Step by Step solution about How to resolve the algorithm Angles (geometric), normalization and conversion step by step in the C programming language

The provided C code defines a set of functions to normalize and convert angles between different units of measurement: degrees, grads, mils, and radians.

1. Normalization Functions:

   • normalize2deg(double a): Normalizes an angle a to the range [0, 360) degrees.
   • normalize2grad(double a): Normalizes an angle a to the range [0, 400) grads.
   • normalize2mil(double a): Normalizes an angle a to the range [0, 6400) mils.
   • normalize2rad(double a): Normalizes an angle a to the range [0, 2π) radians.

2. Conversion Functions:

   • Degree Conversions:

     • deg2grad(double a): Converts an angle a from degrees to grads.
     • deg2mil(double a): Converts an angle a from degrees to mils.
     • deg2rad(double a): Converts an angle a from degrees to radians.

   • Grad Conversions:

     • grad2deg(double a): Converts an angle a from grads to degrees.
     • grad2mil(double a): Converts an angle a from grads to mils.
     • grad2rad(double a): Converts an angle a from grads to radians.

   • Mil Conversions:

     • mil2deg(double a): Converts an angle a from mils to degrees.
     • mil2grad(double a): Converts an angle a from mils to grads.
     • mil2rad(double a): Converts an angle a from mils to radians.

   • Radian Conversions:

     • rad2deg(double a): Converts an angle a from radians to degrees.
     • rad2grad(double a): Converts an angle a from radians to grads.
     • rad2mil(double a): Converts an angle a from radians to mils.

The code also defines constants for π and 2π.

Example Usage:

• To convert 60 degrees to radians: double rad = deg2rad(60);
• To normalize an angle of -170 degrees to the range [0, 360): double deg = normalize2deg(-170);

This code is a set of functions that convert angles from one unit of measurement to another. The functions are:

• normalize2deg: normalizes an angle to the range [0, 360) degrees.
• normalize2grad: normalizes an angle to the range [0, 400) grads.
• normalize2mil: normalizes an angle to the range [0, 6400) mils.
• normalize2rad: normalizes an angle to the range [0, 2π) radians.
• deg2grad: converts an angle from degrees to grads.
• deg2mil: converts an angle from degrees to mils.
• deg2rad: converts an angle from degrees to radians.
• grad2deg: converts an angle from grads to degrees.
• grad2mil: converts an angle from grads to mils.
• grad2rad: converts an angle from grads to radians.
• mil2deg: converts an angle from mils to degrees.
• mil2grad: converts an angle from mils to grads.
• mil2rad: converts an angle from mils to radians.
• rad2deg: converts an angle from radians to degrees.
• rad2grad: converts an angle from radians to grads.
• rad2mil: converts an angle from radians to mils.

The code defines the constants PI and TWO_PI to represent the values of π and 2π, respectively. These constants are used in the normalize2rad() and rad2*() functions.

The normalize2*() functions work by adding or subtracting the appropriate amount to the input angle until it is within the desired range. For example, the normalize2deg() function adds 360 degrees to the input angle if it is negative, and subtracts 360 degrees from the input angle if it is greater than or equal to 360 degrees.

The conversion functions work by multiplying the input angle by the appropriate conversion factor. For example, the deg2rad() function multiplies the input angle by PI / 180 to convert it from degrees to radians.

#define PI 3.141592653589793
#define TWO_PI 6.283185307179586

double normalize2deg(double a) {
  while (a < 0) a += 360;
  while (a >= 360) a -= 360;
  return a;
}
double normalize2grad(double a) {
  while (a < 0) a += 400;
  while (a >= 400) a -= 400;
  return a;
}
double normalize2mil(double a) {
  while (a < 0) a += 6400;
  while (a >= 6400) a -= 6400;
  return a;
}
double normalize2rad(double a) {
  while (a < 0) a += TWO_PI;
  while (a >= TWO_PI) a -= TWO_PI;
  return a;
}

double deg2grad(double a) {return a * 10 / 9;}
double deg2mil(double a) {return a * 160 / 9;}
double deg2rad(double a) {return a * PI / 180;}

double grad2deg(double a) {return a * 9 / 10;}
double grad2mil(double a) {return a * 16;}
double grad2rad(double a) {return a * PI / 200;}

double mil2deg(double a) {return a * 9 / 160;}
double mil2grad(double a) {return a / 16;}
double mil2rad(double a) {return a * PI / 3200;}

double rad2deg(double a) {return a * 180 / PI;}
double rad2grad(double a) {return a * 200 / PI;}
double rad2mil(double a) {return a * 3200 / PI;}