Program Listing for File angles.h
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#ifndef GEOMETRY_ANGLES_UTILS_H
#define GEOMETRY_ANGLES_UTILS_H
#define _USE_MATH_DEFINES
#include <algorithm>
#include <cmath>
namespace angles
{
static inline double from_degrees(double degrees)
{
return degrees * M_PI / 180.0;
}
static inline double to_degrees(double radians)
{
return radians * 180.0 / M_PI;
}
static inline double normalize_angle_positive(double angle)
{
const double result = fmod(angle, 2.0*M_PI);
if(result < 0) return result + 2.0*M_PI;
return result;
}
static inline double normalize_angle(double angle)
{
const double result = fmod(angle + M_PI, 2.0*M_PI);
if(result <= 0.0) return result + M_PI;
return result - M_PI;
}
static inline double shortest_angular_distance(double from, double to)
{
return normalize_angle(to-from);
}
static inline double two_pi_complement(double angle)
{
//check input conditions
if (angle > 2*M_PI || angle < -2.0*M_PI)
angle = fmod(angle, 2.0*M_PI);
if(angle < 0)
return (2*M_PI+angle);
else if (angle > 0)
return (-2*M_PI+angle);
return(2*M_PI);
}
static bool find_min_max_delta(double from, double left_limit, double right_limit, double &result_min_delta, double &result_max_delta)
{
double delta[4];
delta[0] = shortest_angular_distance(from,left_limit);
delta[1] = shortest_angular_distance(from,right_limit);
delta[2] = two_pi_complement(delta[0]);
delta[3] = two_pi_complement(delta[1]);
if(delta[0] == 0)
{
result_min_delta = delta[0];
result_max_delta = std::max<double>(delta[1],delta[3]);
return true;
}
if(delta[1] == 0)
{
result_max_delta = delta[1];
result_min_delta = std::min<double>(delta[0],delta[2]);
return true;
}
double delta_min = delta[0];
double delta_min_2pi = delta[2];
if(delta[2] < delta_min)
{
delta_min = delta[2];
delta_min_2pi = delta[0];
}
double delta_max = delta[1];
double delta_max_2pi = delta[3];
if(delta[3] > delta_max)
{
delta_max = delta[3];
delta_max_2pi = delta[1];
}
// printf("%f %f %f %f\n",delta_min,delta_min_2pi,delta_max,delta_max_2pi);
if((delta_min <= delta_max_2pi) || (delta_max >= delta_min_2pi))
{
result_min_delta = delta_max_2pi;
result_max_delta = delta_min_2pi;
if(left_limit == -M_PI && right_limit == M_PI)
return true;
else
return false;
}
result_min_delta = delta_min;
result_max_delta = delta_max;
return true;
}
static inline bool shortest_angular_distance_with_large_limits(double from, double to, double left_limit, double right_limit, double &shortest_angle)
{
// Shortest steps in the two directions
double delta = shortest_angular_distance(from, to);
double delta_2pi = two_pi_complement(delta);
// "sort" distances so that delta is shorter than delta_2pi
if(std::fabs(delta) > std::fabs(delta_2pi))
std::swap(delta, delta_2pi);
if(left_limit > right_limit) {
// If limits are something like [PI/2 , -PI/2] it actually means that we
// want rotations to be in the interval [-PI,PI/2] U [PI/2,PI], ie, the
// half unit circle not containing the 0. This is already gracefully
// handled by shortest_angular_distance_with_limits, and therefore this
// function should not be called at all. However, if one has limits that
// are larger than PI, the same rationale behind shortest_angular_distance_with_limits
// does not hold, ie, M_PI+x should not be directly equal to -M_PI+x.
// In this case, the correct way of getting the shortest solution is to
// properly set the limits, eg, by saying that the interval is either
// [PI/2, 3*PI/2] or [-3*M_PI/2, -M_PI/2]. For this reason, here we
// return false by default.
shortest_angle = delta;
return false;
}
// Check in which direction we should turn (clockwise or counter-clockwise).
// start by trying with the shortest angle (delta).
double to2 = from + delta;
if(left_limit <= to2 && to2 <= right_limit) {
// we can move in this direction: return success if the "from" angle is inside limits
shortest_angle = delta;
return left_limit <= from && from <= right_limit;
}
// delta is not ok, try to move in the other direction (using its complement)
to2 = from + delta_2pi;
if(left_limit <= to2 && to2 <= right_limit) {
// we can move in this direction: return success if the "from" angle is inside limits
shortest_angle = delta_2pi;
return left_limit <= from && from <= right_limit;
}
// nothing works: we always go outside limits
shortest_angle = delta; // at least give some "coherent" result
return false;
}
static inline bool shortest_angular_distance_with_limits(double from, double to, double left_limit, double right_limit, double &shortest_angle)
{
double min_delta = -2*M_PI;
double max_delta = 2*M_PI;
double min_delta_to = -2*M_PI;
double max_delta_to = 2*M_PI;
bool flag = find_min_max_delta(from,left_limit,right_limit,min_delta,max_delta);
double delta = shortest_angular_distance(from,to);
double delta_mod_2pi = two_pi_complement(delta);
if(flag)//from position is within the limits
{
if(delta >= min_delta && delta <= max_delta)
{
shortest_angle = delta;
return true;
}
else if(delta_mod_2pi >= min_delta && delta_mod_2pi <= max_delta)
{
shortest_angle = delta_mod_2pi;
return true;
}
else //to position is outside the limits
{
find_min_max_delta(to,left_limit,right_limit,min_delta_to,max_delta_to);
if(fabs(min_delta_to) < fabs(max_delta_to))
shortest_angle = std::max<double>(delta,delta_mod_2pi);
else if(fabs(min_delta_to) > fabs(max_delta_to))
shortest_angle = std::min<double>(delta,delta_mod_2pi);
else
{
if (fabs(delta) < fabs(delta_mod_2pi))
shortest_angle = delta;
else
shortest_angle = delta_mod_2pi;
}
return false;
}
}
else // from position is outside the limits
{
find_min_max_delta(to,left_limit,right_limit,min_delta_to,max_delta_to);
if(fabs(min_delta) < fabs(max_delta))
shortest_angle = std::min<double>(delta,delta_mod_2pi);
else if (fabs(min_delta) > fabs(max_delta))
shortest_angle = std::max<double>(delta,delta_mod_2pi);
else
{
if (fabs(delta) < fabs(delta_mod_2pi))
shortest_angle = delta;
else
shortest_angle = delta_mod_2pi;
}
return false;
}
shortest_angle = delta;
return false;
}
}
#endif