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196 lines
6.3 KiB
Markdown
196 lines
6.3 KiB
Markdown
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[](https://github.com/marketplace/actions/arduino_ci)
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[](https://github.com/RobTillaart/AverageAngle/actions/workflows/arduino-lint.yml)
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[](https://github.com/RobTillaart/AverageAngle/actions/workflows/jsoncheck.yml)
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[](https://github.com/RobTillaart/AverageAngle/blob/master/LICENSE)
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[](https://github.com/RobTillaart/AverageAngle/releases)
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# AverageAngle
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Arduino library to calculate correctly the average of multiple angles.
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## Description
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AverageAngle is a class to calculate the average of angles.
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This is especially useful when angles are around 0 degrees,
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e.g. from a compass sensor or the resultant of a track.
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Example, the average angle of 359 and 1 is 0, not 179 (most of the time)
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Furthermore the AverageAngle can also include the **length (weight)** of the angle as if it is a vector.
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Default this length is set to 1 so all angles are by default of equal weight.
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Example: The average angle of 359 (length = 2) and 1 (length = 1) is 359.something not zero.
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The average angle is calculated by converting the added angle (in DEGREES, etc) to polar coordinates.
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These (x,y) are added to a (sumX, sumY) and divided by the number of angles added so far.
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#### Related
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- https://github.com/RobTillaart/Angle
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- https://github.com/RobTillaart/AngleConvertor
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- https://github.com/RobTillaart/AverageAngle
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- https://github.com/RobTillaart/runningAngle
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#### AngleType
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- **enum AngleType { DEGREES, RADIANS, GRADIANS }** idem.
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| value | name | range |
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|:-------:|:-----------|:-----------|
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| 0 | DEGREES | 0 .. 360 |
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| 1 | RADIANS | 0 .. 2PI |
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| 2 | GRADIANS | 0 .. 400 | 100 GRADIANS == 90 DEGREES.
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## Interface
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```cpp
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#include "AverageAngle.h"
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```
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#### Constructor
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- **AverageAngle(AngleType type = DEGREES)** constructor, defaults to degrees.
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- **AngleType type()** returns DEGREES, RADIANS or GRADIANS.
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- **void setType(AngleType type)** changes type DEGREES, RADIANS or GRADIANS.
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Type can be changed run time and still continue to add.
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- **void reset()** clears internal counters.
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#### Core
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- **uint32_t add(float alpha, float length = 1.0)** add a new angle,
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optional with length other than 1.
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Returns the number of elements (count).
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If the internal sumx or sumy is >= 10000, the error **AVERAGE_ANGLE_OVERFLOW** is set.
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This indicates that the internal math is near or over its accuracy limits.
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- **uint32_t count()** the number of angles added.
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If count == 0, there is no average.
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- **float getAverage()** returns the average, unless count == 0
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or the internal sums == (0,0) in which case we have a singularity ==> NAN (not a number)
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If NAN the error **AVERAGE_ANGLE_SINGULARITY** is set.
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- **float getTotalLength()** the length of the resulting 'angle' when we see them as vectors.
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If count == 0 ==> total length = 0.
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- **float getAverageLength()** returns the average length of the angles added.
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If count == 0 ==> average length = 0.
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#### Error handling
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- **int lastError()** return the last error detected.
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| name | value |
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|:----------------------------|:-------:|
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| AVERAGE_ANGLE_OK | 0 |
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| AVERAGE_ANGLE_OVERFLOW | -10 |
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| AVERAGE_ANGLE_SINGULARITY | -20 |
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#### Experimental Overflow
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(since 0.2.0)
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When the internal sumx or sumy is large (> 10000) the accuracy of the addition
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becomes critical, leading to serious errors in the average and length functions.
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To detect this the function **add()** sets the error **AVERAGE_ANGLE_OVERFLOW**.
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This error can be checked with **lastError()**.
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The function **add()** will add the new angle as good as possible.
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Note this condition is independent of the **AngleType** as the internal math
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uses radians. The condition will be triggered faster when the length parameter
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is used.
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The overflow threshold of 10000 can be patched in the .cpp file if needed.
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As this feature is **experimental**, the trigger condition for overflow will
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probably be redesigned in the future. See future section below.
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## Gradians
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Gradians a.k.a. **gon**, is a less often used unit for angles.
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There are 100 gradians in a right angle. A full circle = 400 gradians.
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https://en.wikipedia.org/wiki/Gradian
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See also AngleConvertor library.
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## Operation
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If you want to average 5 compass readings you can just add the angles and
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do not use the length parameter.
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```cpp
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AA.reset();
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for (int i = 0; i < 5; i++)
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{
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AA.add(compass.readHeading());
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delay(100); // e.g. compass read needs some time
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}
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Serial.println(AA.getAverage());
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```
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If you want to average a track, e.g. 5 steps North, 3 steps west etc,
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you need to include the length of each step.
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```cpp
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AA.reset();
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AA.add(90, 5); // 5 steps north
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AA.add(180, 3); // 3 steps west
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Serial.println(AA.getAverage());
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Serial.println(AA.getTotalLength());
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```
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If you want to average an angle in DEGREES and an angle in RADIANS,
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just change the type runtime.
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```cpp
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AA.reset();
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AA.setType(DEGREES);
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AA.add(90);
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AA.setType(RADIANS);
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AA.add(PI/3);
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AA.setType(DEGREES);
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Serial.println(AA.getAverage());
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```
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## Future
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#### Must
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- investigate if and how the internal math can be made more robust against overflow.
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- use double iso float (will work on certain platforms) (must)
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- uint32_t?
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- accuracy threshold depends on float/double usage. (sizeof(double)==8)
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- threshold depends on the units of length.
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if all add's are using 10000 as length they have equal weight.
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normalizing the weight? how? user responsibility?
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- get set threshold via API?
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- use of threshold versus error detection (sum - angle == previous or not)
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- split OVERFLOW error in X and Y
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#### Should
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- add performance example
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- add overflow example
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- add singularity example
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#### Could
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- add a USER AngleType, in which the user can map 0..360 degrees to any range.
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- float userFactor = 1.0; (default)
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- can even be negative?
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- use cases? e.g 0..4 quadrant?
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- maybe better for the AngleConvertor class.
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#### Wont
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