PX4-Autopilot/src/lib/mathlib/math/Functions.hpp
2020-12-03 18:19:42 +01:00

202 lines
6.0 KiB
C++

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/**
* @file Functions.hpp
*
* collection of rather simple mathematical functions that get used over and over again
*/
#pragma once
#include "Limits.hpp"
#include <matrix/matrix/math.hpp>
namespace math
{
// Type-safe signum function with zero treated as positive
template<typename T>
int signNoZero(T val)
{
return (T(0) <= val) - (val < T(0));
}
/*
* So called exponential curve function implementation.
* It is essentially a linear combination between a linear and a cubic function.
* @param value [-1,1] input value to function
* @param e [0,1] function parameter to set ratio between linear and cubic shape
* 0 - pure linear function
* 1 - pure cubic function
* @return result of function output
*/
template<typename T>
const T expo(const T &value, const T &e)
{
T x = constrain(value, (T) - 1, (T) 1);
T ec = constrain(e, (T) 0, (T) 1);
return (1 - ec) * x + ec * x * x * x;
}
/*
* So called SuperExpo function implementation.
* It is a 1/(1-x) function to further shape the rc input curve intuitively.
* I enhanced it compared to other implementations to keep the scale between [-1,1].
* @param value [-1,1] input value to function
* @param e [0,1] function parameter to set ratio between linear and cubic shape (see expo)
* @param g [0,1) function parameter to set SuperExpo shape
* 0 - pure expo function
* 0.99 - very strong bent curve, stays zero until maximum stick input
* @return result of function output
*/
template<typename T>
const T superexpo(const T &value, const T &e, const T &g)
{
T x = constrain(value, (T) - 1, (T) 1);
T gc = constrain(g, (T) 0, (T) 0.99);
return expo(x, e) * (1 - gc) / (1 - fabsf(x) * gc);
}
/*
* Deadzone function being linear and continuous outside of the deadzone
* 1 ------
* /
* --
* /
* -1 ------
* -1 -dz +dz 1
* @param value [-1,1] input value to function
* @param dz [0,1) ratio between deazone and complete span
* 0 - no deadzone, linear -1 to 1
* 0.5 - deadzone is half of the span [-0.5,0.5]
* 0.99 - almost entire span is deadzone
*/
template<typename T>
const T deadzone(const T &value, const T &dz)
{
T x = constrain(value, (T) - 1, (T) 1);
T dzc = constrain(dz, (T) 0, (T) 0.99);
// Rescale the input such that we get a piecewise linear function that will be continuous with applied deadzone
T out = (x - matrix::sign(x) * dzc) / (1 - dzc);
// apply the deadzone (values zero around the middle)
return out * (fabsf(x) > dzc);
}
template<typename T>
const T expo_deadzone(const T &value, const T &e, const T &dz)
{
return expo(deadzone(value, dz), e);
}
/*
* Constant, linear, constant function with the two corner points as parameters
* y_high -------
* /
* /
* /
* y_low -------
* x_low x_high
*/
template<typename T>
const T gradual(const T &value, const T &x_low, const T &x_high, const T &y_low, const T &y_high)
{
if (value < x_low) {
return y_low;
} else if (value > x_high) {
return y_high;
} else {
/* linear function between the two points */
T a = (y_high - y_low) / (x_high - x_low);
T b = y_low - a * x_low;
return a * value + b;
}
}
/*
* Constant, linear, linear, constant function with the three corner points as parameters
* y_high -------
* /
* /
* y_middle /
* /
* /
* /
* y_low -------
* x_low x_middle x_high
*/
template<typename T>
const T gradual3(const T &value,
const T &x_low, const T &x_middle, const T &x_high,
const T &y_low, const T &y_middle, const T &y_high)
{
if (value < x_middle) {
return gradual(value, x_low, x_middle, y_low, y_middle);
} else {
return gradual(value, x_middle, x_high, y_middle, y_high);
}
}
/*
* Squareroot, linear function with fixed corner point at intersection (1,1)
* /
* linear /
* /
* 1 /
* /
* sqrt |
* |
* 0 -------
* 0 1
*/
template<typename T>
const T sqrt_linear(const T &value)
{
if (value < static_cast<T>(0)) {
return static_cast<T>(0);
} else if (value < static_cast<T>(1)) {
return sqrtf(value);
} else {
return value;
}
}
} /* namespace math */