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Feret Diameter
The Feret diameter or Feret's diameter is a measure of an object size along a specified direction. In general, it can be defined as the distance between the two parallel planes restricting the object perpendicular to that direction. It is therefore also called the caliper diameter, referring to the measurement of the object size with a caliper. This measure is used in the analysis of particle sizes, for example in microscopy, where it is applied to projections of a three-dimensional (3D) object on a 2D plane. In such cases, the Feret diameter is defined as the distance between two parallel tangential ''lines'' rather than ''planes''. Mathematical properties From Cauchy's theorem it follows that for a 2D convex body, the Feret diameter averaged over all directions (〈F〉) is equal to the ratio of the object perimeter (P) and pi, i.e.,〈F〉= P/. There is no such relation between〈F〉and P for a concave object. Applications Feret diameter is used in the analysis of parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feret Diameter
The Feret diameter or Feret's diameter is a measure of an object size along a specified direction. In general, it can be defined as the distance between the two parallel planes restricting the object perpendicular to that direction. It is therefore also called the caliper diameter, referring to the measurement of the object size with a caliper. This measure is used in the analysis of particle sizes, for example in microscopy, where it is applied to projections of a three-dimensional (3D) object on a 2D plane. In such cases, the Feret diameter is defined as the distance between two parallel tangential ''lines'' rather than ''planes''. Mathematical properties From Cauchy's theorem it follows that for a 2D convex body, the Feret diameter averaged over all directions (〈F〉) is equal to the ratio of the object perimeter (P) and pi, i.e.,〈F〉= P/. There is no such relation between〈F〉and P for a concave object. Applications Feret diameter is used in the analysis of parti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Caliper
A caliper (British spelling also calliper, or in plurale tantum sense a pair of calipers) is a device used to measure the dimensions of an object. Many types of calipers permit reading out a measurement on a ruled scale, a dial, or a digital display. Some calipers can be as simple as a compass with inward or outward-facing points, but no scale. The tips of the caliper are adjusted to fit across the points to be measured and the dimension read by measuring between the tips with another measuring tool, such as a ruler. It is used in many fields such as mechanical engineering, metalworking, forestry, woodworking, science and medicine. Plural vs. singular A single tool might be referred to as a "caliper" or as "calipers", like a pair of scissors or glasses (a "plural only" or '' plurale tantum'' form). In colloquial usage, the phrase "pair of verniers" or just " vernier" might refer to a vernier caliper. Colloquially these phrases can also refer to dial calipers, although they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particle Size (grain Size)
Grain size (or particle size) is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain. A single grain can be composed of several crystals. Granular material can range from very small colloidal particles, through clay, silt, sand, gravel, and cobbles, to boulders. Krumbein phi scale Size ranges define limits of classes that are given names in the Wentworth scale (or Udden–Wentworth scale) used in the United States. The Krumbein ''phi'' (φ) scale, a modification of the Wentworth scale created by W. C. Krumbein in 1934, is a logarithmic scale computed by the equation :\varphi=-\log_2, where :\varphi is the Krumbein phi scale, :D is the diameter of the particle or grain in millimeters (Krumbein and Monk's equation) and :D_0 is a reference diameter, equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microscopy
Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of microscopy: optical, electron, and scanning probe microscopy, along with the emerging field of X-ray microscopy. Optical microscopy and electron microscopy involve the diffraction, reflection, or refraction of electromagnetic radiation/electron beams interacting with the specimen, and the collection of the scattered radiation or another signal in order to create an image. This process may be carried out by wide-field irradiation of the sample (for example standard light microscopy and transmission electron microscopy) or by scanning a fine beam over the sample (for example confocal laser scanning microscopy and scanning electron microscopy). Scanning probe microscopy involves the interaction of a scanning probe with the surface of the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Projection
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. 3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret that the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display. 3D objects are largely displayed on two-dimensional mediums (i.e. paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in engineering drawing, drafting, and computer graphics. Projections can be calculated through employment of mathematical analysis and formulae, or by using various geometric and opt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy's Theorem (geometry)
Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is, any polyhedral net formed by unfolding the faces of the polyhedron onto a flat surface, together with gluing instructions describing which faces should be connected to each other, uniquely determines the shape of the original polyhedron. For instance, if six squares are connected in the pattern of a cube, then they must form a cube: there is no convex polyhedron with six square faces connected in the same way that does not have the same shape. This is a fundamental result in rigidity theory: one consequence of the theorem is that, if one makes a physical model of a convex polyhedron by connecting together rigid plates for each of the polyhedron faces with flexible hinges along the polyhedron edges, then this ensemble of plates and hinges will necessarily form a rigid structure. S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Body
In mathematics, a convex body in n-dimensional Euclidean space \R^n is a compact convex set with non-empty interior. A convex body K is called symmetric if it is centrally symmetric with respect to the origin; that is to say, a point x lies in K if and only if its antipode, - x also lies in K. Symmetric convex bodies are in a one-to-one correspondence with the unit balls of norms on \R^n. Important examples of convex bodies are the Euclidean ball, the hypercube and the cross-polytope In geometry, a cross-polytope, hyperoctahedron, orthoplex, or cocube is a regular, convex polytope that exists in ''n''- dimensional Euclidean space. A 2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahe .... See also * * References * {{Authority control Multi-dimensional geometry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perimeter
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter. Formulas The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with \int_0^L \mathrms, where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise smooth plane curv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concave
Concave or concavity may refer to: Science and technology * Concave lens * Concave mirror Mathematics * Concave function, the negative of a convex function * Concave polygon, a polygon which is not convex * Concave set * The concavity of a function, determined by its second derivative See also * {{disambiguation, math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Diameter
The Martin diameter is the length of the area bisector of an irregular object in a specified measuring direction. It is used to measure particle size in microscopy Microscopy is the technical field of using microscopes to view objects and areas of objects that cannot be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of micr ....Operating Manual, Particle size analysis system CAMSIZER, Retsch Technology GmbH, Germany, 2010 See also * Feret diameter References External links Martin's diameter, Photonics Dictionary Plus Microscopy {{optics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
