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Vertex (geometry) A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex ( pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra ...
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [ 2] It was popularized in English by Hugo Steinhaus in the 1950 edition of his book Mathematical ...
3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex . A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that ...
The vertices of the arrangement are isolated points belonging to two or more lines, where those lines cross each other. The boundary of a cell is the system of edges that touch it, and the boundary of an edge is the set of vertices that touch it (one vertex for a ray and two for a line segment).
Miquel's theorem. Miquel's theorem is a result in geometry, named after Auguste Miquel, [1] concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles in Euclidean geometry due to Miquel, whose work was published in Liouville's ...
A Bézier curve is defined by a set of control points P0 through Pn, where n is called the order of the curve ( n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the curve; however, the intermediate control points generally do not lie on the curve.
Plane "hexagonal cupolae" in the rhombitrihexagonal tilingThe above-mentioned three polyhedra are the only non-trivial convex cupolae with regular faces: The "hexagonal cupola" is a plane figure, and the triangular prism might be considered a "cupola" of degree 2 (the cupola of a line segment and a square).
Example of a low poly triangle mesh representing a dolphin. In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object. The faces usually consist of triangles ( triangle mesh ), quadrilaterals (quads), or other simple convex polygons ( n-gons ), since ...
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