Convex hull
A convex hull is the smallest convex set containing a given set of points or geometric objects.
Optimization Algorithms: AI techniques for design, planning, and control problems
The convex hull problem is the computational problem of finding the smallest convex boundary containing a given set of points.
- How it is used
- Frames convex hull as a sequential combinatorial optimization task whose output selects points from a variable-length input.
- How deep it goes
- Explains geometric validity and a pointer-network implementation, including training and evaluation, but does not derive a classical geometric algorithm.
- Examples
- Uses rubber-band intuition, random two-dimensional datasets, index sequences, SciPy comparisons, and predicted-versus-true hull visualizations.
- What you can do after
- Apply it via PyTorch and SciPy by training, testing, visualizing, and measuring a pointer-network hull predictor.
Advanced Algorithms and Data Structures
A convex hull is the smallest convex set containing a given set or geometric shape.
- How it is used
- Uses convex-hull overlap as an early filter for Bézier-curve intersection testing.
- How deep it goes
- Defines the hull and outlines recursive subdivision, but defers detailed Bézier clipping and formal derivations.
- Examples
- Uses quadratic and cubic Bézier curves whose control points define polygons for overlap comparison.
- What you can do after
- Apply Bézier subdivision to reject nonintersecting curves and reduce remaining cases to segment tests.
Read how Advanced Algorithms and Data Structures explains convex hull →
Sutskever's List
A convex hull is the smallest convex set containing a given set of points.
- How it is used
- Uses hull selection as a combinatorial task for comparing sequence-model architectures.
- How deep it goes
- Defines the point-selection task and its scaling challenge but does not explain geometric construction algorithms.
- Examples
- Compares model results on 50-point inputs and Pointer Network performance on 500-point tests.
- What you can do after
- Evaluate architecture performance using exact accuracy and geometric area measures.
Outlier Detection in Python
An iterative outlier-detection method that assigns scores according to the successive layers of a convex hull around the data points.
- How it is used
- Detects global outliers by repeatedly removing boundary points from a small-feature, single-cluster dataset.
- How deep it goes
- Explains iterative peeling, scoring, stopping, robustness, runtime, and dimensionality limits without deriving hull geometry.
- Examples
- Uses successive hull-layer figures and contrasts suitable single-cluster data with unsuitable multi-cluster data.
- What you can do after
- Apply it via SciPy's ConvexHull implementation to score boundary layers and select a preset number of outliers.
Related concepts
- Bézier subdivisionused by · Bézier subdivision is a technique that recursively splits Bézier curves into smaller curve sections for geometric analysis.
- anomaly scoreproduces · An anomaly score is a numerical measure of how anomalous an observation or event is relative to a reference or expected pattern.
- high-dimensional datacontrasts with · High-dimensional data consists of observations represented by a large number of features, variables, coordinates, or other dimensions.
- SciPyuses · SciPy is an open-source Python library providing algorithms and numerical utilities for scientific and technical computing.
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