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Topic: Distance function

	Bounded Distance
		Although D is not bounded whereas d is, when one is close to 0 so is the other.Thus both distances induce the same notion of nearness in the sense that sets closed in one are also closed in the other and vice versa.
		Let f be a 1-1 function from a set X into a metric space Y with the metric function D.
		With the assumption that it's easier to tell apart more distant numbers, we are looking for a distance function for which the distance between, say, 5 and 10 is greater than the distance between 55 and 60 which, in turn, exceeds the distance between 105 and 110.
	www.cut-the-knot.org /do_you_know/bounded_dist.shtml (0 words)

	I ran the menu planning problem with the following inputs: cuisine = swedish, number of diners = 4, diet-restrictions = ...
		The purpose of this function is to assign a value to the closeness of the cuisine chosen in the current-problem and the cuisine’s that exist in the example-problems.
		Function description: Called by cuisine-dist. One of the many functions used to determine the closeness of cuisine’s from the current-problem and example-problem.
		Function description: Uses not-in and recursion to walk through the tree searching for the depth of node in the tree, where node is the cuisine type found in lowest-common-ancestor and tree is the cuisines tree.
	www.ecst.csuchico.edu /~depontje/CSCI322/lab2/csci322lab2.html (3316 words)

	flipcode - Fast Approximate Distance Functions (Site not responding. Last check: )
		In these cases, if you cannot afford to compute the standard distance function, there are classes of functions which give a pretty good approximation to the distance function and which are composed entirely of easy to compute linear pieces.
		The functions I will be discussing can generally approximate the distance within 2.5% average error, and with about a 5% maximum error with a small number of linear components and are therefore very fast to run.
		Consider that for the true distance function, for any given distance X you get points on a circle with radius X. So you are essentially trying to make an approximation of a circular graph using straight lines.
	www.flipcode.com /articles/article_fastdistance.shtml (1088 words)

	Improved Heterogeneous Distance Functions
		A variety of distance functions are available for such uses, including the Minkowsky (Batchelor, 1978), Mahalanobis (Nadler and Smith, 1993), Camberra, Chebychev, Quadratic, Correlation, and Chi-square distance metrics (Michalski, Stepp and Diday, 1981; Diday, 1974); the Context-Similarity measure (Biberman, 1994); the Contrast Model (Tversky, 1977); hyperrectangle distance functions (Salzberg, 1991; Domingos, 1995) and others.
		The Euclidean and Manhattan distance functions are equivalent to the Minkowskian r-distance function (Batchelor, 1978) with r = 2 and 1, respectively.
		For the purposes of comparison during testing, we define a heterogeneous distance function that is similar to that used by IB1, IB2 and IB3 (Aha, Kibler and Albert, 1991; Aha, 1992) as well as that used by Giraud-Carrier and Martinez (1995).
	axon.cs.byu.edu /~randy/jair/wilson2.html (1867 words)

	NMath Stats User's Guide - 9.2 Hierarchical Cluster Analysis
		This distance measure may be appropriate in cases when you want to define two objects as different if they differ on any one of the dimensions.
		The linkage function is encapsulated in a Linkage.Function delegate.
		The within-group sum of squares of a cluster is defined as the sum of the squares of the distance between all objects in the cluster and the centroid of the cluster.
	www.centerspace.net /doc/NMath/Stats/user/multivariate3.html (1562 words)

	A generalized distance function and the analysis of production efficiency. \| Management from AllBusiness.com
		In a multi-input multioutput framework, Shephard defines two distance functions: an input distance function that rescales all inputs toward the frontier technology and an output distance function that rescales all outputs toward the frontier.
		Also, to be empirically meaningful, Shephard's distance functions rely on an "attainability assumption." This assumption states that all output vectors can be obtained from the rescaling of any nonzero input vector or that all input vectors are feasible in the production of any rescaled nonzero output vector (see Shephard 1970, Chapter 9).
		Using Shephard's output distance function, Ray and Desli (1997) were unable to report empirical estimates of technical change and scale efficiency for Ireland because the associated data did not satisfy the attainability assumption (Ray and Desli 1997, p.
	www.allbusiness.com /management/340099-1.html (0 words)

	Improved Heterogeneous Distance Functions
		As discussed in the previous section, the Euclidean distance function is inappropriate for nominal attributes, and VDM is inappropriate for continuous attributes, so neither is sufficient on its own for use on a heterogeneous application, i.e., one with both nominal and continuous attributes.
		The function HVDM is similar to the function HOEM given in Section 2.3, except that it uses VDM instead of an overlap metric for nominal values and it also normalizes differently.
		When computing the distance for each attribute, the normalized_diff function was used for linear attributes, and the normalized_vdm function N1, N2, or N3 was used (in each of the three respective experiments) for nominal attributes.
	axon.cs.byu.edu /~randy/jair/wilson3.html (1952 words)

	Using EvalViewer as a comparison tool
		The searchsize that was used resulted in an average distance computation of 2.2 points on set B for every point on set A. The large the searchsize parameter, the larger the number in parenthesis will be, and the more computation will be required.
		RMS distance is basically a special kind of average number that is computed by squaring all the distances, computing the average of the squared distances, and then taking the square root of that average of squares.
		The average distance vector, known as the Bias between the two point sets, is given as an XYZ vector.
	www.alias.com /eng/support/studiotools/documentation/EvalViewer/EvalOvervw13.html (1559 words)

	Worley (Site not responding. Last check: )
		The basic idea of the function is to compute the distance from any render point on the surface of the object to some cell centers.
		C1, C2, C3 and C4 are respectively the distance from the render point to the nearest cell, to the second nearest cell, to the third nearest cell and to the fourth nearest cell.
		Those constants are multipliers which mean that any distance where the multiplier is 0 is not taken into account in the output.
	www.ypoart.com /Downloads/worley.htm (1396 words)

	Wen Chen (Site not responding. Last check: )
		The present study is not limited within the RBF and concerns general kernel distance functions and distance function wavelets, establishing on the fundamental solution and the general solution of partial differential equations (PDE).
		The above issues may be tackled in the framework of kernel distance functions, building on the firm grounds of integral equation theory (distribution theory), and in terms of physics, the potential theory.
		As the motto goes "the laws of universe are written in the language of partial differential equation", the distance function and wavelets are not an exception.
	heim.ifi.uio.no /~wenc/html/distance.htm (515 words)

	distance.htm
		A geometry with a distance function is called a metric geometry and the existence of a distance function allows one to define a variety of basic notions in an intuitively plausible fashion.
		In addition to discussing abstract properties of distance functions, we will look at how changing the way we compute distance changes which rotations and reflections are isometries.
		The `Ruler Postulate' is used to establish a connection between lines and the distance function and appears, in one form or another, in several secondary school geometry texts.
	www.math.ohiou.edu /~connor/330b/distance.htm (793 words)

	Distance Estimator, Mu-Ency at MROB
		Distance Estimator allows you to see every pixel that contains any points in the Mandelbrot Set (no matter how few such points there are).
		The algorithm is based on the derivative of the iteration function and works because the dwell bands are spaced closer together as you approach a point in the Mandelbrot set.
		The Distance Estimator method was pioneered by Thurston, and was made known to the general community by Peitgen and Richter in their book The Beauty Of Fractals.
	www.mrob.com /pub/muency/distanceestimator.html (361 words)

	Clausal Function Definitions
		Application of such a function proceeds much as before, except that the argument value is matched against the parameter pattern to determine the bindings of zero or more variables, which are then used during the evaluation of the body of the function.
		This function may then be applied to a pair (two-tuple!) of arguments to yield the distance between them.
		Functions with multiple results may be thought of as functions yielding tuples (or records).
	www.cs.cmu.edu /afs/cs/usr/rwh/public/www/introsml/core/clauses.htm (1537 words)

	Volumetric integration
		The function we represent is the weighted signed distance of each point to the nearest range surface along the line of sight to the sensor.
		In two and three dimensions, the depth measurements correspond to curves or surfaces with weight functions, and the signed distance ramps have directions that are consistent with the primary directions of sensor uncertainty.
		The signed distance contribution is computed by making the difference between the depth read out at the projection of the grid point in the depth map and the actual distance between the point and the camera projection center.
	www.cs.unc.edu /~marc/tutorial/node129.html (891 words)

	Christopher Johnson - 301031577 - Lab 3
		I also intend to add alterations to Worley's function in the form of linear combination of nth nearest neighbour distance functions and fractal versions to produce a variety of textures that can be applied to many different scenes.
		When all the points have been generated and their distances from the sample location have been sorted, the value can be returned and mapped to a color or shade to form the appearance of a texture.
		After the distance to the feature points in the initial cube are placed in the distance array I then calculate which neighbouring cubes might have a closer distance.
	www.cs.sfu.ca /~crjohnso/personal/final.html (2153 words)

	Spacetime - General Relativity, Quantum Gravity, and the Existence of Time
		If Observer A measures a distance of one mile on their ruler, another observer B who is in relative motion to observer A may measure a distance of 1/2 mile on their ruler.
		We don't see time or distance shrinking on earth because the effect is virtually undetectable until the relative motion of the two observers approaches the speed of light (299,792,458 meters per second).
		None-the-less, the time and distance measured by two observers in relative motion to each other is different, only the speed of light measured by all observers is the same.
	ws5.com /spacetime (7532 words)

	PlanetMath: metric space
		(called a metric, or sometimes a distance function) such that, for every
		distance metric, metric, distance, metric topology, open ball, closed ball
		Cross-references: Euclidean space, isomorphic, finite dimensional, vector space, structure, normed vector space, closed subset, basis, topology, Hausdorff topological space, union, open set, radius, equality, function, real
	planetmath.org /encyclopedia/Distance.html (195 words)

	LSMLIB: lsm_initialization2d.h File Reference
		In the region phi > 0, it is a signed distance function everywhere except for regions where phi > 0 simultaneously for the level set functions of multiple circles.
		Within the region phi < 0, it is equal to the signed distance function; in the region phi > 0, it is a signed distance function everywhere except for regions where phi > 0 simultaneously for multiple half-spaces.
		Within the region phi < 0, it is equal to the signed distance function; in the region phi > 0, it is a signed distance function everywhere except for regions where phi > 0 simultaneously for any two of the half-spaces that define the rectangles.
	www.princeton.edu /~ktchu/software/lsmlib/lsmlib_doc/lsm__initialization2d_8h.html (1297 words)

	Procedural Dylan -- A Simple Function
		The last important detail to notice is that, aside from the issue of spaces, the expression used to calculate the distance is the same in both Dylan and Pascal.
		If we had used the original version of the distance function, we would have gotten the error when we tried to call distance.
		Another way to rewrite the distance function to only do the substractions once would be to abstract out the squaring operation as a local function.
	www.webcom.com /haahr/procedural-dylan/1-distance.html (0 words)

	Chapter 5: Fruitful functions
		Calling the function generates a new value, which we usually assign to a variable or use as part of an expression.
		We chose these values so that the horizontal distance equals 3 and the vertical distance equals 4; that way, the result is 5 (the hypotenuse of a 3-4-5 triangle).
		Then use this function in a function called intercept(x1, y1, x2, y2) that returns the y-intercept of the line through the points (x1, y1) and (x2, y2).
	ibiblio.org /obp/thinkCS/python/english/chap05.htm (2505 words)

	Office of Science and Technology
		Properties of the Stochastic Distance Function and its Role in Fisheries Analyses
		The distance function is a natural tool for fishery production models in that it does not require cost data (only data on input and output quantities are necessary), which is often unavailable, and it can accommodate multi-input, multi-output relationships (common in fisheries).
		However, Monte Carlo experiments have indicated that data characterized by certain characteristics may not be properly approximated by the normalized stochastic distance function.
	www.st.nmfs.gov /st5/abstracts/Properties_of_the_Stochastic_Distance_Function.htm (164 words)

	Lesson 6, Geometry & command functions
		The angle function returns a real number which is the radian measure of the angle from the first point to the second.
		Don't confuse the distance function with either the DIST command (which allows the user to pick two points and reports the 3D distance between them as well as delta-x, delta-y, and delta-z), or with the DISTANCE system variable (which holds the most recent distance reported by the DIST command).
		The polar function always returns a point that is in the same X-Y construction plane (that is, at the same Z level) as the base point.
	ronleigh.info /autolisp/ales06.htm (3259 words)

	Skew Voronoi Diagrams
		What we need is a distance function that takes into account the difference in height between two points.
		Since the skew distance is not symmetric, two different circles can be defined: the outgoing circle and the incoming circle.
		Note also that once again, since the skew distance is not symmetric, there are two versions of the problem: the incoming version and the outgoing version.
	cg.scs.carleton.ca /~mathieu/mcouture/node3.html (1315 words)

	Estimate the Distance Curve, Integration and Graphs Lesson (Site not responding. Last check: )
		You will use this distance function to calculate the car's distance at the time when the car's speed is zero -- this is the distance it takes the car to come to a complete stop.
		This equation is an estimate of the car's distance as a function of time.
		The distince you calculate is your estimate of the distance it takes the car to come to a complete stop.
	www.sci.wsu.edu /math/Lessons/CarSkid/distance.html (518 words)

	IntegrationAccumulation
		Most students know that if you are walking at a constant velocity, then the distance that you walk is equal to your velocity times the amount of time that you walk, that is, s = v t.
		Watch the area (total distance walked) under the plotted velocity function accumulate as a function of time.
		Let's extend the above concept of "distance walked as the total accumulated area under the velocity curve" to velocity functions that are not constant.
	www2.umassd.edu /temath/TEMATH2/Examples/IntegrationAccumulation.html (575 words)

	Kernel Distance Function and rbf (Site not responding. Last check: )
		The function expressed in the Euclidean distance variable is usually termed as the radial basis function in literature.
		Thus, the term “radial basis function” is really a misnomer in referring to general distance functions and their applications.
		The conventional use of the RBF instead of general distance function may unnecessarily confuse the nascent researchers with an implication of narrowly-defined rotational invariant problems under a radially symmetric domain.
	folk.uio.no /wenc/html/why.htm (360 words)

	Into the STL distance function - The Code Project - STL
		Given two iterators on the same container, we wish to create a generic function that returns the number of elements between them, or the distance between them.
		The main reason is that, from definition, functions return values at run-time and we want flow control at compile-time.
		If tags are "attributes" used to identify certain properties of certain types, function overloading is the tool we use to control the flow, given those attributes (tags).
	www.codeproject.com /vcpp/stl/stl_distance.asp (0 words)

	HI-TECH Software Forums: Distance function sqrt(aa+bb [+c*c...])
		Given two or three numbers, byte or int16, what is the best way to compute the "distance" function (square root of the sum of squares)?
		Certainly computing the square root of the sum of squares is possible, but it seems needlessly expensive in terms of CPU time.
		In this application, for compatibility reasons, it is probably necessary to compute the actual distance (the PIC feeds numbers to another micro).
	www.htsoft.com /forum/all/showflat.php?Cat=0&Number=5510&page=0&fpart=1&vc=1 (0 words)

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