reentering polygon

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Definition

Noun: A reentering polygon is a polygon that has at least one interior angle greater than 180 degrees. This inward-pointing angle creates a "dent" or indentation in the shape's outline.

Usage

The term is used in geometry and computer graphics to classify shapes based on their vertex angles. * A simple square is not a reentering polygon because all its interior angles are less than 180 degrees. * A star shape or a shape resembling a "C" often is a reentering polygon because it contains angles pointing inward.

Examples
  • In computational geometry, algorithms for polygon triangulation must account for reentering polygons.
  • The architect's sketch included a reentering polygon to create an interesting indentation in the building's facade.
  • Identifying a reentering polygon is the first step in decomposing it into convex components.
Advanced Usage
  • Reentrant Polygon: This is a direct synonym and is often used interchangeably with "reentering polygon."
  • Non-convex Polygon: This is a broader category that includes all polygons that are not convex. Every reentering polygon is a non-convex polygon, but not all non-convex polygons are reentering (e.g., a complex star polygon may have intersecting sides but no single interior angle > 180 degrees).
Variants and Related Words
  • Reentrant (adjective): Describing the angle or the polygon itself. Example: "The shape has a angle."
  • Concave Polygon: A more common general term for a non-convex polygon, which includes reentering polygons. A reentering polygon is a specific type of concave polygon where the concavity is defined by an interior angle exceeding 180 degrees.
Synonyms
  • Concave polygon (in a specific sense)
  • Reentrant polygon
Antonyms
  • Convex polygon
  • Non-reentrant polygon
Noun
  1. a polygon with one or more reentrant angles

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