TOPICS
Projection
A projection is the transformation ofpoints andlines in oneplane onto anotherplane by connecting corresponding points on the two planes withparallel lines. This can be visualized as shining a (point) light source (located at infinity) through a translucent sheet of paper and making an image of whatever is drawn on it on a second sheet of paper. The branch of geometry dealing with the properties and invariants of geometric figures under projection is calledprojective geometry.
The projection of avector
onto avector
is given by
 |
where
is thedot product, and the length of this projection is
 |
General projections are considered by Foley and VanDam (1983).
The average projected area over all orientations of anyellipsoid is 1/4 the totalsurface area. This theorem also holds for any convex solid.
See also
Bicentric Perspective,Dot Product,Map Projection,Möbius Net,Point-Plane Distance,Projection Matrix,Projection Operator,Projection Theorem,Projective Collineation,Projective Geometry,Reflection,Shadow,Stereology,Trip-Let,Vector Space Projection,Vertical Perspective ProjectionExplore with Wolfram|Alpha
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References
Casey, J. "Theory of Projections." Ch. 11 inA Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 349-367, 1893.Foley, J. D. and VanDam, A.Fundamentals of Interactive Computer Graphics, 2nd ed. Reading, MA: Addison-Wesley, 1990.Referenced on Wolfram|Alpha
ProjectionCite this as:
Weisstein, Eric W. "Projection." FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/Projection.html