Fundamental principles of 2D and 3D computer graphics, vector representations, homogeneous transformation matrices, projections, rasterization, and real-time graphics pipelines.
2D Geometric Transformations (Part 1)
Mathematical formulation, 3x3 homogeneous coordinate matrices, and interactive dynamic simulations of translation, scaling, rotation, and shearing with live Canvas manipulation.
2D Geometric Transformations (Part 2)
Inverse transformations, composite transformations (matrix order & non-commutativity), fixed-point rotation & scaling, reflections, shearing, and interactive sandbox playground.
2D Geometric Transformations (Part 3)
Transformations between 2D coordinate systems (change of basis), Method 1 (rotation angle $\theta$), Method 2 (orthonormal basis without angles), transformations in HTML5 Canvas, execution order, and pipeline integration with WebGL & Three.js.
3D Geometric Transformations (Part 1)
Transition from 2D to 3D spaces, 4D homogeneous coordinates & $4 \times 4$ matrices, 3D translation vectors, uniform/non-uniform scaling, right-hand Cartesian coordinate system, and principal axis rotations ($R_x, R_y, R_z$) with geometric derivation.
3D Geometric Transformations (Part 2)
Rotation about parallel and arbitrary axes via matrix decomposition ($T \cdot R \cdot T^{-1}$ and coordinate alignment), 3D transformation composition order, 3D reflection across coordinate planes, and 3D shearing.