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Two perspective triangles, with their perspective axis and center. Two figures in a plane are perspective from a point O, called the center of perspectivity, if the lines joining corresponding points of the figures all meet at O.
In projective geometry, Desargues's theorem, named after Girard Desargues, states: Two triangles are in perspective axially if and only if they are in perspective centrally. Denote the three vertices of one triangle by a, b and c, and those of the other by A, B and C.
They are in perspective axially if the intersection points of the corresponding triangle sides, =, =, and = all lie on a common line, the axis of perspectivity. Desargues's theorem in geometry states that these two conditions are equivalent: if two triangles are in perspective centrally then they must also be in perspective axially, and vice versa.
A perspectivity: ′ ′ ′ ′, In projective geometry the points of a line are called a projective range, and the set of lines in a plane on a point is called a pencil.. Given two lines and in a projective plane and a point P of that plane on neither line, the bijective mapping between the points of the range of and the range of determined by the lines of the pencil on P is called a ...
Penrose triangle The Penrose triangle , also known as the Penrose tribar , the impossible tribar , [ 1 ] or the impossible triangle , [ 2 ] is a triangular impossible object , an optical illusion consisting of an object which can be depicted in a perspective drawing.
The triangle A'B'C' is the cevian triangle of Y. The ABC and the cevian triangle A'B'C' are in perspective and let DEF be the axis of perspectivity of the two triangles. The line DEF is the trilinear polar of the point Y. DEF is the central line associated with the triangle center X.
Diagonal triangle P, Q, R of quadrangle A, B, J, K on conic. Polars of diagonal points are colored the same as the points. Polars of diagonal points are colored the same as the points. The theory of poles and polars of a conic in a projective plane can be developed without the use of coordinates and other metric concepts.
Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. [ citation needed ] [ dubious – discuss ] Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by ...