Replaced spline interpolation with interpolation from https://github.com/tuxcell/interpolationArduino
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/*
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* interpolation.h |
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* |
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* interpolation - An interpolation library for Arduino. |
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* Author: Jose Gama 2015 |
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* |
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* This library is free software; you can redistribute it |
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* and/or modify it under the terms of the GNU Lesser |
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* General Public License as published by the Free Software |
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* Foundation; either version 3 of the License, or (at |
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* your option) any later version. |
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* |
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* This library is distributed in the hope that it will |
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* be useful, but WITHOUT ANY WARRANTY; without even the |
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* implied warranty of MERCHANTABILITY or FITNESS FOR A |
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* PARTICULAR PURPOSE. See the GNU Lesser General Public |
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* License for more details. |
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* |
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* You should have received a copy of the GNU Lesser |
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* General Public License along with this library; if not, |
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* write to the Free Software Foundation, Inc., |
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* 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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* |
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*/ |
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/*
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* From: https://github.com/tuxcell/interpolationArduino
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* replaced all doubles by float (wirtz@parasitstudio.de) |
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*/ |
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#include "interpolation.h" |
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interpolation::interpolation(void) { |
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_valInterp = 0; |
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_lenXY = 0; |
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} |
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interpolation::interpolation( float x[], float y[], int lenXY){ |
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_x = x;_y = y;_lenXY = lenXY; |
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_valInterp = 0; |
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} |
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interpolation::interpolation( float x[], float y[], int lenXY, float valInterp){ |
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_x = x;_y = y;_lenXY = lenXY; |
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_valInterp = valInterp; |
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} |
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void interpolation::valueI( float valInterp ) { |
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_valInterp = valInterp; |
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} |
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void interpolation::valuelenXY( int lenXY ) { |
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_lenXY = lenXY; |
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} |
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void interpolation::valueX( float x[]) { |
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_x = x; |
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} |
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void interpolation::valueY( float y[]) { |
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_y = y; |
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} |
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void interpolation::valueXM( float XM[]) { |
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_XM = XM; |
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} |
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void interpolation::valueZ( float Z[]) { |
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_Z = Z; |
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} |
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float interpolation::LinearInterpolate() {return(LinearInterp( _x, _y, _lenXY, _valInterp));} |
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float interpolation::CosineInterpolate() {return(CosineInterp( _x, _y, _lenXY, _valInterp));} |
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float interpolation::CubicInterpolate() {return(CubicInterp( _x, _y, _lenXY, _valInterp));} |
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float interpolation::LagrangeInterpolate() {return(LagrangeInterp( _x, _y, _lenXY, _valInterp));} |
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float interpolation::QuadraticInterpolate() {return(QuadraticInterp( _x, _y, _lenXY, _valInterp));} |
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float interpolation::AkimaInterpolate() {return(AkimaInterp( _x, _y, _XM, _Z, _lenXY, _valInterp));} |
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float interpolation::LinearInterp( float* x, float* y, int n, float p ) |
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{ |
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//http://paulbourke.net/miscellaneous/interpolation/
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int i; |
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float mu; |
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for( i = 0; i < n-1; i++ ) |
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{ |
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if (( x[i] <= p && x[i+1] >= p )||( x[i] >= p && x[i+1] <= p )) |
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{ |
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mu=(p - x[i])/(x[i] - x[i+1]); |
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if (mu<0) mu=-mu; |
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return(y[i]*(1-mu)+y[i+1]*mu); |
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} |
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} |
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return 0; // Not in Range
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} |
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float interpolation::CosineInterp (float* x, float* y, int n, float p ) |
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{ |
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int i; |
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float mu, mu2; |
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for( i = 0; i < n-1; i++ ) |
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{ |
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if (( x[i] <= p && x[i+1] >= p )||( x[i] >= p && x[i+1] <= p )) |
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{ |
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mu=(p - x[i])/(x[i] - x[i+1]); |
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if (mu<0) mu=-mu; |
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mu2 = (1.0-cos(3.1415926535897*mu))/2.0; |
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return(y[i]*(1.0-mu2)+y[i+1]*mu2); |
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} |
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} |
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return 0; // Not in Range
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} |
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float interpolation::CubicInterp(float* x, float* y, int n, float p ) |
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{ |
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int i; |
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float a0,a1,a2,a3,mu, mu2; |
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for( i = 0; i < n-1; i++ ) |
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{ |
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if (( x[i] <= p && x[i+1] >= p )||( x[i] >= p && x[i+1] <= p )) |
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{ |
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mu=(p - x[i])/(x[i] - x[i+1]); |
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if (mu<0) mu=-mu; |
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mu2 = mu*mu; |
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a0 = y[i+2] - y[i+1] - y[i-1] + y[i]; |
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a1 = y[i-1] - y[i] - a0; |
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a2 = y[i+1] - y[i-1]; |
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a3 = y[i]; |
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return(a0*mu*mu2+a1*mu2+a2*mu+a3); |
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} |
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} |
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return 0; // Not in Range
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} |
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float interpolation::LagrangeInterp( float* x, float* y, int n, float p ) |
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{ |
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//http://www.dailyfreecode.com/code/lagranges-interpolation-method-finding-2376.aspx
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int i, j, k; |
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float t, r=0; |
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for(i=0;i<n;i++) |
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{ |
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t = 1; |
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k = i; |
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for(j=0;j<n;j++) |
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{ |
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if(k==j) |
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{ |
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continue; |
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} |
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else |
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{ |
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t = t * ((p-x[j])/(x[k]-x[j])); |
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} |
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} |
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r+=y[i]*t; |
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} |
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return r; // Not in Range
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} |
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float interpolation::QuadraticInterp(float* x, float* y, int n, float p ) |
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{ |
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//view-source:http://www.johndcook.com/quadratic_interpolator.html
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int i; |
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float xi2, k; |
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for( i = 0; i < n-1; i++ ) |
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{ |
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if (( x[i] <= p && x[i+1] >= p )||( x[i] >= p && x[i+1] <= p )) |
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{ |
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if (i<(n-3)) xi2=x[i+2]; else xi2=0; |
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k = y[i]*(p - x[i+1])*(p - xi2)/((x[i] - x[i+1])*(x[i] - xi2)); |
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k += y[i+1]*(p - x[i])*(p - xi2)/((x[i+1] - x[i])*(x[i+1] - xi2)); |
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k += y[i+2]*(p - x[i])*(p - x[i+1])/((xi2 - x[i])*(xi2 - x[i+1])); |
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return(k); |
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} |
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} |
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return 0; // Not in Range
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} |
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float interpolation::AkimaInterp( float* x, float* y, float* XM, float* Z, int n, float p ) { |
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//http://jean-pierre.moreau.pagesperso-orange.fr/Cplus/akima_cpp.txt
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int i; |
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float a,b,r; |
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//special case p=0
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if (p==0.0) { |
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return(0); |
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} |
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//Check to see if interpolation point is correct
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if (p<x[1] || p>=x[n-3]) { |
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return(-330); |
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} |
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x[0]=2.0*x[1]-x[2]; |
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//Calculate Akima coefficients, a and b
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for (i=1; i<n; i++) |
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//Shift i to i+2
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XM[i+2]=(y[i+1]-y[i])/(x[i+1]-x[i]); |
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XM[n+2]=2.0*XM[n+1]-XM[n]; |
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XM[n+3]=2.0*XM[n+2]-XM[n+1]; |
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XM[2]=2.0*XM[3]-XM[4]; |
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XM[1]=2.0*XM[2]-XM[3]; |
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for (i=1; i<n+1; i++) { |
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a=fabs(XM[i+3]-XM[i+2]); |
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b=fabs(XM[i+1]-XM[i]); |
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if (a+b==0) Z[i]=(a*XM[i+1]+b*XM[i+2])/(a+b); else Z[i]=(XM[i+2]+XM[i+1])/2.0; |
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} |
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//Find relevant table interval
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i=0; |
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while (p>x[i]) i++; |
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i--; |
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//Begin interpolation
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b=x[i+1]-x[i]; |
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a=p-x[i]; |
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r=y[i]+Z[i]*a+(3.0*XM[i+2]-2.0*Z[i]-Z[i+1])*a*a/b; |
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r=r+(Z[i]+Z[i+1]-2.0*XM[i+2])*a*a*a/(b*b); |
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return(r); |
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} |
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@ -0,0 +1,79 @@ |
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/*
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* interpolation.h |
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* |
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* interpolation - An interpolation library for Arduino. |
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* Author: Jose Gama 2015 |
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* |
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* This library is free software; you can redistribute it |
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* and/or modify it under the terms of the GNU Lesser |
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* General Public License as published by the Free Software |
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* Foundation; either version 3 of the License, or (at |
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* your option) any later version. |
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* |
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* This library is distributed in the hope that it will |
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* be useful, but WITHOUT ANY WARRANTY; without even the |
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* implied warranty of MERCHANTABILITY or FITNESS FOR A |
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* PARTICULAR PURPOSE. See the GNU Lesser General Public |
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* License for more details. |
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* |
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* You should have received a copy of the GNU Lesser |
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* General Public License along with this library; if not, |
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* write to the Free Software Foundation, Inc., |
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* 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA |
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* |
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*/ |
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/*
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* From: https://github.com/tuxcell/interpolationArduino
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* replaced all doubles by float (wirtz@parasitstudio.de) |
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*/ |
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#ifndef interpolation_h |
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#define interpolation_h |
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#if defined(ARDUINO) && ARDUINO >= 100 |
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#include <Arduino.h> |
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#else |
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#include <WProgram.h> |
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#endif |
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class interpolation |
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{ |
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public: |
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// constructor
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interpolation( void ); |
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interpolation( float x[], float y[], int lenXY); |
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interpolation( float x[], float y[], int lenXY, float valInterp); |
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void valueI( float valInterp ); |
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void valuelenXY( int lenXY ); |
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void valueX( float x[]); |
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void valueY( float y[]); |
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void valueXM( float XM[]); |
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void valueZ( float Z[]); |
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float LinearInterpolate(); |
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float CosineInterpolate(); |
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float CubicInterpolate(); |
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float LagrangeInterpolate(); |
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float QuadraticInterpolate(); |
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float AkimaInterpolate(); |
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private: |
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float* _x; |
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float* _y; |
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float* _XM; |
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float* _Z; |
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int _lenXY; |
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float _valInterp; |
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float LinearInterp( float x[], float y[], int n, float p ); |
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float CosineInterp( float x[], float y[], int n, float p ); |
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float CubicInterp( float x[], float y[], int n, float p ); |
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float LagrangeInterp( float x[], float y[], int n, float p ); |
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float QuadraticInterp( float x[], float y[], int n, float p ); |
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float AkimaInterp( float x[], float y[], float XM[], float Z[], int n, float p ); |
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}; |
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#endif |
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@ -1,124 +0,0 @@ |
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/*
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From: https://raw.githubusercontent.com/kerinin/arduino-splines
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*/ |
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#include "Arduino.h" |
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#include "spline.h" |
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#include <math.h> |
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Spline::Spline(void) { |
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_prev_point = 0; |
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} |
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Spline::Spline( float x[], float y[], int numPoints, int degree ) |
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{ |
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setPoints(x, y, numPoints); |
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setDegree(degree); |
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_prev_point = 0; |
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} |
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Spline::Spline( float x[], float y[], float m[], int numPoints ) |
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{ |
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setPoints(x, y, m, numPoints); |
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setDegree(Hermite); |
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_prev_point = 0; |
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} |
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void Spline::setPoints( float x[], float y[], int numPoints ) { |
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_x = x; |
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_y = y; |
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_length = numPoints; |
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} |
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void Spline::setPoints( float x[], float y[], float m[], int numPoints ) { |
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_x = x; |
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_y = y; |
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_m = m; |
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_length = numPoints; |
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} |
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void Spline::setDegree( int degree ) { |
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_degree = degree; |
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} |
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float Spline::value( float x ) |
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{ |
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if ( _x[0] > x ) { |
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return _y[0]; |
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} |
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else if ( _x[_length - 1] < x ) { |
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return _y[_length - 1]; |
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} |
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else { |
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for (int i = 0; i < _length; i++ ) |
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{ |
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int index = ( i + _prev_point ) % _length; |
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if ( _x[index] == x ) { |
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_prev_point = index; |
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return _y[index]; |
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} else if ( (_x[index] < x) && (x < _x[index + 1]) ) { |
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_prev_point = index; |
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return calc( x, index ); |
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} |
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} |
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} |
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return (0.0); |
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} |
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float Spline::calc( float x, int i ) |
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{ |
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switch ( _degree ) { |
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case 0: |
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return _y[i]; |
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case 1: |
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if ( _x[i] == _x[i + 1] ) { |
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// Avoids division by 0
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return _y[i]; |
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} else { |
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return _y[i] + (_y[i + 1] - _y[i]) * ( x - _x[i]) / ( _x[i + 1] - _x[i] ); |
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} |
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case Hermite: |
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return hermite( ((x - _x[i]) / (_x[i + 1] - _x[i])), _y[i], _y[i + 1], _m[i], _m[i + 1], _x[i], _x[i + 1] ); |
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case Catmull: |
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if ( i == 0 ) { |
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// x prior to spline start - first point used to determine tangent
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return _y[1]; |
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} else if ( i == _length - 2 ) { |
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// x after spline end - last point used to determine tangent
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return _y[_length - 2]; |
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} else { |
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float t = (x - _x[i]) / (_x[i + 1] - _x[i]); |
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float m0 = (i == 0 ? 0 : catmull_tangent(i) ); |
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float m1 = (i == _length - 1 ? 0 : catmull_tangent(i + 1) ); |
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return hermite( t, _y[i], _y[i + 1], m0, m1, _x[i], _x[i + 1]); |
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} |
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} |
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return(0.0); |
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} |
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float Spline::hermite( float t, float p0, float p1, float m0, float m1, float x0, float x1 ) { |
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return (hermite_00(t) * p0) + (hermite_10(t) * (x1 - x0) * m0) + (hermite_01(t) * p1) + (hermite_11(t) * (x1 - x0) * m1); |
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} |
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float Spline::hermite_00( float t ) { |
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return (2 * pow(t, 3)) - (3 * pow(t, 2)) + 1; |
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} |
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float Spline::hermite_10( float t ) { |
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return pow(t, 3) - (2 * pow(t, 2)) + t; |
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} |
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float Spline::hermite_01( float t ) { |
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return (3 * pow(t, 2)) - (2 * pow(t, 3)); |
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} |
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float Spline::hermite_11( float t ) { |
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return pow(t, 3) - pow(t, 2); |
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} |
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float Spline::catmull_tangent( int i ) |
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{ |
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if ( _x[i + 1] == _x[i - 1] ) { |
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// Avoids division by 0
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return 0; |
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} else { |
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return (_y[i + 1] - _y[i - 1]) / (_x[i + 1] - _x[i - 1]); |
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} |
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} |
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@ -1,45 +0,0 @@ |
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/*
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From: https://github.com/kerinin/arduino-splines
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Library for 1-d splines |
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Copyright Ryan Michael |
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Licensed under the LGPLv3 |
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*/ |
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#ifndef spline_h |
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#define spline_h |
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#include "Arduino.h" |
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#define Hermite 10 |
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#define Catmull 11 |
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class Spline |
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{ |
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public: |
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Spline( void ); |
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Spline( float x[], float y[], int numPoints, int degree = 1 ); |
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Spline( float x[], float y[], float m[], int numPoints ); |
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float value( float x ); |
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void setPoints( float x[], float y[], int numPoints ); |
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void setPoints( float x[], float y[], float m[], int numPoints ); |
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void setDegree( int degree ); |
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private: |
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float calc( float, int); |
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float* _x; |
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float* _y; |
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float* _m; |
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int _degree; |
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int _length; |
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int _prev_point; |
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float hermite( float t, float p0, float p1, float m0, float m1, float x0, float x1 ); |
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float hermite_00( float t ); |
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float hermite_10( float t ); |
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float hermite_01( float t ); |
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float hermite_11( float t ); |
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float catmull_tangent( int i ); |
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}; |
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#endif |
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