Fixed issue causing NaN azimuth

[Nick806]

Fixed issue causing NaN azimuth when azimuth was close to 0-360 or 180

Description:

The issue causing the azimuth to return NaN when it was close to 0-360 or 180 has been fixed.

Example of the problem:

CODE:

#include <SunPosition.h>
#include "Arduino.h"

#define PRECISION 5

unsigned long int t = 1700000000;
float lat = 45;
float lon = 11;

float getSunElevation() {
  SunPosition sun(lat, lon, t);
  return sun.altitude();
}

float getSunAzimuth() {
  SunPosition sun(lat, lon, t);
  return sun.azimuth();
}

void setup() {
  Serial.begin(115200);
  while (!Serial) {}
}

void loop() {
  t++;

  if (isnan(getSunElevation()) || isnan(getSunAzimuth())){
    t--; 
    do{
      Serial.println("Time: " + String(t) + " - Ele: " + String(getSunElevation(), PRECISION) + " - Azi:" + String(getSunAzimuth(), PRECISION));
      t++;
    } while (isnan(getSunElevation()) || isnan(getSunAzimuth()));

    Serial.println("Time: " + String(t) + " - Ele: " + String(getSunElevation(), PRECISION) + " - Azi:" + String(getSunAzimuth(), PRECISION));
    Serial.println();
  }
}

SERIAL OUTPUT:

Time: 1700175624 - Ele: -63.18660 - Azi:359.93439
Time: 1700175625 - Ele: -63.18661 - Azi:    nan
Time: 1700175626 - Ele: -63.18661 - Azi:    nan
Time: 1700175627 - Ele: -63.18661 - Azi:    nan
Time: 1700175628 - Ele: -63.18661 - Azi:    nan
Time: 1700175629 - Ele: -63.18661 - Azi:    nan
Time: 1700175630 - Ele: -63.18661 - Azi:    nan
Time: 1700175631 - Ele: -63.18661 - Azi:    nan
Time: 1700175632 - Ele: -63.18661 - Azi:    nan
Time: 1700175633 - Ele: -63.18660 - Azi:0.06561

Time: 1700218835 - Ele: 26.55935 - Azi:180.00000
Time: 1700218836 - Ele: 26.55936 - Azi:    nan
Time: 1700218837 - Ele: 26.55936 - Azi:    nan
Time: 1700218838 - Ele: 26.55936 - Azi:    nan
Time: 1700218839 - Ele: 26.55936 - Azi:    nan
Time: 1700218840 - Ele: 26.55936 - Azi:    nan
Time: 1700218841 - Ele: 26.55936 - Azi:    nan
Time: 1700218842 - Ele: 26.55935 - Azi:180.00000

Time: 1700262034 - Ele: -63.44598 - Azi:359.94064
Time: 1700262035 - Ele: -63.44599 - Azi:    nan
Time: 1700262036 - Ele: -63.44599 - Azi:    nan
Time: 1700262037 - Ele: -63.44599 - Azi:    nan
Time: 1700262038 - Ele: -63.44599 - Azi:    nan
Time: 1700262039 - Ele: -63.44599 - Azi:    nan
Time: 1700262040 - Ele: -63.44599 - Azi:    nan
Time: 1700262041 - Ele: -63.44599 - Azi:    nan
Time: 1700262042 - Ele: -63.44599 - Azi:    nan
Time: 1700262043 - Ele: -63.44598 - Azi:0.05936

......

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How the issue was fixed:

The issue was in the following line of code:

azm = degrees(acos(((sin(lat) * cos(zen)) - sin(decl)) / (cos(lat) * sin(zen)))); // Azimuth

The acos() function accepts values only in the range of -1 to 1. Due to floating-point rounding errors, the expression ((sin(lat) * cos(zen)) - sin(decl)) / (cos(lat) * sin(zen)) could result in values slightly outside this range, which causes the acos() function to return NaN.

For example, in some cases, the calculation produced values slightly greater than 1 or slightly less than -1:

Unix:1700175628   Lat:45   Lon:11   ((sin(lat)*cos(zen))-sin(decl))/(cos(lat)*sin(zen)):-1.0000001192
Unix:1700218838   Lat:45   Lon:11   ((sin(lat)*cos(zen))-sin(decl))/(cos(lat)*sin(zen)):1.0000001192

Solution:
To address this issue, the calculation has been modified to clamp the result between -1 and 1 before passing it to acos(). This ensures that the value remains within the valid range for acos() and prevents it from returning NaN:

azm = degrees(acos(max(min(((sin(lat) * cos(zen)) - sin(decl)) / (cos(lat) * sin(zen)),-1),1))); // Azimuth

This adjustment prevents the expression from exceeding the allowable range for acos(), thereby eliminating the errors and returning valid azimuth values.

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