reentrant angle
Definition
Noun: An interior angle of a polygon that is greater than 180 degrees. It is an angle that points inward, creating an indentation or notch in the shape's outline.
Usage
A reentrant angle is a geometric term used to describe a specific feature of a concave polygon. It is the angle formed at a vertex where the polygon "caves in" on itself. A polygon with at least one reentrant angle is classified as a concave polygon.
Examples
- The star shape has several reentrant angles where its points indent inward.
- To be a convex polygon, the shape must have no reentrant angles; all its interior angles must be less than 180 degrees.
- The surveyor noted the property's irregular boundary, which included a reentrant angle where the fence line turned sharply back into the lot.
Advanced Usage
- In computer graphics and computational geometry, algorithms for polygon filling or collision detection must account for reentrant angles to function correctly with concave shapes.
- The concept is often contrasted with a salient angle, which is an interior angle less than 180 degrees, typical of convex polygons.
Variants and Related Words
- Reentrant (adjective): Describing the angle or the polygon vertex itself. (e.g., ).
- Concave polygon (noun phrase): A polygon that has at least one reentrant angle.
- Reflex angle (noun): In general geometry, an angle greater than 180° but less than 360°; a reentrant angle is a specific type of reflex angle located inside a polygon.
Synonyms
- Reflex interior angle
Antonyms
- Salient angle
Noun
-
an interior angle of a polygon that is greater than 180 degrees
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