Concepts inOn the support of recursive subdivision
Convex and concave polygons
In geometry, a polygon can be either convex or concave (non-convex or reentrant).
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Line segment
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve).
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Convex hull
In mathematics, the convex hull or convex envelope for a set X of points in the Euclidean plane or Euclidean space is the minimal convex set containing X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X. Formally, the convex hull may be defined as the intersection of all convex sets containing X, the intersection of all halfspaces containing X, or the set of all convex combinations of points in X.
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Fractal
A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far" Fractals may be exactly the same at every scale, or as illustrated in Figure 1, they may be nearly the same at different scales.
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Vertex (geometry)
In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.
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Edge (geometry)
In geometry, an edge is a line segment joining two adjacent vertices in a polygon. Thus applied, an edge is a connector for a one-dimensional line segment and two zero-dimensional objects. A planar closed sequence of edges forms a polygon. In a polyhedron, exactly two faces meet at every edge, while in higher dimensional polytopes, three or more faces meet at an edge. In a polygon, an edge can also be called a facet or side, bounding the polygon.
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Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain or circuit. A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e. , by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides.
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Point (geometry)
In geometry, topology, and related branches of mathematics, a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e. , they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics dealing with set theory, an element is sometimes referred to as a point.
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