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# ellipse

Arduino library with ellipse math


## Description

This experimental library provides basic ellipse math. 
It was written to test different perimeter algorithms.

Trigger was a video of Dr. Matt Parker.
 https://www.youtube.com/watch?v=5nW3nJhBHL0


## Interface

- **ellipse(float a, float b)** constructor, a >= b 
- **float area()** returns the area of the ellipse.
- **float circumference()** good algorithm (= Ramanujan 1).
- **float eccentricity()** return the eccentricity e. 
This is an indication of flatness of the ellipse. 0 is a circle 1 is flat line.
- **void  setA(float a)** change the long radius.
- **void  setB(float b)** change the short radius.
- **float getA()** return long radius of the ellipse.
- **float getB()** return short radius of the ellipse.
- **float getC()** distance to focus point form centre along the longer axis. 


#### Perimeter algorithms

- **float perimeter_ref()** slower but best known algorithm (Ramanujan 2)
- **float perimeter_Keppler()** good and fast algorithm for eccentricity between 1 and 2.
- **float perimeter_Ramanujan1()** good algorithm.
- **float perimeter_Ramanujan2()** slow but best known algorithm.

See performance example for differences in timing.


#### Misc

- **bool isCircle(float epsilon = 0.0)**  | a - b | < eps.
- **bool isFlat()** true if a > 4b, where a = longest radius.


#### Experimental

- **float angle()** returns the angle if the ellipse was the
shadow of a circle, Returns 0..90°, 0° == circle, 90° == line.


## Operation

See examples.


## Future

- make constructor symmetric (a < b or a > b ==> all possible.
- make other code symmetric.
- additional functions
  - Bresenham to draw ellipse?
- documentation
  - refer Wikipedia.