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  2. Collinearity equation - Wikipedia

    en.wikipedia.org/wiki/Collinearity_equation

    The equations originate from the central projection of a point of the object through the optical centre of the camera to the image on the sensor plane. [1] The three points P, Q and R are projected on the plane S through the projection centre C x- and z-axis of the projection of P through the projection centre C

  3. Collinearity - Wikipedia

    en.wikipedia.org/wiki/Collinearity

    In particular, for three points in the plane (n = 2), the above matrix is square and the points are collinear if and only if its determinant is zero; since that 3 × 3 determinant is plus or minus twice the area of a triangle with those three points as vertices, this is equivalent to the statement that the three points are collinear if and only ...

  4. No-three-in-line problem - Wikipedia

    en.wikipedia.org/wiki/No-three-in-line_problem

    They proved that the maximum number of points in the grid with no three points collinear is (). Similarly to Erdős's 2D construction, this can be accomplished by using points ( x , y , x 2 + y 2 {\displaystyle (x,y,x^{2}+y^{2}} mod p ) {\displaystyle p)} , where p {\displaystyle p} is a prime congruent to 3 mod 4 . [ 20 ]

  5. Menger curvature - Wikipedia

    en.wikipedia.org/wiki/Menger_curvature

    If the three points are collinear, R can be informally considered to be +∞, and it makes rigorous sense to define c(x, y, z) = 0. If any of the points x, y and z are coincident, again define c(x, y, z) = 0. Using the well-known formula relating the side lengths of a triangle to its area, it follows that

  6. Simson line - Wikipedia

    en.wikipedia.org/wiki/Simson_line

    In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. [1] The line through these points is the Simson line of P, named for Robert Simson. [2] The concept was first published, however, by William Wallace in 1799, [3] and is sometimes called the Wallace line. [4]

  7. Projective harmonic conjugate - Wikipedia

    en.wikipedia.org/wiki/Projective_harmonic_conjugate

    In projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction: Given three collinear points A, B, C , let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively.

  8. Delaunay triangulation - Wikipedia

    en.wikipedia.org/wiki/Delaunay_triangulation

    The Euclidean minimum spanning tree of a set of points is a subset of the Delaunay triangulation of the same points, [22] and this can be exploited to compute it efficiently. For modelling terrain or other objects given a point cloud , the Delaunay triangulation gives a nice set of triangles to use as polygons in the model.

  9. Projective geometry - Wikipedia

    en.wikipedia.org/wiki/Projective_geometry

    (L3) at least dimension 2 if it has at least 3 non-collinear points (or two lines, or a line and a point not on the line), (L4) at least dimension 3 if it has at least 4 non-coplanar points. The maximum dimension may also be determined in a similar fashion. For the lowest dimensions, they take on the following forms. A projective space is of: