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111 lines
2.8 KiB
111 lines
2.8 KiB
// 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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