Category: Blog
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How to Learn GJK Collision Detection: Minkowski Difference, Support Mappings, Simplexes and Robust Convex Geometry
Quick Read: GJK, the Gilbert–Johnson–Keerthi algorithm, answers a geometric question with a beautiful reduction: do two convex shapes overlap? Instead of comparing their boundaries directly, transform the problem into asking whether the origin lies inside their Minkowski difference. From there, support mappings and a moving simplex drive an iterative search. Why collision detection is an…
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How to Learn Tonelli–Shanks: Quadratic Residues, Modular Square Roots, Euler’s Criterion and Finite-Field Reasoning
Quick Read: Tonelli–Shanks solves a deceptively simple problem: given an odd prime p and a number n, find x such that x² ≡ n (mod p), when such a square root exists. Learning it well develops modular arithmetic, proof technique, loop invariants, finite-group reasoning and implementation discipline. Start with the ordinary square root Over the…
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How to Learn the Four Russians Technique: Block Decomposition, Lookup Tables, Boolean Matrix Multiplication and Word-Level Speedups
Quick Read: The Four Russians technique is not one single algorithm. It is a reusable design idea: break a large computation into small blocks, precompute every possible answer for those blocks, and then reuse table lookups so the main algorithm performs fewer expensive operations. It is a powerful bridge from ordinary dynamic programming and matrix…
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How to Learn Knuth Optimization: Interval Dynamic Programming, Monotone Split Points, Quadrangle Inequalities and O(n²) Speedups
A beginner-to-professional guide to Knuth optimization covering interval DP, monotone argmins, quadrangle inequalities, O(n²) analysis, proof obligations and professional validation.
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How to Learn Marching Cubes: Isosurfaces, Case Tables, Interpolation, Topology and Production Mesh Extraction
A beginner-to-professional guide to Marching Cubes covering scalar fields, case tables, interpolation, ambiguity, topology-correct variants, mesh indexing and production extraction.
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How to Learn CORDIC: Shift–Add Rotations, Vectoring, Fixed-Point Arithmetic and Hardware Trigonometry
A beginner-to-professional guide to CORDIC covering micro-rotations, rotation and vectoring modes, gain, convergence, fixed-point error, FPGA architecture and hardware validation.
