To get resolution finer than a clock period, there are time interpolation circuits.

For 3D animation Bézier curves are often used to define 3D paths as well as 2D curves for keyframe interpolation.

In automatic systems this can be done using a binary search algorithm or interpolation search ; manual searching may be performed using a roughly similar procedure, though this will often be done unconsciously.

have often been regarded as a post-Pauline interpolation.

Y Gododdin is known only from a 13th-century manuscript, so it is impossible to determine whether this passage is original or a later interpolation, but John Koch's view that the passage dates from a 7th-century or earlier version is regarded as unproven ; 9th-or 10th-century dates are often proposed for it.

Before the advent of modern computers numerical methods often depended on hand interpolation in large printed tables.

Again, convergence is asymptotically faster than the secant method, but inverse quadratic interpolation often behaves poorly when the iterates are not close to the root.

Linear interpolation is often used to approximate a value of some function f using two known values of that function at other points.

Linear interpolation is often used to fill the gaps in a table.

They are often used as building blocks for more complex operations: for example, a bilinear interpolation can be accomplished in three lerps.

Linear interpolation has been used since antiquity for filling the gaps in tables, often with astronomical data.

Differences often extend beyond minor variations and may involve, for instance, interpolation of material central to issues of historicity and doctrine, such as the ending of Mark 16.

This relatively primitive technique ( as opposed to digital interpolation ) is often visually detectable by the casual viewer.

In interpolating problems, spline interpolation is often referred to as polynomial interpolation because it yields similar results, even when using low-degree polynomials, while avoiding Runge's phenomenon for higher degrees.

They are often used as nodes in polynomial interpolation because the resulting interpolation polynomial minimizes the Runge's phenomenon.

Z-fighting which cannot be entirely eliminated in this manner is often resolved by the use of a stencil buffer, or by applying a post transformation screen space z-buffer offset to one polygon which does not affect the projected shape on screen, but does affect the z-buffer value to eliminate the overlap during pixel interpolation and comparison.

In mathematics, the Riesz – Thorin theorem, often referred to as the Riesz – Thorin interpolation theorem or the Riesz – Thorin convexity theorem is a result about interpolation of operators.

In hip hop music, interpolation refers to using a melody – or portions of a melody ( often with modified lyrics ) – from a previously recorded song, but re-recording the melody instead of sampling it.

In image processing, bicubic interpolation is often chosen over bilinear interpolation or nearest neighbor in image resampling, when speed is not an issue.

These processes most often achieve a smooth transition through interpolation.

Modern scholars have developed techniques for recognising interpolation, which are often apparent to modern observers, but would have been less so for medieval copyists.

* Cam drums with toolpaths of the type that in CNC milling terms would require 4-or 5-axis contouring or turn-mill cylindrical interpolation

The filtered signal can subsequently be reconstructed without significant additional distortion, for example by the Whittaker – Shannon interpolation formula.

After 6. cxd5 Nxg5 7. Nxg5 e6, White has 8. Qd2 exd5 9. Qe3 +, with attacking chances, or the more usual 8. Nf3 exd5 ( though the interpolation 8 ... h6 9. Nf3 exd5 is a significant alternative ), after which play generally proceeds on lines analogous to the Queen's Gambit Declined, Exchange Variation, with a queenside minority attack by White ( b2 – b4 – b5xc6 ), as Black aims for his traditional kingside play with ... f7 – f5 – f4 and, in this case, ... g6 – g5.

As the final PAL DVD release shows, the film was shot 50i ( interlaced ), and only special effects shots were deinterlaced by means of smart field blending ( imitating a progressive-type amount of motion blur due to a different shutter speed of progressive modes ) during post-production, as the special effects crew obviously was in demand of progressive frames which are easier to process for special effects, before for the final release all normal shots were deinterlaced by means of simple line interpolation instead.

For decimation by an integer amount, only a single sampled filter is necessary ; for interpolation by an integer amount, different samplings are needed for different phases – for instance, if one is upsampling by a factor of 4, then one sampled filter is used for the half-way point, while a different sampled filter is used for the point 1 / 4 of the way from one point to another.

Richard Van Voorst also states that the interpolation likely took place some time between Origen and Eusebius.

In the end the whole process can be implemented for discrete sound signals as interpolation between values with similar phase and similar time.

Shen Kuo was also known for hydraulic clockworks, as he invented a new overflow-tank clepsydra which had more efficient higher-order interpolation instead of linear interpolation in calibrating the measure of time.

Some simulators estimate the time of collision by linear interpolation, roll back the simulation, and calculate the collision by the more abstract methods of conservation laws.

Some iterate the linear interpolation ( Newton's method ) to calculate the time of collision with a much higher precision than the rest of the simulation.

Given Bluestein's algorithm, such a transform can be used, for example, to obtain a more finely spaced interpolation of some portion of the spectrum ( although the frequency resolution is still limited by the total sampling time ), enhance arbitrary poles in transfer-function analyses, etcetera.

* the high degree of re-expansion ( a macro's arguments get expanded twice: once during scanning and once at interpolation time )

For interpolation on a grid with points for, interpolation is performed on one subinterval at a time ( given that tangent values are predetermined ).

Other research centers were working on interpolation at this time, particularly University of Kansas and their SURFACE II program.

The loop played throughout the chorus is an interpolation of " Gymnopédie No. 1 " by French classical composer Erik Satie, played in 4 / 4 time instead of the original 3 / 4.

Due to the simplicity of the bilinear filter, the quarter-pixel interpolation requires little CPU time ; the comparatively complex 6-tap interpolation has already been done.

Polynomial interpolation is also essential to perform sub-quadratic multiplication and squaring such as Karatsuba multiplication and Toom – Cook multiplication, where an interpolation through points on a polynomial which defines the product yields the product itself.

IBM support included customer service and hardware circuit modifications needed to tabulate numbers, create mathematical tables, add, subtract, multiply, reproduce, verify, create tables of differences, create tables of logarithms and perform Lagrangian interpolation, all to solve differential equations for astronomical applications.

The key idea is to perform linear interpolation first in one direction, and then again in the other direction.

Next, we perform linear interpolation between C000 and C100 to find C00, C001 and C101 to find C01, C011 and C111 to find C11, C010 and C110 to find C10.

Indeed, area coordinates will also allow us to perform a linear interpolation at all points in the triangle if the values of the function are known at the vertices.

Bilinear filtering uses these points to perform bilinear interpolation between the four texels nearest to the point that the pixel represents ( in the middle or upper left of the pixel, usually ).

Pain perform an interpolation of the song's chorus, in their 2009 song, " Wir sind Aliens ".