Pedro Rafael
Lecture notes, interactive slide decks, and academic resources prepared for undergraduate and graduate computer science courses.
Fundamental principles of 2D and 3D computer graphics, vector representations, homogeneous transformation matrices, projections, rasterization, and real-time graphics pipelines.
Mathematical formulation, 3x3 homogeneous coordinate matrices, and interactive dynamic simulations of translation, scaling, rotation, and shearing with live Canvas manipulation.
Asymptotic time and space complexity analysis, Big-O / Big-Omega / Big-Theta notation, recurrence relations (Master Theorem), algorithmic design paradigms (divide-and-conquer, greedy methods, dynamic programming), and graph algorithms.
3-step complexity calculation method, quadratic sorting analysis (Selection Sort & optimized Bubble Sort with triangular sums), best/worst/average cases (Linear Search), $O(n \cdot m)$ nested loops, $O(\sqrt{n})$ primality testing, Two Pointers technique, and 10 solved exercises with interactive live step simulators.