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{"type": "library", "name": "InterpolationLib", "version": "1.0.2", "spec": {"owner": "luisllamasbinaburo", "id": 6733, "name": "InterpolationLib", "requirements": null, "uri": null}}

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# Arduino Interpolation Library
Arduino library that provides interpolation methods step, linear, smooth, catmull spline and constrained spline.
All methods recieves X-Values and Y-Values, the size of this arrays and the X point to interpolate, and return the estimated Y at the point X.
## Modes
### Step
Simple step interpolation. Estimated value is Yn-1 or Yn. The relative 'change point' int he interval (or threshold) is an optional parameter. 0.0 means change at the start of the interval, 1.0 at the and of the interval, and 0.5 in the mid point interval.
![Image](https://github.com/luisllamasbinaburo/Arduino-Interpolation/blob/master/images/arduino-interpolation-step.png)
### Linear
Linear interpolation. Adicional parameter controls the interpolation out of the provided X-Values arrays.
![Image](https://github.com/luisllamasbinaburo/Arduino-Interpolation/blob/master/images/arduino-interpolation-linear.png)
### Smooth
Applies a cubic smooth step between value changes
![Image](https://github.com/luisllamasbinaburo/Arduino-Interpolation/blob/master/images/arduino-interpolation-smooth.png)
### Catmull spline
Typical Catmull spline interpolation
![Image](https://github.com/luisllamasbinaburo/Arduino-Interpolation/blob/master/images/arduino-interpolation-catmull-spline.png)
### Constrained spline
A special kind of spline that doesn't overshoot
![Image](https://github.com/luisllamasbinaburo/Arduino-Interpolation/blob/master/images/arduino-interpolation-constrained-spline.png)
## Example
```c++
#include "InterpolationLib.h"
const int numValues = 10;
double xValues[10] = { 5, 12, 30, 50, 60, 70, 74, 84, 92, 100 };
double yValues[10] = { 150, 200, 200, 200, 180, 100, 100, 150, 220, 320 };
void setup()
{
while (!Serial) { ; }
Serial.begin(115200);
for (float xValue = 0; xValue <= 110; xValue += .25)
{
Serial.print(Interpolation::Step(xValues, yValues, numValues, xValue, 0.0));
Serial.print(',');
Serial.print(Interpolation::Step(xValues, yValues, numValues, xValue, 0.5));
Serial.print(',');
Serial.print(Interpolation::Step(xValues, yValues, numValues, xValue, 1.0));
Serial.print(',');
Serial.print(Interpolation::SmoothStep(xValues, yValues, numValues, xValue));
Serial.print(',');
Serial.print(Interpolation::Linear(xValues, yValues, numValues, xValue, false));
Serial.print(',');
Serial.print(Interpolation::Linear(xValues, yValues, numValues, xValue, true));
Serial.print(',');
Serial.print(Interpolation::CatmullSpline(xValues, yValues, numValues, xValue));
Serial.print(',');
Serial.println(Interpolation::ConstrainedSpline(xValues, yValues, numValues, xValue));
}
}
void loop()
{
}
```
## Auxiliar tools
Aditional utils
### Float map
A simple map function that uses templates, so it works with integer (like normal 'map' function), float, double, or any other comparable type.
```c++
Interpolation::Map<float>(2.0, 0.0, 10, 100, 200)
```
### Range generator
A simple utility that generates static double arrays with fixed size, and values between 'min' and 'max'. Useful for fast generating
homogeneously distributed X-values arrays to use as parameter in the interpolations methods.
```c++
double* ptr = Range<size>::Generate(min, max);
```

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/***************************************************
Copyright (c) 2019 Luis Llamas
(www.luisllamas.es)
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License
****************************************************/
#include "InterpolationLib.h"
const int numValues = 10;
double xValues[10] = { 5, 12, 30, 50, 60, 70, 74, 84, 92, 100 };
double yValues[10] = { 150, 200, 200, 200, 180, 100, 100, 150, 220, 320 };
void setup()
{
while (!Serial) { ; }
Serial.begin(115200);
for (float xValue = 0; xValue <= 110; xValue += .25)
{
Serial.print(Interpolation::Step(xValues, yValues, numValues, xValue, 0.0));
Serial.print(',');
Serial.print(Interpolation::Step(xValues, yValues, numValues, xValue, 0.5));
Serial.print(',');
Serial.print(Interpolation::Step(xValues, yValues, numValues, xValue, 1.0));
Serial.print(',');
Serial.print(Interpolation::SmoothStep(xValues, yValues, numValues, xValue));
Serial.print(',');
Serial.print(Interpolation::Linear(xValues, yValues, numValues, xValue, false));
Serial.print(',');
Serial.print(Interpolation::Linear(xValues, yValues, numValues, xValue, true));
Serial.print(',');
Serial.print(Interpolation::CatmullSpline(xValues, yValues, numValues, xValue));
Serial.print(',');
Serial.println(Interpolation::ConstrainedSpline(xValues, yValues, numValues, xValue));
}
}
void loop()
{
}

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/***************************************************
Copyright (c) 2019 Luis Llamas
(www.luisllamas.es)
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License
****************************************************/
#include "InterpolationLib.h"
void setup()
{
while (!Serial) { ; }
Serial.begin(115200);
Serial.print(Interpolation::Map<float>(2.0, 0.0, 10, 100, 200));
}
void loop()
{
}

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/***************************************************
Copyright (c) 2019 Luis Llamas
(www.luisllamas.es)
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License
****************************************************/
#include "InterpolationLib.h"
void setup()
{
while (!Serial) { ; }
Serial.begin(115200);
double* ptr = Range<10>::Generate(3, 4);
for (auto i = 0; i < 10; i++)
{
Serial.println(ptr[i]);
}
}
void loop()
{
}

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#######################################
# Syntax Coloring Map MyName
#######################################
#######################################
# Datatypes (KEYWORD1)
#######################################
Interpolation KEYWORD1
#######################################
# Methods and Functions (KEYWORD2)
#######################################
function KEYWORD2
Step KEYWORD2
SmoothStep KEYWORD2
Linear KEYWORD2
CatmullSpline KEYWORD2
ConstrainedSpline KEYWORD2
#######################################
# Constants (LITERAL1)
#######################################

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name=InterpolationLib
version=1.0.2
author=Luis Llamas
maintainer=Luis Llamas
sentence=Arduino library that provides interpolation methods step, linear, smooth, catmull spline and constrained spline.
paragraph=Arduino library that provides interpolation methods step, linear, smooth, catmull spline and constrained spline.
category=Other
url=https://github.com/luisllamasbinaburo/Arduino-Interpolation
architectures=*

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/***************************************************
Copyright (c) 2019 Luis Llamas
(www.luisllamas.es)
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License
****************************************************/
#include "InterpolationLib.h"
double Interpolation::Step(double xValues[], double yValues[], int numValues, double pointX, double threshold)
{
// extremos
if (pointX <= xValues[0]) return yValues[0];
if (pointX >= xValues[numValues - 1]) return yValues[numValues - 1];
auto i = 0;
while (pointX >= xValues[i + 1]) i++;
if (pointX == xValues[i + 1]) return yValues[i + 1]; // coincidencia exacta
auto t = (pointX - xValues[i]) / (xValues[i + 1] - xValues[i]); // punto relativo en el intervalo
return t < threshold ? yValues[i] : yValues[i + 1];
}
double Interpolation::Linear(double xValues[], double yValues[], int numValues, double pointX, bool trim)
{
if (trim)
{
if (pointX <= xValues[0]) return yValues[0];
if (pointX >= xValues[numValues - 1]) return yValues[numValues - 1];
}
auto i = 0;
double rst = 0;
if (pointX <= xValues[0])
{
i = 0;
auto t = (pointX - xValues[i]) / (xValues[i + 1] - xValues[i]);
rst = yValues[i] * (1 - t) + yValues[i + 1] * t;
}
else if (pointX >= xValues[numValues - 1])
{
auto t = (pointX - xValues[numValues - 2]) / (xValues[numValues - 1] - xValues[numValues - 2]);
rst = yValues[numValues - 2] * (1 - t) + yValues[numValues - 1] * t;
}
else
{
while (pointX >= xValues[i + 1]) i++;
auto t = (pointX - xValues[i]) / (xValues[i + 1] - xValues[i]);
rst = yValues[i] * (1 - t) + yValues[i + 1] * t;
}
return rst;
}
double Interpolation::SmoothStep(double xValues[], double yValues[], int numValues, double pointX, bool trim)
{
if (trim)
{
if (pointX <= xValues[0]) return yValues[0];
if (pointX >= xValues[numValues - 1]) return yValues[numValues - 1];
}
auto i = 0;
if (pointX <= xValues[0]) i = 0;
else if (pointX >= xValues[numValues - 1]) i = numValues - 1;
else while (pointX >= xValues[i + 1]) i++;
if (pointX == xValues[i + 1]) return yValues[i + 1];
auto t = (pointX - xValues[i]) / (xValues[i + 1] - xValues[i]);
t = t * t * (3 - 2 * t);
return yValues[i] * (1 - t) + yValues[i + 1] * t;
}
// double Interpolation::CatmullSpline(double xValues[], double yValues[], int numValues, double pointX, bool trim);
// double Interpolation::CatmullSpline(double xValues[], double yValues[], int numValues, double pointX, bool trim)
// {
// if (trim)
// {
// if (pointX <= xValues[0]) return yValues[0];
// if (pointX >= xValues[numValues - 1]) return yValues[numValues - 1];
// }
// auto i = 0;
// if (pointX <= xValues[0]) i = 0;
// else if (pointX >= xValues[numValues - 1]) i = numValues - 1;
// else while (pointX >= xValues[i + 1]) i++;
// if (pointX == xValues[i + 1]) return yValues[i + 1];
// auto t = (pointX - xValues[i]) / (xValues[i + 1] - xValues[i]);
// auto t_2 = t * t;
// auto t_3 = t_2 * t;
// auto h00 = 2 * t_3 - 3 * t_2 + 1;
// auto h10 = t_3 - 2 * t_2 + t;
// auto h01 = 3 * t_2 - 2 * t_3;
// auto h11 = t_3 - t_2;
// auto x0 = xValues[i];
// auto x1 = xValues[i + 1];
// auto y0 = yValues[i];
// auto y1 = yValues[i + 1];
// double m0;
// double m1;
// if (i == 0)
// {
// m0 = (yValues[1] - yValues[0]) / (xValues[1] - xValues[0]);
// m1 = (yValues[2] - yValues[0]) / (xValues[2] - xValues[0]);
// }
// else if (i == numValues - 2)
// {
// m0 = (yValues[numValues - 1] - yValues[numValues - 3]) / (xValues[numValues - 1] - xValues[numValues - 3]);
// m1 = (yValues[numValues - 1] - yValues[numValues - 2]) / (xValues[numValues - 1] - xValues[numValues - 2]);
// }
// else
// {
// m0 = catmullSlope(xValues, yValues, numValues, i);
// m1 = catmullSlope(xValues, yValues, numValues, i + 1);
// }
// auto rst = h00 * y0 + h01 * y1 + h10 * (x1 - x0) * m0 + h11 * (x1 - x0) * m1;
// return rst;
// }
float Interpolation::CatmullSpline(float xValues[], float yValues[], int numValues, float pointX, bool trim)
{
if (trim)
{
if (pointX <= xValues[0]) return yValues[0];
if (pointX >= xValues[numValues - 1]) return yValues[numValues - 1];
}
auto i = 0;
if (pointX <= xValues[0]) i = 0;
else if (pointX >= xValues[numValues - 1]) i = numValues - 1;
else while (pointX >= xValues[i + 1]) i++;
if (pointX == xValues[i + 1]) return yValues[i + 1];
auto t = (pointX - xValues[i]) / (xValues[i + 1] - xValues[i]);
auto t_2 = t * t;
auto t_3 = t_2 * t;
auto h00 = 2 * t_3 - 3 * t_2 + 1;
auto h10 = t_3 - 2 * t_2 + t;
auto h01 = 3 * t_2 - 2 * t_3;
auto h11 = t_3 - t_2;
auto x0 = xValues[i];
auto x1 = xValues[i + 1];
auto y0 = yValues[i];
auto y1 = yValues[i + 1];
double m0;
double m1;
if (i == 0)
{
m0 = (yValues[1] - yValues[0]) / (xValues[1] - xValues[0]);
m1 = (yValues[2] - yValues[0]) / (xValues[2] - xValues[0]);
}
else if (i == numValues - 2)
{
m0 = (yValues[numValues - 1] - yValues[numValues - 3]) / (xValues[numValues - 1] - xValues[numValues - 3]);
m1 = (yValues[numValues - 1] - yValues[numValues - 2]) / (xValues[numValues - 1] - xValues[numValues - 2]);
}
else
{
m0 = catmullSlope(xValues, yValues, numValues, i);
m1 = catmullSlope(xValues, yValues, numValues, i + 1);
}
auto rst = h00 * y0 + h01 * y1 + h10 * (x1 - x0) * m0 + h11 * (x1 - x0) * m1;
return rst;
}
double Interpolation::catmullSlope(float x[], float y[], int n, int i)
{
if (x[i + 1] == x[i - 1]) return 0;
return (y[i + 1] - y[i - 1]) / (x[i + 1] - x[i - 1]);
}
// double Interpolation::catmullSlope(double x[], double y[], int n, int i)
// {
// if (x[i + 1] == x[i - 1]) return 0;
// return (y[i + 1] - y[i - 1]) / (x[i + 1] - x[i - 1]);
// }
double Interpolation::ConstrainedSpline(double xValues[], double yValues[], int numValues, double pointX, bool trim)
{
if (trim)
{
if (pointX <= xValues[0]) return yValues[0];
if (pointX >= xValues[numValues - 1]) return yValues[numValues - 1];
}
//auto i = 0;
//while (pointX >= xValues[i + 1]) i++;
//if (pointX == xValues[i + 1]) return yValues[i + 1];
auto i = 0;
if (pointX <= xValues[0]) i = 0;
else if (pointX >= xValues[numValues - 1]) i = numValues - 1;
else while (pointX >= xValues[i + 1]) i++;
if (pointX == xValues[i + 1]) return yValues[i + 1];
auto x0 = xValues[i + 1];
auto x1 = xValues[i];
auto y0 = yValues[i + 1];
auto y1 = yValues[i];
auto fd2i_xl1 = getLeftSecondDerivate(xValues, yValues, numValues - 1, i + 1);
auto fd2i_x = getRightSecondDerivate(xValues, yValues, numValues - 1, i + 1);
auto d = (fd2i_x - fd2i_xl1) / (6.0f * (x0 - x1));
auto c = (x0 * fd2i_xl1 - x1 * fd2i_x) / 2.0f / (x0 - x1);
auto b = (y0 - y1 - c * (x0 * x0 - x1 * x1) - d * (x0 * x0 * x0 - x1 * x1 * x1)) / (x0 - x1);
auto a = y1 - b * x1 - c * x1 * x1 - d * x1 * x1 * x1;
auto rst = a + pointX * (b + pointX * (c + pointX * d));
return rst;
}
double Interpolation::getFirstDerivate(double x[], double y[], int n, int i)
{
double fd1_x;
if (i == 0)
{
fd1_x = 3.0f / 2.0f * (y[1] - y[0]) / (x[1] - x[0]);
fd1_x -= getFirstDerivate(x, y, n, 1) / 2.0f;
}
else if (i == n)
{
fd1_x = 3.0f / 2.0f * (y[n] - y[n - 1]) / (x[n] - x[n - 1]);
fd1_x -= getFirstDerivate(x, y, n, n - 1) / 2.0f;
}
else
{
if ((x[i + 1] - x[i]) / (y[i + 1] - y[i]) * (x[i] - x[i - 1]) / (y[i] - y[i - 1]) < 0)
{
fd1_x = 0;
}
else
{
fd1_x = 2.0f / ((x[i + 1] - x[i]) / (y[i + 1] - y[i]) + (x[i] - x[i - 1]) / (y[i] - y[i - 1]));
}
}
return fd1_x;
}
double Interpolation::getLeftSecondDerivate(double x[], double y[], int n, int i)
{
auto fdi_x = getFirstDerivate(x, y, n, i);
auto fdi_xl1 = getFirstDerivate(x, y, n, i - 1);
auto fd2l_x = -2.0f * (fdi_x + 2.0f * fdi_xl1) / (x[i] - x[i - 1]);
fd2l_x += 6.0f * (y[i] - y[i - 1]) / (x[i] - x[i - 1]) / (x[i] - x[i - 1]);
return fd2l_x;
}
double Interpolation::getRightSecondDerivate(double x[], double y[], int numValues, int i)
{
auto fdi_x = getFirstDerivate(x, y, numValues, i);
auto fdi_xl1 = getFirstDerivate(x, y, numValues, i - 1);
auto fd2r_x = 2.0f * (2.0f * fdi_x + fdi_xl1) / (x[i] - x[i - 1]);
fd2r_x -= 6.0f * (y[i] - y[i - 1]) / (x[i] - x[i - 1]) / (x[i] - x[i - 1]);
return fd2r_x;
}

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/***************************************************
Copyright (c) 2019 Luis Llamas
(www.luisllamas.es)
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License
****************************************************/
#ifndef _INTERPOLATIONLIB_h
#define _INTERPOLATIONLIB_h
#if defined(ARDUINO) && ARDUINO >= 100
#include "Arduino.h"
#else
#include "WProgram.h"
#endif
template<size_t n>
struct Range
{
double list[n];
Range()
{
for (size_t m = 0; m != n; ++m)
{
list[m] = m + 1;
}
}
Range(double min, double max)
{
for (size_t m = 0; m < n; ++m)
{
list[m] = min + (max - min) / (n - 1) * m;
}
}
double& operator[](size_t index)
{
return list[index];
}
double* ToArray()
{
return list;
}
static double* Generate(double min, double max)
{
Range<10> range(min, max);
return range.ToArray();
}
};
class Interpolation
{
public:
template <typename T>
static T Map(T x, T in_min, T in_max, T out_min, T out_max);
static double Step(double yValues[], int numValues, double pointX, double threshold = 1);
static double Step(double minX, double maxX, double yValues[], int numValues, double pointX, double threshold = 1);
static double Step(double xValues[], double yValues[], int numValues, double pointX, double threshold = 1);
static double Linear(double yValues[], int numValues, double pointX, bool trim = true);
static double Linear(double minX, double maxX, double yValues[], int numValues, double pointX, bool trim = true);
static double Linear(double xValues[], double yValues[], int numValues, double pointX, bool trim = true);
static double SmoothStep(double xValues[], double yValues[], int numValues, double pointX, bool trim = true);
// static double CatmullSpline(double xValues[], double yValues[], int numValues, double pointX, bool trim = true);
static double ConstrainedSpline(double xValues[], double yValues[], int numValues, double pointX, bool trim = true);
static float CatmullSpline(float xValues[], float yValues[], int numValues, float pointX, bool trim = true);///////////////////////////
private:
// static double catmullSlope(double x[], double y[], int n, int i);
static double catmullSlope(float x[], float y[], int n, int i);///////////////////////////
static double getFirstDerivate(double x[], double y[], int n, int i);
static double getLeftSecondDerivate(double x[], double y[], int n, int i);
static double getRightSecondDerivate(double x[], double y[], int n, int i);
};
// Esto esta aqui porque Arduino la lia con los Templates
template <typename T>
T Interpolation::Map(T x, T in_min, T in_max, T out_min, T out_max)
{
return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}
#endif