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Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
It uses a combination of the energy, momentum, and continuity equations to determine water depth with a given a friction slope (), channel slope (), channel geometry, and also a given flow rate. In practice, this technique is widely used through the computer program HEC-RAS , developed by the US Army Corps of Engineers Hydrologic Engineering ...
Side channel spillways are typically used to discharge floods perpendicular to the general direction of flow by placing the control weir parallel to the upper portion of the discharge channel. [4] It offers low flow velocities upstream and minimizes erosion. However, it can cause a sudden increase in reservoir level if the channel is submerged.
Linear interpolation is equivalent to a triangular impulse response; windowed sinc approximates a brick-wall filter (it approaches the desirable brick-wall filter as the number of points increases). The length of the impulse response of the filter in method 1 corresponds to the number of points used in interpolation in method 2.
Motion interpolation is a programming technique in data-driven character animation that creates transitions between example motions and extrapolates new motions. Example motions are often created through keyframing or motion capture. However, keyframing is labor-intensive and lacks varieties of motion, and both processes result in motions that ...
Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners. Use a pre-built lookup table, keyed on the cell index, to describe the output geometry for the cell. Apply linear interpolation along the boundaries of the cell to calculate the exact contour position.
This process yields p 0,4 (x), the value of the polynomial going through the n + 1 data points (x i, y i) at the point x. This algorithm needs O(n 2) floating point operations to interpolate a single point, and O(n 3) floating point operations to interpolate a polynomial of degree n.
The function is named in honor of von Hann, who used the three-term weighted average smoothing technique on meteorological data. [6] [2] However, the term Hanning function is also conventionally used, [7] derived from the paper in which the term hanning a signal was used to mean applying the Hann window to it.