implement arbitrary 2D transformation operations. These transformations include translation, rotation, scaling, and other geometric modifications, allowing for flexible and precise graphical manipulation. In MATLAB implementation, affine transformations are typically achieved using transformation matrices that manipulate coordinate points. The basic transformation matrix structure follows: [x' y' 1] = [x y 1] × T where T represents the specific transformation matrix. Key MATLAB functions include: - maketform() or affine2d() for creating transformation structures - imtransform() or imwarp() for applying transformations to images - For translation: T = [1 0 0; 0 1 0; tx ty 1] - For rotation: T = [cosθ -sinθ 0; sinθ cosθ 0; 0 0 1] - For scaling: T = [sx 0 0; 0 sy 0; 0 0 1] The implementation allows combining multiple transformations through matrix multiplication, enabling complex compound transformations while maintaining linearity and parallelism properties characteristic of affine transformations.