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Concepts11

Groups

📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
⚙️AlgorithmIntermediate

Circle Geometry

Circle geometry in computational geometry relies on precise vector math, quadratic equations, and careful floating-point handling with an EPS tolerance.

#circle geometry#line circle intersection#circle circle intersection+12
⚙️AlgorithmAdvanced

Half-Plane Intersection

Half-plane intersection (HPI) computes the common region that satisfies many linear side-of-line constraints in the plane.

#half-plane intersection
Advanced
Filtering by:
#computational geometry
#computational geometry
#convex polygon
+12
⚙️AlgorithmAdvanced

Minkowski Sum

The Minkowski sum A ⊕ B adds every point of set A to every point of set B, and for convex polygons it can be computed in O(n + m) by merging edge directions.

#minkowski sum#convex polygon#edge merge+12
⚙️AlgorithmIntermediate

Closest Pair of Points

The closest pair of points problem asks for the minimum Euclidean distance between any two points in the plane.

#closest pair of points#divide and conquer#plane sweep+11
⚙️AlgorithmIntermediate

Line Sweep

Line sweep (plane sweep) is a technique that processes geometric objects by moving an imaginary line and handling events in sorted order.

#line sweep#plane sweep#event queue+12
⚙️AlgorithmIntermediate

Polygon Area and Centroid

The signed area of a simple polygon can be computed in O(n) using the shoelace formula, which sums cross products of consecutive vertices.

#shoelace formula#polygon area#centroid+12
⚙️AlgorithmIntermediate

Rotating Calipers

Rotating calipers is a geometric two-pointer technique that sweeps two (or more) parallel support lines around a convex polygon.

#rotating calipers#antipodal pairs#convex hull+12
⚙️AlgorithmIntermediate

Basic Geometry - Lines and Segments

A line can be represented by two points, a point with a direction vector, or the general form ax + by + c = 0, and these forms are interconvertible.

#line intersection#segment intersection#orientation test+12
⚙️AlgorithmIntermediate

Convex Hull

The convex hull is the smallest convex polygon that contains all given points, like a rubber band snapped around nails on a board.

#convex hull#graham scan#monotone chain+12
⚙️AlgorithmIntermediate

Point in Polygon

Point-in-polygon decides whether a point lies outside, inside, or on the boundary of a polygon.

#point in polygon#ray casting#winding number+11
⚙️AlgorithmIntermediate

Orientation and CCW

Orientation (CCW test) tells whether three points make a left turn, right turn, or are collinear by using the sign of a 2D cross product.

#orientation#ccw#cross product+12