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The 3D interpretation is a solid truncated cone, with the small end pointing toward the viewer. The front view is, therefore, two concentric circles. The fact that the inner circle is drawn with a solid line instead of dashed identifies this view as the front view, not the rear view. The side view is an isosceles trapezoid.
It is always possible to partition a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex polygons as possible is described by Chazelle & Dobkin (1985). [5] A triangle can never be concave, but there exist concave polygons with n sides for any n > 3.
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. When this happens, the ten points and ten lines of the two perspectivities (the six triangle vertices, three crossing points, and center of perspectivity ...
In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
In computational geometry, a fan triangulation is a simple way to triangulate a polygon by choosing a vertex and drawing edges to all of the other vertices of the polygon. Not every polygon can be triangulated this way, so this method is usually only used for convex polygons .
A regular triangle, heptagon, and 42-gon can completely fill a plane vertex. However, there is no tiling of the plane with only these polygons, because there is no way to fit one of them onto the third side of the triangle without leaving a gap or creating an overlap. In the hyperbolic plane, tilings by regular heptagons are possible. There are ...
The ten lines involved in Desargues's theorem (six sides of triangles, the three lines Aa, Bb and Cc, and the axis of perspectivity) and the ten points involved (the six vertices, the three points of intersection on the axis of perspectivity, and the center of perspectivity) are so arranged that each of the ten lines passes through three of the ...
Dually, the figures are said to be perspective from a line if the points of intersection of corresponding lines all lie on one line. The proper setting for this concept is in projective geometry where there will be no special cases due to parallel lines since all lines meet. Although stated here for figures in a plane, the concept is easily ...