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98 lines
1.7 KiB
C++
98 lines
1.7 KiB
C++
//
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// FILE: ellipse.cpp
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// AUTHOR: Rob Tillaart
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// DATE: 2021-10-31
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// VERSION: 0.1.0
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// PURPOSE: Arduino library for ellipse maths
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// URL: https://github.com/RobTillaart/ellipse
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// TRIGGER: https://www.youtube.com/watch?v=5nW3nJhBHL0
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//
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// HISTORY:
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// 0.1.0 2021-10-31 initial version
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#include "ellipse.h"
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ellipse::ellipse(float a, float b)
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{
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_a = abs(a);
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_b = abs(b);
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}
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//////////////////////////////////////////////////////////////////
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//
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// unknown - see youtube link.
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// p = 2 * PI * sqrt((a*a + b*b)/2);
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//
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float ellipse::circumference()
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{
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return perimeter_Ramanujan1();
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}
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float ellipse::perimeter_ref()
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{
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return perimeter_Ramanujan2();
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}
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float ellipse::perimeter_Keppler()
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{
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// Keppler
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float p = 2 * PI * (_a + _b) / 2; // very fast for a ~ b
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return p;
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}
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float ellipse::perimeter_Ramanujan1()
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{
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// Srinivasa Ramanujan I - very good
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// float p = PI * (3 * (_a + _b) - sqrt((3 * _a +_b)*(_a + 3 * _b)));
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float a3 = 3 * _a;
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float b3 = 3 * _b;
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float p = PI * (a3 + b3 - sqrt( (a3 + _b)*(_a + b3)));
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// one float operation less (~7% faster)
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return p;
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}
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float ellipse::perimeter_Ramanujan2()
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{
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// Srinivasa Ramanujan II - extremely good
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float x = _a - _b;
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float y = _a + _b;
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float h3 = 3 * (x * x) / (y * y);
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float p = PI * y * ( 1 + h3 / (10 + sqrt(4 - h3)));
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return p;
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}
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//////////////////////////////////////////////////////////
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float ellipse::area()
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{
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return PI * _a * _b;
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}
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float ellipse::eccentricity()
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{
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float x = _a * _a - _b * _b;
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if (x < 0) x = -1 * x;
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return sqrt(x)/ _a;
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}
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float ellipse::getC()
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{
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float e = eccentricity();
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if (_a > _b) return e * _a;
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return e * _b;
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}
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// -- END OF FILE --
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