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Use of Polygons in Real-time imagery. The imaging system calls up the structure of polygons needed for the scene to be created from the database. This is transferred to active memory and finally, to the display system (screen, TV monitors, etc.) so that the scene can be viewed. During this process, the imaging system renders polygons in correct perspective ready for transmission of the processed data to the display system. Although polygons are two dimensional, through the system computer they are placed in a visual scene in the correct three-dimensional orientation so that as the viewing point moves through the scene, it is perceived in 3D.

Morphing. To avoid artificial effects at polygon boundaries where the planes of contiguous polygons are at different angle, so called 'Morphing Algorithms' are used. These blend, soften or smooth the polygon edges so that the scene looks less artificial and more like the real world.

Polygon Count. Since a polygon can have many sides and need many points to define it, in order to compare one imaging system with another, "polygon count" is generally taken as a triangle. A triangle is processed as three points in the x, y, and z axes, needing nine geometrical descriptors. In addition, coding is applied to each polygon for color, brightness, shading, texture, NVG (intensifier or night vision), Infra-Red characteristics and so on. When analyzing the characteristics of a particular imaging system, the exact definition of polygon count should be obtained as it applies to that system.

Meshed Polygons. The number of meshed polygons ('meshed' is like a fish net) can be up to twice that of free-standing unmeshed polygons, particularly if the polygons are contiguous. If a square mesh has n + 1 points (vertices) per side, there are n squared squares in the mesh, or 2n squared triangles since there are two triangles in a square. There are (n+1) 2/2n2 vertices per triangle. Where n is large, this approaches one half. Or, each vertex inside the square mesh connects four edges (lines).

Vertex Count. Because of effects such as the above, a count of Vertices may be more reliable than Polygon count as an indicator of the capability of an imaging system.

Point in polygon test. In computer graphics and computational geometry, it is often necessary to determine whether a given point P = (x0,y0) lies inside a simple polygon given by a sequence of line segments. It is known as the Point in polygon test.

See also

  • Hexagon
  • Parallelogram
  • Polyhedron
  • Polytope
  • Square (geometry)
  • Triangle

Notes

  1. ↑ Paul Bourke. 1988. Polygon Area and Centroid. University of Western Australia. Retrieved November 3, 2007.
  2. ↑ A.M. Lopshits, J. Massalski and C. Mills, Jr. trans. 1963. Computation of areas of oriented figures. (Boston, MA: DC Heath and Company, 1963.)

References

  • Arnone, Wendy. 2001. Geometry for Dummies. Hoboken, NJ: For Dummies (Wiley). ISBN 0764553240.
  • Hartshorne, Robin. 2002. Geometry: Euclid and Beyond. Undergraduate Texts in Mathematics. New York: Springer. ISBN 0387986502.
  • Leff, Lawrence S. 1997. Geometry the Easy Way. Hauppauge, NY: Barron's Educational Series. ISBN 0764101102.
  • Stillwell, John. 2005. The Four Pillars of Geometry. Undergraduate Texts in Mathematics. New York: Springer. ISBN 0387255303.

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