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A polygon soup is a set of unorganized polygons, typically triangles, before the application of any structuring operation, such as e.g. octree grouping. [1]The term must not to be confused with the "PolySoup" [2] operation available in the 3D package Houdini, whose goal is to optimize the storage space needed by some piece of geometry through the reduction of the underlying number of polygon ...
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
Star polygon – there are multiple types of stars Pentagram - star polygon with 5 sides; Hexagram – star polygon with 6 sides Star of David (example) Heptagram – star polygon with 7 sides; Octagram – star polygon with 8 sides Star of Lakshmi (example) Enneagram - star polygon with 9 sides; Decagram - star polygon with 10 sides
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
A polygon with m vertices can be partitioned into m–2 triangles. Which can be shown by induction starting from a triangle. There are numerous algorithms to triangulate a polygon efficiently, the fastest having O(n) worst case time. Therefore, we can decompose each polygon of our subdivision in triangles, and restrict our data structure to the ...
If the interior point is the circumcenter of the reference triangle, the vertices of the pedal triangle are the midpoints of the reference triangle's sides, and so the pedal triangle is called the midpoint triangle or medial triangle. The midpoint triangle subdivides the reference triangle into four congruent triangles which are similar to the ...
A winding number of 0 means the point is outside the polygon; other values indicate the point is inside the polygon. An improved algorithm to calculate the winding number was developed by Dan Sunday in 2001. [6] It does not use angles in calculations, nor any trigonometry, and functions exactly the same as the ray casting algorithms described ...
A point-set triangulation is a polygon triangulation of the convex hull of a set of points. A Delaunay triangulation is another way to create a triangulation based on a set of points. The associahedron is a polytope whose vertices correspond to the triangulations of a convex polygon. Polygon triangle covering, in which the triangles may overlap.