Holger Wirtz
5 years ago
parent
55b6718219
commit
6dd9bb923b
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// From: https://raw.githubusercontent.com/kerinin/arduino-splines/master/spline.cpp
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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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} |
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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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} |
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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 ) { return (2*pow(t,3)) - (3*pow(t,2)) + 1;} |
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float Spline::hermite_10( float t ) { return pow(t,3) - (2*pow(t,2)) + t; } |
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float Spline::hermite_01( float t ) { return (3*pow(t,2)) - (2*pow(t,3)); } |
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float Spline::hermite_11( float t ) { return pow(t,3) - pow(t,2); } |
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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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@ -1,43 +0,0 @@ |
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// From https://raw.githubusercontent.com/kerinin/arduino-splines/master/spline.h
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/*
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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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