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Space-filling Polyhedra
Space filling or spacefilling may refer to: * Space-filling curve * Space-filling model, in chemistry * Space-filling polyhedron * Space-filling tree *Space-filling bubble in a foam {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Curve
In mathematical analysis, a space-filling curve is a curve whose Range of a function, range reaches every point in a higher dimensional region, typically the unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, space-filling curves in the plane (mathematics), 2-dimensional plane are sometimes called ''Peano curves'', but that phrase also refers to the Peano curve, the specific example of a space-filling curve found by Peano. The closely related FASS curves (approximately space-Filling, self-Avoiding, Simple, and Self-similar curves) can be thought of as finite approximations of a certain type of space-filling curves. Definition Intuitively, a curve in two or three (or higher) dimensions can be thought of as the path of a continuously moving point. To eliminate the inherent vagueness of this notion, Camille Jordan, Jordan in 1887 introduced the following rigorous definition, which has since been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Model
In chemistry, a space-filling model, also known as a ''calotte model'', is a type of three-dimensional (3D) molecular model where the atoms are represented by spheres whose radii are proportional to the radii of the atoms and whose center-to-center distances are proportional to the distances between the atomic nuclei, all in the same scale. Atoms of different chemical elements are usually represented by spheres of different colors. Space-filling calotte models are also referred to as CPK models after the chemists Robert Corey, Linus Pauling, and Walter Koltun, who over a span of time developed the modeling concept into a useful form. They are distinguished from other 3D representations, such as the ball-and-stick and skeletal models, by the use of the "full size" space-filling spheres for the atoms. The models are tactile and manually rotatable. They are useful for visualizing the effective shape and relative dimensions of a molecule, and (because of the rotatability) the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Polyhedron
In geometry, a space-filling polyhedron is a polyhedron that can be used to fill all of three-dimensional space via translations, rotations and/or reflections, where ''filling'' means that; taken together, all the instances of the polyhedron constitute a partition of three-space. Any periodic tiling or honeycomb of three-space can in fact be generated by translating a primitive cell polyhedron. If a polygon can tile the plane, its prism is space-filling; examples include the cube, triangular prism, and the hexagonal prism. Any parallelepiped tessellates Euclidean 3-space, as do the five parallelohedra including the cube, hexagonal prism, truncated octahedron, and rhombic dodecahedron. Other space-filling polyhedra include the pyramid, plesiohedra and stereohedra, polyhedra whose tilings have symmetries taking every tile to every other tile, including the gyrobifastigium, the triakis truncated tetrahedron, and the trapezo-rhombic dodecahedron. The cube is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space-filling Tree
Space-filling trees are geometric constructions that are analogous to space-filling curves, but have a branching, tree-like structure and are rooted. A space-filling tree is defined by an incremental process that results in a tree for which every point in the space has a finite-length path that converges to it. In contrast to space-filling curves, individual paths in the tree are short, allowing any part of the space to be quickly reached from the root. The simplest examples of space-filling trees have a regular, self-similar, fractal structure, but can be generalized to non-regular and even randomized/ Monte-Carlo variants (see Rapidly exploring random tree). Space-filling trees have interesting parallels in nature, including fluid distribution systems, vascular networks, and fractal plant growth, and many interesting connections to L-systems in computer science. Definition A space-filling tree is defined by an iterative process whereby a single point in a continuous space ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
