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In computer graphics, an Euler filter is a filter intended to prevent gimbal lock and related discontinuities in animation data sets in which rotation is expressed in terms of Euler angles.
These discontinuities are caused by the existence of many-to-one mappings between the Euler angle parameterization of the set of 3D rotations. This allows the data set to flip between different Euler angle combinations which correspond to a single 3D rotation, which, although remaining continuous in the space of rotation, are discontinuous in the Euler angle parameter space.
The Euler filter chooses on a sample-by-sample basis between the possible Euler angle representations of each 3D rotation in the data set in such a way as to preserve the continuity of the Euler angle time series, without changing the actual 3D rotations.
Euler filtering is available in a number of 3D animation packages.
In computer graphics, an Eulerfilter is a filter intended to prevent gimbal lock and related discontinuities in animation data sets in which rotation...
between triangle centers Euler operator – set of functions to create polygon meshes EulerfilterEuler's rotation theorem Euler spiral – a curve whose curvature...
numerical analysis and scientific computing, the backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the...
as by Christian Weise in 1712 (Nucleus Logicoe Wiesianoe) and Leonhard Euler (Letters to a German Princess) in 1768. The idea was popularised by Venn...
{\displaystyle {\frac {\sin(\pi x)}{\pi x}}={\frac {1}{\Gamma (1+x)\Gamma (1-x)}}.} Euler discovered that sin ( x ) x = ∏ n = 1 ∞ cos ( x 2 n ) , {\displaystyle...
feedforward comb filter: H ( e j ω ) = 1 + α e − j ω K {\displaystyle H\left(e^{j\omega }\right)=1+\alpha e^{-j\omega K}} Using Euler's formula, the frequency...
EulerCalc← cos + 0j1 × sin ⍝ 0j1 is what's usually written as i EulerDirect← *0J1×⊢ ⍝ Same as ¯12○⊢ ⍝ Do the 2 methods produce the same result? EulerCheck←...
as total variation regularization or total variation filtering, is a noise removal process (filter). It is based on the principle that signals with excessive...
Wheel Factorized basic sieve of Eratosthenes for practical sieving ranges. Euler's proof of the zeta product formula contains a version of the sieve of Eratosthenes...
A resistor–inductor circuit (RL circuit), or RL filter or RL network, is an electric circuit composed of resistors and inductors driven by a voltage or...
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such...
significantly higher than the filter's cutoff frequency. Crest (physics) Complex exponential Damped sine wave Euler's formula Fourier transform Harmonic...
(Lf)}{(1-L^{2}f^{2})}}={\frac {\sin(\pi Lf)}{2\pi Lf(1-L^{2}f^{2})}}} Derivation Using Euler's formula to expand the cosine term in w 0 ( x ) , {\displaystyle w_{0}(x)...
be simplified by removing terms describing viscous actions to yield the Euler equations. Further simplification, by removing terms describing vorticity...
the sum of two primes, in a 1742 letter to Euler. Euler proved Alhazen's conjecture (now the Euclid–Euler theorem) that all even perfect numbers can be...
and botany in 1721. He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was...
however, the most common are Rotation matrices, Quaternions, and Euler angles. While Euler angles are oftentimes the most straightforward representation...
(e.g. "⌀ 55 mm"), indicating that it represents diameter. Photographic filter thread sizes are often denoted in this way. The symbol has a Unicode code...
bandpass filter. They are key components in many electronic devices, particularly radio equipment, used in circuits such as oscillators, filters, tuners...
physical quantities. Examples of analog signal processing include crossover filters in loudspeakers, "bass", "treble" and "volume" controls on stereos, and...
Difference polynomials Digamma function Egorychev method Erdős–Ko–Rado theorem Euler–Mascheroni constant Faà di Bruno's formula Factorial Factorial moment Factorial...
}}~\left|\operatorname {Arg} (x)\right|<\pi ~,} where γ ≈ 0.57721566 ... is the Euler–Mascheroni constant. Some texts use ci instead of Ci. Ci(x) is the antiderivative...
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