convex hull: meaning, definition, pronunciation and examples
C2Formal Technical/Academic
Quick answer
What does “convex hull” mean?
The smallest convex set that contains all points of a given set in Euclidean space.
Audio
Pronunciation
Definition
Meaning and Definition
The smallest convex set that contains all points of a given set in Euclidean space.
In computational geometry, the tightest-fitting convex boundary that encloses a set of points, lines, or shapes. More broadly, it represents the minimal convex container or envelope for a collection of objects.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Spelling of related terms may vary (e.g., 'centre' vs. 'center').
Connotations
Purely technical and neutral in both varieties.
Frequency
Equally low-frequency in general discourse but standard in technical fields in both regions.
Grammar
How to Use “convex hull” in a Sentence
the convex hull of [a set of points/NP]to compute/find/determine the convex hullVocabulary
Collocations
Usage
Meaning in Context
Business
Virtually never used in general business contexts. May appear in highly specialised tech, logistics, or R&D discussions involving geometric modelling or optimisation.
Academic
Core concept in mathematics (geometry, optimisation), computer science (algorithms, graphics), engineering (CAD, robotics), and geography (mapping).
Everyday
Extremely rare. Would only be used in explaining a technical concept to a layperson.
Technical
The primary domain. Used precisely to refer to the result of a specific geometric computation.
Vocabulary
Synonyms of “convex hull”
Strong
Neutral
Weak
Vocabulary
Antonyms of “convex hull”
Watch out
Common Mistakes When Using “convex hull”
- Using 'convex hull' to describe any bounding shape, even if it's concave or not minimal.
- Treating it as a plural noun (e.g., 'The convex hull are...' is incorrect).
- Confusing it with a 'bounding box', which is rectangular and axis-aligned.
FAQ
Frequently Asked Questions
In 2D, for a finite set of points, the convex hull is a convex polygon. In 3D, it is a convex polyhedron. In higher dimensions, it is a convex polytope.
Graham's scan and the Jarvis march (gift wrapping) are two classic algorithms for computing the convex hull in two dimensions.
Yes, if the original set of points is already in a convex configuration (e.g., all points are vertices of a convex polygon), then the convex hull is exactly that set of points.
A convex hull has no indentations—lines between any two points lie entirely within it. A concave hull (or alpha shape) can have indentations, potentially fitting the points more tightly but losing the convexity property.
The smallest convex set that contains all points of a given set in Euclidean space.
Convex hull is usually formal technical/academic in register.
Convex hull: in British English it is pronounced /ˈkɒn.veks hʌl/, and in American English it is pronounced /ˈkɑːn.veks hʌl/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Imagine a set of nails hammered into a board. The CONVEX HULL is the shape made by a rubber band stretched around the outermost nails.
Conceptual Metaphor
THE TIGHTEST RUBBER BAND AROUND A SET OF POINTS.
Practice
Quiz
What is the defining property of a convex hull?