#ifndef _BGC_ANGLE_H_ #define _BGC_ANGLE_H_ #include #include "utilities.h" #define BGC_PI_FP32 3.1415926536f #define BGC_TWO_PI_FP32 6.2831853072f #define BGC_HALF_OF_PI_FP32 1.5707963268f #define BGC_THIRD_OF_PI_FP32 1.0471975512f #define BGC_FOURTH_OF_PI_FP32 0.7853981634f #define BGC_SIXTH_OF_PI_FP32 0.5235987756f #define BGC_DEGREES_IN_RADIAN_FP32 57.295779513f #define BGC_TURNS_IN_RADIAN_FP32 0.1591549431f #define BGC_RADIANS_IN_DEGREE_FP32 1.745329252E-2f #define BGC_TURNS_IN_DEGREE_FP32 2.7777777778E-3f #define BGC_PI_FP64 3.14159265358979324 #define BGC_TWO_PI_FP64 6.28318530717958648 #define BGC_HALF_OF_PI_FP64 1.57079632679489662 #define BGC_THIRD_OF_PI_FP64 1.04719755119659775 #define BGC_FOURTH_OF_PI_FP64 0.78539816339744831 #define BGC_SIXTH_OF_PI_FP64 0.523598775598298873 #define BGC_DEGREES_IN_RADIAN_FP64 57.2957795130823209 #define BGC_TURNS_IN_RADIAN_FP64 0.159154943091895336 #define BGC_RADIANS_IN_DEGREE_FP64 1.74532925199432958E-2 #define BGC_TURNS_IN_DEGREE_FP64 2.77777777777777778E-3 typedef enum { BGC_ANGLE_UNIT_RADIANS = 1, BGC_ANGLE_UNIT_DEGREES = 2, BGC_ANGLE_UNIT_TURNS = 3 } BgcAngleUnitEnum; typedef enum { /** * The measure of an angle with a range of: * [0, 360) degrees, [0, 2xPI) radians, [0, 1) turns, [0, 400) gradians */ BGC_ANGLE_RANGE_UNSIGNED = 1, /** * The measure of an angle with a range of: * (-180, 180] degrees, (-PI, PI] radians, (-0.5, 0.5] turns, (-200, 200] gradians */ BGC_ANGLE_RANGE_SIGNED = 2 } BgcAngleRangeEnum; // !================= Radians ==================! // // ========= Convert radians to degrees ========= // inline float bgc_radians_to_degrees_fp32(const float radians) { return radians * BGC_DEGREES_IN_RADIAN_FP32; } inline double bgc_radians_to_degrees_fp64(const double radians) { return radians * BGC_DEGREES_IN_RADIAN_FP64; } // ========== Convert radians to turns ========== // inline float bgc_radians_to_turns_fp32(const float radians) { return radians * BGC_TURNS_IN_RADIAN_FP32; } inline double bgc_radians_to_turns_fp64(const double radians) { return radians * BGC_TURNS_IN_RADIAN_FP64; } // ========= Convert radians to any unit ======== // inline float bgc_radians_to_units_fp32(const float radians, const BgcAngleUnitEnum to_unit) { if (to_unit == BGC_ANGLE_UNIT_DEGREES) { return radians * BGC_DEGREES_IN_RADIAN_FP32; } if (to_unit == BGC_ANGLE_UNIT_TURNS) { return radians * BGC_TURNS_IN_RADIAN_FP32; } return radians; } inline double bgc_radians_to_units_fp64(const double radians, const BgcAngleUnitEnum to_unit) { if (to_unit == BGC_ANGLE_UNIT_DEGREES) { return radians * BGC_DEGREES_IN_RADIAN_FP64; } if (to_unit == BGC_ANGLE_UNIT_TURNS) { return radians * BGC_TURNS_IN_RADIAN_FP64; } return radians; } // ============ Normalize radians ============= // inline float bgc_radians_normalize_fp32(const float radians, const BgcAngleRangeEnum range) { if (range == BGC_ANGLE_RANGE_UNSIGNED) { if (0.0f <= radians && radians < BGC_TWO_PI_FP32) { return radians; } } else { if (-BGC_PI_FP32 < radians && radians <= BGC_PI_FP32) { return radians; } } float turns = radians * BGC_TURNS_IN_RADIAN_FP32; turns -= floorf(turns); if (range == BGC_ANGLE_RANGE_SIGNED && turns > 0.5f) { turns -= 1.0f; } return turns * BGC_TWO_PI_FP32; } inline double bgc_radians_normalize_fp64(const double radians, const BgcAngleRangeEnum range) { if (range == BGC_ANGLE_RANGE_UNSIGNED) { if (0.0 <= radians && radians < BGC_TWO_PI_FP64) { return radians; } } else { if (-BGC_PI_FP64 < radians && radians <= BGC_PI_FP64) { return radians; } } double turns = radians * BGC_TURNS_IN_RADIAN_FP64; turns -= floor(turns); if (range == BGC_ANGLE_RANGE_SIGNED && turns > 0.5) { turns -= 1.0; } return turns * BGC_TWO_PI_FP64; } // !================= Degrees ==================! // // ========= Convert degrees to radians ========= // inline float bgc_degrees_to_radians_fp32(const float degrees) { return degrees * BGC_RADIANS_IN_DEGREE_FP32; } inline double bgc_degrees_to_radians_fp64(const double degrees) { return degrees * BGC_RADIANS_IN_DEGREE_FP64; } // ========== Convert degrees to turns ========== // inline float bgc_degrees_to_turns_fp32(const float radians) { return radians * BGC_TURNS_IN_DEGREE_FP32; } inline double fp64_degrees_to_turns(const double radians) { return radians * BGC_TURNS_IN_DEGREE_FP64; } // ========= Convert degreess to any unit ======== // inline float bgc_degrees_to_units_fp32(const float degrees, const BgcAngleUnitEnum to_unit) { if (to_unit == BGC_ANGLE_UNIT_RADIANS) { return degrees * BGC_RADIANS_IN_DEGREE_FP32; } if (to_unit == BGC_ANGLE_UNIT_TURNS) { return degrees * BGC_TURNS_IN_DEGREE_FP32; } return degrees; } inline double bgc_degrees_to_units_fp64(const double degrees, const BgcAngleUnitEnum to_unit) { if (to_unit == BGC_ANGLE_UNIT_RADIANS) { return degrees * BGC_RADIANS_IN_DEGREE_FP64; } if (to_unit == BGC_ANGLE_UNIT_TURNS) { return degrees * BGC_TURNS_IN_DEGREE_FP64; } return degrees; } // ============ Normalize degrees ============= // inline float bgc_degrees_normalize_fp32(const float degrees, const BgcAngleRangeEnum range) { if (range == BGC_ANGLE_RANGE_UNSIGNED) { if (0.0f <= degrees && degrees < 360.0f) { return degrees; } } else { if (-180.0f < degrees && degrees <= 180.0f) { return degrees; } } float turns = degrees * BGC_TURNS_IN_DEGREE_FP32; turns -= floorf(turns); if (range == BGC_ANGLE_RANGE_SIGNED && turns > 0.5f) { turns -= 1.0f; } return turns * 360.0f; } inline double bgc_degrees_normalize_fp64(const double degrees, const BgcAngleRangeEnum range) { if (range == BGC_ANGLE_RANGE_UNSIGNED) { if (0.0 <= degrees && degrees < 360.0) { return degrees; } } else { if (-180.0 < degrees && degrees <= 180.0) { return degrees; } } double turns = degrees * BGC_TURNS_IN_DEGREE_FP64; turns -= floor(turns); if (range == BGC_ANGLE_RANGE_SIGNED && turns > 0.5) { turns -= 1.0; } return turns * 360.0; } // !================== Turns ===================! // // ========== Convert turns to radians ========== // inline float bgc_turns_to_radians_fp32(const float turns) { return turns * BGC_TWO_PI_FP32; } inline double bgc_turns_to_radians_fp64(const double turns) { return turns * BGC_TWO_PI_FP64; } // ========== Convert turns to degrees ========== // inline float bgc_turns_to_degrees_fp32(const float turns) { return turns * 360.0f; } inline double bgc_turns_to_degrees_fp64(const double turns) { return turns * 360.0; } // ========= Convert turns to any unit ======== // inline float bgc_turns_to_units_fp32(const float turns, const BgcAngleUnitEnum to_unit) { if (to_unit == BGC_ANGLE_UNIT_RADIANS) { return turns * BGC_TWO_PI_FP32; } if (to_unit == BGC_ANGLE_UNIT_DEGREES) { return turns * 360.0f; } return turns; } inline double bgc_turns_to_units_fp64(const double turns, const BgcAngleUnitEnum to_unit) { if (to_unit == BGC_ANGLE_UNIT_RADIANS) { return turns * BGC_TWO_PI_FP64; } if (to_unit == BGC_ANGLE_UNIT_DEGREES) { return turns * 360.0; } return turns; } // ============= Normalize turns ============== // inline float bgc_turns_normalize_fp32(const float turns, const BgcAngleRangeEnum range) { if (range == BGC_ANGLE_RANGE_UNSIGNED) { if (0.0f <= turns && turns < 1.0f) { return turns; } } else { if (-0.5f < turns && turns <= 0.5f) { return turns; } } float rest = turns - floorf(turns); if (range == BGC_ANGLE_RANGE_SIGNED && rest > 0.5f) { return rest - 1.0f; } return rest; } inline double bgc_turns_normalize_fp64(const double turns, const BgcAngleRangeEnum range) { if (range == BGC_ANGLE_RANGE_UNSIGNED) { if (0.0 <= turns && turns < 1.0) { return turns; } } else { if (-0.5 < turns && turns <= 0.5) { return turns; } } double rest = turns - floor(turns); if (range == BGC_ANGLE_RANGE_SIGNED && rest > 0.5) { return rest - 1.0; } return rest; } // !================== Angle ===================! // // ========= Convert any unit to radians ======== // inline float bgc_angle_to_radians_fp32(const float angle, const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return angle * BGC_RADIANS_IN_DEGREE_FP32; } if (unit == BGC_ANGLE_UNIT_TURNS) { return angle * BGC_TWO_PI_FP32; } return angle; } inline double bgc_angle_to_radians_fp64(const double angle, const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return angle * BGC_RADIANS_IN_DEGREE_FP64; } if (unit == BGC_ANGLE_UNIT_TURNS) { return angle * BGC_TWO_PI_FP64; } return angle; } // ========= Convert any unit to degreess ======== // inline float bgc_angle_to_degrees_fp32(const float angle, const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_RADIANS) { return angle * BGC_DEGREES_IN_RADIAN_FP32; } if (unit == BGC_ANGLE_UNIT_TURNS) { return angle * 360.0f; } return angle; } inline double bgc_angle_to_degrees_fp64(const double angle, const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_RADIANS) { return angle * BGC_DEGREES_IN_RADIAN_FP64; } if (unit == BGC_ANGLE_UNIT_TURNS) { return angle * 360.0; } return angle; } // ========= Convert any unit to turns ======== // inline float bgc_angle_to_turns_fp32(const float angle, const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_RADIANS) { return angle * BGC_TURNS_IN_RADIAN_FP32; } if (unit == BGC_ANGLE_UNIT_DEGREES) { return angle * BGC_TURNS_IN_DEGREE_FP32; } return angle; } inline double bgc_angle_to_turns_fp64(const double angle, const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_RADIANS) { return angle * BGC_TURNS_IN_RADIAN_FP64; } if (unit == BGC_ANGLE_UNIT_DEGREES) { return angle * BGC_TURNS_IN_DEGREE_FP64; } return angle; } // ============= Get Full Circle ============== // inline float bgc_angle_get_full_circle_fp32(const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return 360.0f; } if (unit == BGC_ANGLE_UNIT_TURNS) { return 1.0f; } return BGC_TWO_PI_FP32; } inline double bgc_angle_get_full_circle_fp64(const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return 360.0; } if (unit == BGC_ANGLE_UNIT_TURNS) { return 1.0; } return BGC_TWO_PI_FP64; } // ============= Get Half Circle ============== // inline float bgc_angle_get_half_circle_fp32(const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return 180.0f; } if (unit == BGC_ANGLE_UNIT_TURNS) { return 0.5f; } return BGC_PI_FP32; } inline double bgc_angle_get_half_circle_fp64(const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return 180.0; } if (unit == BGC_ANGLE_UNIT_TURNS) { return 0.5; } return BGC_PI_FP64; } // ============= Get Half Circle ============== // inline float bgc_angle_get_quater_circle_fp32(const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return 90.0f; } if (unit == BGC_ANGLE_UNIT_TURNS) { return 0.25f; } return BGC_HALF_OF_PI_FP32; } inline double bgc_angle_get_quater_circle_fp64(const BgcAngleUnitEnum unit) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return 90.0; } if (unit == BGC_ANGLE_UNIT_TURNS) { return 0.25; } return BGC_HALF_OF_PI_FP64; } // ================ Normalize ================= // inline float bgc_angle_normalize_fp32(const float angle, const BgcAngleUnitEnum unit, const BgcAngleRangeEnum range) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return bgc_degrees_normalize_fp32(angle, range); } if (unit == BGC_ANGLE_UNIT_TURNS) { return bgc_turns_normalize_fp32(angle, range); } return bgc_radians_normalize_fp32(angle, range); } inline double bgc_angle_normalize_fp64(const double angle, const BgcAngleUnitEnum unit, const BgcAngleRangeEnum range) { if (unit == BGC_ANGLE_UNIT_DEGREES) { return bgc_degrees_normalize_fp64(angle, range); } if (unit == BGC_ANGLE_UNIT_TURNS) { return bgc_turns_normalize_fp64(angle, range); } return bgc_radians_normalize_fp64(angle, range); } #endif