Переименование tangent pair в числа Котса, выделение комплексных чисел из двумерных векторов, добавление возведения в спебень для веросорв и чисел Котса
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Andrey Pokidov
parent
34ee460873
commit
74be89f1f8
17 changed files with 1233 additions and 646 deletions
374
basic-geometry/cotes-number.h
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374
basic-geometry/cotes-number.h
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#ifndef _BGC_COTES_NUMBER_H_
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#define _BGC_COTES_NUMBER_H_
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#include <math.h>
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#include "utilities.h"
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#include "angle.h"
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#include "vector2.h"
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#include "matrix2x2.h"
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// =================== Types ==================== //
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typedef struct
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{
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const float cos, sin;
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} BgcCotesNumberFP32;
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typedef struct
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{
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const double cos, sin;
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} BgcCotesNumberFP64;
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// ================= Dark Twins ================= //
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typedef struct {
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float cos, sin;
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} _BgcTwinCotesNumberFP32;
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typedef struct {
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double cos, sin;
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} _BgcTwinCotesNumberFP64;
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// ================= Constants ================== //
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extern const BgcCotesNumberFP32 BGC_IDLE_COTES_NUMBER_FP32;
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extern const BgcCotesNumberFP64 BGC_IDLE_COTES_NUMBER_FP64;
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// =================== Reset ==================== //
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inline void bgc_cotes_number_reset_fp32(BgcCotesNumberFP32* number)
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{
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_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)number;
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twin->cos = 1.0f;
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twin->sin = 0.0f;
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}
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inline void bgc_cotes_number_reset_fp64(BgcCotesNumberFP64* number)
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{
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_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)number;
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twin->cos = 1.0;
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twin->sin = 0.0;
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}
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// ==================== Set ===================== //
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void _bgc_cotes_number_normalize_fp32(const float square_modulus, _BgcTwinCotesNumberFP32* twin);
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void _bgc_cotes_number_normalize_fp64(const double square_modulus, _BgcTwinCotesNumberFP64* twin);
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inline void bgc_cotes_number_set_values_fp32(const float x1, const float x2, BgcCotesNumberFP32* number)
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{
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const float square_modulus = x1 * x1 + x2 * x2;
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_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)number;
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twin->cos = x1;
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twin->sin = x2;
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if (!bgc_is_sqare_unit_fp32(square_modulus)) {
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_bgc_cotes_number_normalize_fp32(square_modulus, twin);
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}
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}
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inline void bgc_cotes_number_set_values_fp64(const double x1, const double x2, BgcCotesNumberFP64* number)
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{
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const double square_modulus = x1 * x1 + x2 * x2;
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_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)number;
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twin->cos = x1;
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twin->sin = x2;
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if (!bgc_is_sqare_unit_fp64(square_modulus)) {
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_bgc_cotes_number_normalize_fp64(square_modulus, twin);
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}
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}
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// ================== Set Turn ================== //
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inline void bgc_cotes_number_set_turn_fp32(const float angle, const BgcAngleUnitEnum unit, BgcCotesNumberFP32* number)
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{
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const float radians = bgc_angle_to_radians_fp32(angle, unit);
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_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)number;
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twin->cos = cosf(radians);
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twin->sin = sinf(radians);
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}
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inline void bgc_cotes_number_set_turn_fp64(const double angle, const BgcAngleUnitEnum unit, BgcCotesNumberFP64* number)
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{
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const double radians = bgc_angle_to_radians_fp64(angle, unit);
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_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)number;
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twin->cos = cos(radians);
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twin->sin = sin(radians);
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}
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// =================== Angle =================== //
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inline float bgc_cotes_number_get_angle_fp32(const BgcCotesNumberFP32* number, const BgcAngleUnitEnum unit)
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{
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if (number->cos >= 1.0f - BGC_EPSYLON_FP32) {
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return 0.0f;
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}
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if (number->cos <= -1.0f + BGC_EPSYLON_FP32) {
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return bgc_angle_get_half_circle_fp32(unit);
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}
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if (number->sin >= 1.0f - BGC_EPSYLON_FP32) {
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return bgc_angle_get_quater_circle_fp32(unit);
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}
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if (number->sin <= -1.0f + BGC_EPSYLON_FP32) {
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return 0.75f * bgc_angle_get_full_circle_fp32(unit);
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}
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return bgc_radians_to_units_fp32(atan2f(number->sin, number->cos), unit);
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}
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inline double bgc_cotes_number_get_angle_fp64(const BgcCotesNumberFP64* number, const BgcAngleUnitEnum unit)
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{
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if (number->cos >= 1.0 - BGC_EPSYLON_FP64) {
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return 0.0;
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}
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if (number->cos <= -1.0 + BGC_EPSYLON_FP64) {
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return bgc_angle_get_half_circle_fp64(unit);
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}
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if (number->sin >= 1.0 - BGC_EPSYLON_FP64) {
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return bgc_angle_get_quater_circle_fp64(unit);
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}
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if (number->sin <= -1.0 + BGC_EPSYLON_FP64) {
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return 0.75 * bgc_angle_get_full_circle_fp64(unit);
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}
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return bgc_radians_to_units_fp64(atan2(number->sin, number->cos), unit);
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}
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// ==================== Copy ==================== //
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inline void bgc_cotes_number_copy_fp32(const BgcCotesNumberFP32* source, BgcCotesNumberFP32* destination)
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{
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_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)destination;
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twin->cos = source->cos;
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twin->sin = source->sin;
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}
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inline void bgc_cotes_number_copy_fp64(const BgcCotesNumberFP64* source, BgcCotesNumberFP64* destination)
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{
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_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)destination;
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twin->cos = source->cos;
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twin->sin = source->sin;
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}
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// ==================== Swap ==================== //
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inline void bgc_cotes_number_swap_fp32(BgcCotesNumberFP32* number1, BgcCotesNumberFP32* number2)
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{
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const float cos = number1->cos;
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const float sin = number1->sin;
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_BgcTwinCotesNumberFP32* twin1 = (_BgcTwinCotesNumberFP32*)number1;
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twin1->cos = number2->cos;
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twin1->sin = number2->sin;
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_BgcTwinCotesNumberFP32* twin2 = (_BgcTwinCotesNumberFP32*)number2;
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twin2->cos = cos;
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twin2->sin = sin;
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}
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inline void bgc_cotes_number_swap_fp64(BgcCotesNumberFP64* number1, BgcCotesNumberFP64* number2)
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{
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const double cos = number1->cos;
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const double sin = number1->sin;
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_BgcTwinCotesNumberFP64* twin1 = (_BgcTwinCotesNumberFP64*)number1;
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twin1->cos = number2->cos;
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twin1->sin = number2->sin;
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_BgcTwinCotesNumberFP64* twin2 = (_BgcTwinCotesNumberFP64*)number2;
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twin2->cos = cos;
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twin2->sin = sin;
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}
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// ================== Convert =================== //
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inline void bgc_cotes_number_convert_fp64_to_fp32(const BgcCotesNumberFP64* source, BgcCotesNumberFP32* destination)
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{
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bgc_cotes_number_set_values_fp32((float)source->cos, (float)source->sin, destination);
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}
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inline void bgc_cotes_number_convert_fp32_to_fp64(const BgcCotesNumberFP32* source, BgcCotesNumberFP64* destination)
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{
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bgc_cotes_number_set_values_fp64((double)source->cos, (double)source->sin, destination);
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}
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// =================== Invert =================== //
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inline void bgc_cotes_number_invert_fp32(const BgcCotesNumberFP32* number, BgcCotesNumberFP32* inverted)
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{
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_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)inverted;
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twin->cos = number->cos;
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twin->sin = -number->sin;
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}
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inline void bgc_cotes_number_invert_fp64(const BgcCotesNumberFP64* number, BgcCotesNumberFP64* inverted)
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{
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_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)inverted;
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twin->cos = number->cos;
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twin->sin = -number->sin;
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}
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// ================= Exponation ================= //
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inline void bgc_cotes_number_get_exponation_fp32(const BgcCotesNumberFP32* base, const float exponent, BgcCotesNumberFP32* power)
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{
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const float power_angle = exponent * atan2f(base->sin, base->cos);
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_BgcTwinCotesNumberFP32* twin = (_BgcTwinCotesNumberFP32*)power;
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twin->cos = cosf(power_angle);
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twin->sin = sinf(power_angle);
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}
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inline void bgc_cotes_number_get_exponation_fp64(const BgcCotesNumberFP64* base, const double exponent, BgcCotesNumberFP64* power)
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{
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const double power_angle = exponent * atan2(base->sin, base->cos);
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_BgcTwinCotesNumberFP64* twin = (_BgcTwinCotesNumberFP64*)power;
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twin->cos = cos(power_angle);
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twin->sin = sin(power_angle);
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}
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// ================ Combination ================= //
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inline void bgc_cotes_number_combine_fp32(const BgcCotesNumberFP32* number1, const BgcCotesNumberFP32* number2, BgcCotesNumberFP32* result)
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{
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bgc_cotes_number_set_values_fp32(
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number1->cos * number2->cos - number1->sin * number2->sin,
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number1->cos * number2->sin + number1->sin * number2->cos,
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result
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);
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}
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inline void bgc_cotes_number_combine_fp64(const BgcCotesNumberFP64* number1, const BgcCotesNumberFP64* number2, BgcCotesNumberFP64* result)
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{
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bgc_cotes_number_set_values_fp64(
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number1->cos * number2->cos - number1->sin * number2->sin,
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number1->cos * number2->sin + number1->sin * number2->cos,
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result
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);
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}
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// ============== Rotation Matrix =============== //
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inline void bgc_cotes_number_get_rotation_matrix_fp32(const BgcCotesNumberFP32* number, BgcMatrix2x2FP32* matrix)
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{
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matrix->r1c1 = number->cos;
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matrix->r1c2 = -number->sin;
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matrix->r2c1 = number->sin;
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matrix->r2c2 = number->cos;
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}
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inline void bgc_cotes_number_get_rotation_matrix_fp64(const BgcCotesNumberFP64* number, BgcMatrix2x2FP64* matrix)
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{
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matrix->r1c1 = number->cos;
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matrix->r1c2 = -number->sin;
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matrix->r2c1 = number->sin;
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matrix->r2c2 = number->cos;
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}
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// ============== Reverse Matrix ================ //
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inline void bgc_cotes_number_get_reverse_matrix_fp32(const BgcCotesNumberFP32* number, BgcMatrix2x2FP32* matrix)
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{
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matrix->r1c1 = number->cos;
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matrix->r1c2 = number->sin;
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matrix->r2c1 = -number->sin;
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matrix->r2c2 = number->cos;
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}
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inline void bgc_cotes_number_get_reverse_matrix_fp64(const BgcCotesNumberFP64* number, BgcMatrix2x2FP64* matrix)
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{
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matrix->r1c1 = number->cos;
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matrix->r1c2 = number->sin;
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matrix->r2c1 = -number->sin;
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matrix->r2c2 = number->cos;
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}
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// ================ Turn Vector ================= //
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inline void bgc_cotes_number_turn_vector_fp32(const BgcCotesNumberFP32* number, const BgcVector2FP32* vector, BgcVector2FP32* result)
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{
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const float x1 = number->cos * vector->x1 - number->sin * vector->x2;
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const float x2 = number->sin * vector->x1 + number->cos * vector->x2;
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result->x1 = x1;
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result->x2 = x2;
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}
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inline void bgc_cotes_number_turn_vector_fp64(const BgcCotesNumberFP64* number, const BgcVector2FP64* vector, BgcVector2FP64* result)
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{
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const double x1 = number->cos * vector->x1 - number->sin * vector->x2;
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const double x2 = number->sin * vector->x1 + number->cos * vector->x2;
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result->x1 = x1;
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result->x2 = x2;
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}
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// ============ Turn Vector Backward ============ //
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inline void bgc_cotes_number_turn_vector_back_fp32(const BgcCotesNumberFP32* number, const BgcVector2FP32* vector, BgcVector2FP32* result)
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{
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const float x1 = number->sin * vector->x2 + number->cos * vector->x1;
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const float x2 = number->cos * vector->x2 - number->sin * vector->x1;
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result->x1 = x1;
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result->x2 = x2;
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}
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inline void bgc_cotes_number_turn_vector_back_fp64(const BgcCotesNumberFP64* number, const BgcVector2FP64* vector, BgcVector2FP64* result)
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{
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const double x1 = number->sin * vector->x2 + number->cos * vector->x1;
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const double x2 = number->cos * vector->x2 - number->sin * vector->x1;
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result->x1 = x1;
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result->x2 = x2;
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}
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// ================== Are Close ================= //
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inline int bgc_cotes_number_are_close_fp32(const BgcCotesNumberFP32* number1, const BgcCotesNumberFP32* number2)
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{
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const float d_cos = number1->cos - number2->cos;
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const float d_sin = number1->sin - number2->sin;
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return d_cos * d_cos + d_sin * d_sin <= BGC_SQUARE_EPSYLON_FP32;
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}
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inline int bgc_cotes_number_are_close_fp64(const BgcCotesNumberFP64* number1, const BgcCotesNumberFP64* number2)
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{
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const double d_cos = number1->cos - number2->cos;
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const double d_sin = number1->sin - number2->sin;
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return d_cos * d_cos + d_sin * d_sin <= BGC_SQUARE_EPSYLON_FP64;
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}
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#endif
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