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The side view is an isosceles trapezoid. In first-angle projection, the front view is pushed back to the rear wall, and the right side view is pushed to the left wall, so the first-angle symbol shows the trapezoid with its shortest side away from the circles.
A regular digon has both angles equal and both sides equal and is represented by Schläfli symbol {2}. It may be constructed on a sphere as a pair of 180 degree arcs connecting antipodal points, when it forms a lune. The digon is the simplest abstract polytope of rank 2. A truncated digon, t{2} is a square, {4}.
The boundary of a Reuleaux triangle is a constant width curve based on an equilateral triangle. All points on a side are equidistant from the opposite vertex. A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. [1]
Fan triangulation of a convex polygon Fan triangulation of a concave polygon with a unique concave vertex. 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.
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.
Hockney tested a technique with a small concave mirror projecting the view from a small open window onto a surface in a darkened room. He associated several of the limitations of the technique and the characteristics of the projected images with the look of many naturalistic paintings: strong lights and shadows, dark backgrounds, limited depth ...
The 42 possible triangulations for a convex heptagon (7-sided convex polygon). This number is given by the 5th Catalan number . It is trivial to triangulate any convex polygon in linear time into a fan triangulation , by adding diagonals from one vertex to all other non-nearest neighbor vertices.
A general approach that works for non-simple polygons as well would be to choose a line not parallel to any of the sides of the polygon and draw a line parallel to this one through each of the vertices of the polygon. This will divide the polygon into triangles and trapezoids, which in turn can be converted into triangles.