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Topic: Linear interpolation

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	Linear interpolation - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		Linear interpolation is a process employed in mathematics, and numerous applications including computer graphics.
		Linear interpolation is often used to fill the gaps in a table.
		Linear interpolation can also be extended to bilinear interpolation for interpolating functions of two variables.
	en.wikipedia.org /wiki/Linear_interpolation (640 words)

	Interpolation - Wikipedia, the free encyclopedia
		One of the simplest methods is linear interpolation (sometimes known as lerp).
		Furthermore, the interpolant is a polynomial and thus infinitely differentiable.
		For instance, rational interpolation is interpolation by rational functions, and trigonometric interpolation is interpolation by trigonometric polynomials.
	en.wikipedia.org /wiki/Interpolation (1051 words)

	Linear interpolation - InfoSearchPoint.com (Site not responding. Last check: 2007-11-07)
		Linear interpolation is a process employed in linear algebra, and numerous applications thereof including computer graphics and numerical analysis.
		In numerical analysis a linear interpolation of certain points that are in reality values of some function $f$ is typically used to approximate the function $f$ .
		Linear interpolatiom can also be extended to Bilinear interpolation, for example to interpolate a function z(x, y) where z can be written in terms of an α factor for the x-direction and a β factor for the y-direction.
	www.infosearchpoint.com /display/Linear_interpolation (375 words)

	Linear interpolation: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-07)
		In the mathematical subfield of numerical analysis, polynomial interpolation is the interpolation of a given data set by a polynomial....
		In the mathematical subfield of numerical analysis spline interpolation is a special form of interpolation where the interpolant is a piecewise polynomial...
		In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables....
	www.absoluteastronomy.com /encyclopedia/l/li/linear_interpolation.htm (1420 words)

	Linear interpolation (Site not responding. Last check: 2007-11-07)
		In numerical analysis a linear interpolation of certain points are in reality values of some function f is typically used to approximate the f.
		Linear interpolation can also be extended to interpolation for interpolating functions of two variables.
		interpolation is often used as a crude anti-aliasing filter.
	www.freeglossary.com /Linear_interpolation (427 words)

	Interpolation
		Interpolation is any procedure for fitting a function to a set of points in such a manner that the function intercepts each of the points.
		Linear interpolation uses a linear polynomial as the interpolation function.
		Quadratic interpolation uses a quadratic polynomial as its interpolation function.
	www.riskglossary.com /articles/interpolation.htm (478 words)

	Image Interpolation for Scaling (Site not responding. Last check: 2007-11-07)
		This is linear interpolation since we are fitting straight lines between the samples.
		For example, the nearest neighbor kernel for tripling is [1 1], and the linear interpolation kernel is 1/3 [1 2 3 2 1].
		Note: while the linear interpolation kernel may resemble the binomial kernels, they are not the same as the sizes grow.
	www.cs.wisc.edu /graphics/Courses/cs-638-1999/image_scaling.htm (1313 words)

	What's the point? Interpolation and extrapolation with a regular grid DEM
		Linear plane interpolation is more likely to be used in triangulated irregular networks (TINs) that have been derived from a regular grid DEM with little or no vertex removal.
		Double linear interpolation attempts to minimise the likelihood of such errors by averaging the linear plane heights of the two triangles into which a grid cell can be divided by one of its diagonals.
		The trend (or slopes) of the surface are important for interpolation, since we should not be constrained to using the nearest 3 or 4 vertices of the DEM cell.
	www.geovista.psu.edu /sites/geocomp99/Gc99/082/gc_082.htm (6132 words)

	NIST X-Ray Form Factor, Atten. Scatt. Tables, Section 8
		This may be limited by extrapolating or interpolating at either end of the energy range with a linear log-log form, while allowing intermediate values to be affected by higher order contributions.
		Interpolating functions may further be limited to symmetric forms about the region interpolated (i.e., to linear, cubic or quintic log-log interpolation using n = 2, 4, or 6 data points).
		This is illustrated in Fig. 4 for medium energy attenuation by uranium, where the asterisk notes the reduction to a linear log-log form for extrapolation, thus avoiding unnecessary oscillations.
	physics.nist.gov /PhysRefData/FFast/Text1995/chap08.html (891 words)

	Interpolation methods (Site not responding. Last check: 2007-11-07)
		Interpolation as used here is different to "smoothing", the techniques discussed here have the characteristic that the estimated curve passes through all the given points.
		Linear interpolation is the simplest method of getting values at positions in between the data points.
		Often a smoother interpolating function is desirable, perhaps the simplest is cosine interpolation.
	astronomy.swin.edu.au /~pbourke/analysis/interpolation (618 words)

	Linear Interpolation - GPWiki
		Linear interpolation is the process of using two known values at two points to determine a third unknown value at a third point.
		Interpolate the points position, so the point moves from its starting position to the other point.
		Linear interpolation can also be used to animate things.
	www.gpwiki.org /index.php/Linear_Interpolation (221 words)

	Matrix and Quaternion FAQ (Site not responding. Last check: 2007-11-07)
		Interpolation between these two vectors can then be performed through the use of the standard linear interpolation equation: Vr = Va + t.(Vb - Va) where Vr is the resulting vector Va is the start position vector Vb is the final position vector This equation may be applied to both translation and rotation vectors.
		As with linear interpolation, the four matrices are converted into their corresponding translation and rotation vectors (Again, either Euler angles or spherical rotation angles).
		Using linear interpolation, the interpolated rotation matrix is generated using a blending equation with the parameter T, which ranges from 0.0 to 1.0.
	skal.planet-d.net /demo/matrixfaq.htm (7526 words)

	A Chronology of Interpolation (Site not responding. Last check: 2007-11-07)
		This Lemma contains his general interpolation formula for unequal-interval data as well as the formula for equal-interval data, the latter of which is in fact a special case of the former and is equal to the one described earlier by Gregory, hence the Gregory-Newton formula.
		Analyzing the frequency content of this interpolant, he observes that all constituents of period 2w, with w the distance between the abscissae, are absent.
		In particular they show that the error introduced by a given interpolation or approximation kernel consists of two parts, one of which is dominant and is determined entirely by the spectrum of the function to be approximated and a certain error function, the latter of which depends only on the kernel.
	imagescience.bigr.nl /meijering/research/chronology (3092 words)

	What are OMDI Math Tools (Site not responding. Last check: 2007-11-07)
		Linear interpolation is a simple numerical method for calculating an arbitrary point between two points that define a straight line.
		Where surface averaging is analogous to linear interpolation, bi-cubic spline interpolation is curvatious, and operates by performing multiple spline interpolations on the rows and columns to estimate the desired point.
		For the first method, the XY interpolants is a selection of n-rows by 2 columns (where the first column is X and the second column is Y), and the XYZ data points are a selection of n-rows by 3 columns (where the columns are X, Y, Z respectively.) Z' is returned.
	www.octavian.com /Layout.jsp?product=xl_math&type=document (3375 words)

	More Accurate Linear Interpolation
		Some form of interpolation is then required to estimate values of the function at intermediate points.
		Linear interpolation is the quickest procedure; however, it is usually the least accurate.
		Thus, almost any application that employs one-dimensional linear interpolation at fixed intervals should be able to realize noticeable improvements in accuracy.
	www.forkosh.dreamhost.com /lint1d.html (1686 words)

	The eighties: an image processing view
		Only a visual comparison of B-spline interpolation to other interpolation methods is given by the authors, whereby they compare it only to nearest neighbor and linear interpolation.
		This cubic convolution kernel then is compared to nearest neighbor and linear interpolation both by comparing their frequency responses and by visual comparison of interpolated images.
		They compared eight different interpolation methods, nearest neighbor (which they call sample-and-hold) and linear interpolation, a truncated sinc filter, B-splines, two types of sharpened cubic splines (which are not explained in more detail), a truncated Gaussian and a truncated sharpened Gaussian filter.
	www.cg.tuwien.ac.at /~theussl/DA/node11.html (1304 words)

	Cross-Linear Interpolation (Site not responding. Last check: 2007-11-07)
		Consider a two-dimensional function y(x,z), and suppose that for any fixed value of z there is a linear relationship between x and y.
		This seemingly simple request is actually ambiguous, because there are really two different senses in which linear interpolation can be applied - and in some circumstances the difference in results can be very significant.
		Depending on the actual form of the relationship between x, y, and z, either one or the other of these two forms of linear interpolation may be correct.
	www.mathpages.com /home/kmath323/kmath323.htm (462 words)

	Linear Waveform Generation with CompactRIO and LabVIEW FPGA - Tutorial - Developer Zone - National Instruments
		Linear waveforms can be described by two points, a start and end point, and any points located on the line connecting these two point.
		For instance, one example of a linear waveform is a waveform that ramps from -10V to 10V in 1V increments with 1 second between the updates.
		The next interpolation value is calculated by adding the result of the initial shifting of 65535 and then that result is ORed with 1 and wired to the shift register for the next iteration.
	zone.ni.com /devzone/conceptd.nsf/webmain/2CFEDAEF383A7AFF86256EE90077CE01?opendocument&node=dz00000_us (3582 words)

	Boolean Expansion as Linear Interpolation (Site not responding. Last check: 2007-11-07)
		To interpolate the value of f at some specific point in this n-dimensional space using linear interpolation, we need to first find the particular "cell" of the table where the point falls.
		The correspondence between interpolation in a Euclidean space and the expansion of the probabilities of logical functions suggests some interesting approaches to dealing with more challenging situations in which the logical variables are NOT independent.
		However, it's important to keep in mind that the general locus given by n-dimensional linear interpolation actually possesses intrinsic curvature, and isn't linear with respect to arbitrary independent basis vectors.
	www.mathpages.com /home/kmath089.htm (434 words)

	Data Interpolation
		Since the coefficients of this linear combination are independent of the tensor indexes, the linear combination of the tensors can be done component-wise.
		We can use trilinear component-wise interpolation because symmetric tensors form a linear subspace in the tensor space: any linear combination of symmetric tensors remains a symmetric tensor, i.e., symmetric tensors are closed under linear combination (the manifold of symmetric tensors is not left).
		On the other hand, component-wise interpolation of eigenvectors and eigenvalues themselves would not lead to correct results, since a linear interpolation between two unit vectors is not a unit vector anymore - the interpolated eigenvector value would leave the manifold of unit vectors.
	www.gg.caltech.edu /~zhukov/research/fiber_tracking/vis02/node5.html (222 words)

	ZAPLIN - Replaces regions in a two-dimensional NDF by bad values or by linear interpolation (Site not responding. Last check: 2007-11-07)
		If interpolation is not possible (for instance, if the selected pixels are at the edge of the array) then the pixels are replaced with bad values.
		Linear interpolation is used to obtain the replacement values.
		As above except that linear interpolation plus cosmetic noise are used to replace the areas to be cleaned rather than bad pixels.
	star-www.rl.ac.uk /cgi-bin/htxserver/sun95.htx/sun95.html?xref_ZAPLIN (2007 words)

	Sba: Controle & Automação Sociedade Brasileira de Automatica - The linear interpolation method: a sampling theorem ... (Site not responding. Last check: 2007-11-07)
		The relationship between piecewise linear approximation and the sampling theorem is highlighted by the use of triangular pulses instead of sampling functions.
		Furthermore, a comparison of the linear interpolation with a series on a nonorthogonal basis composed of equally spaced triangular pulses is provided.
		The interpolation uses the sample values of the function whereas the series coefficients are obtained by minimizing the quadratic error between the original function and the series.
	www.scielo.br /scielo.php?script=sci_arttext&pid=S0103-17592003000400012&lng=en&nrm=iso (1801 words)

	BIG - Turbo-charged linear interpolation
		We demonstrate a new method that improves the quality of piecewise linear interpolation significantly, without adding much to the computation.
		and the new turbo-charged one: bilinear interpolation with shifted knots.
		A package of C routines that implement shifted linear interpolation.
	bigwww.epfl.ch /demo/jshiftlinear/index.html (179 words)

	How Linear Interpolation Works
		The simplest kind of automatic inbetweening is linear inbetweening which is done with a mathematical process of guessing intermediate locations called linear interpolation.
		The points of the interpolated house are halfway between the two initial houses, resulting in a house that is half the size.
		The scaling of the house is a result only of interpolating between the different sized houses in the key frames.
	www.cs.brown.edu /stc/outrea/greenhouse/nursery/interpolation/formal.html (1028 words)

	Linear Interpolation
		Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line.
		Thus, the computational complexity of linear interpolation is one multiply and two additions per sample of output.
		Linear interpolation sounds best when the signal is oversampled.
	ccrma-www.stanford.edu /~jos/waveguide/Linear_Interpolation.html (248 words)

	Interpolation theory
		Likewise, the local 2-point Lagrange interpolation is equivalent to the linear interpolation, defined by the formula
		Because of their simplicity, the nearest-neighbor and linear interpolation methods are very practical and easy to apply.
		show the interpolation error steadily decreasing as we proceed from 1-point nearest-neighbor to 2-point linear and 4-point cubic-convolution interpolation.
	sepwww.stanford.edu /public/docs/sep107/paper_html/node20.html (516 words)

	First Steps in Numerical Analysis (Site not responding. Last check: 2007-11-07)
		The first differences are almost constant locally, so that the table is suitable for linear interpolation.
		As previously indicated, linear interpolation is appropriate only for slowly varying functions.
		The next simple process is quadratic interpolation, based on a quadratic approximating polynomial; one might expect that such an approximation would give better accuracy for functions with larger variations.
	kr.cs.ait.ac.th /~radok/math/mat7/step21.htm (378 words)

	Adaptive tri-linear interpolation for use when switching to a new level-of-detail map (US6184894)
		Using bi-linear interpolation, the four nearest texture pixels or texels are fetched from the texture map in a texture memory and a weighted-average texel generated.
		Tri-linear interpolation eliminates this LOD-transitioning distortion by generating weighted-average texels for both the LOD map and for four texels from a next LOD map.
		An interpolation factor read from the lookup table or generated by shifting the LOD fraction is multiplied by the weighted-texel average for the tri-linear weighting.
	www.delphion.com /details?pn=US06184894__ (657 words)

	Miscellaneous reconstruction methods
		They use nearest neighbor interpolation for constant areas, linear interpolation for linear areas and the Catmull-Rom spline for non-linear areas.
		They conclude that, although the improvement of cubic convolution over linear interpolation is significant, only marginal improvements can be achieved with higher-order schemes.
		The results are that linear interpolation, the still by far most used interpolation method, is the best interpolation kernel with spatial extend two.
	www.cg.tuwien.ac.at /~theussl/DA/node15.html (581 words)

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