Добавление тангентов (аналог версоров, но для двумерных пространств) / Adding of tangent pairs, it is like versors but for 2 dimensional spaces
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7 changed files with 316 additions and 5 deletions
296
basic-geometry/tangent.h
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296
basic-geometry/tangent.h
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#ifndef _GEOMETRY_TANGENT_H_
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#define _GEOMETRY_TANGENT_H_
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#include <math.h>
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#include "basis.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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typedef struct
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{
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float _cos, _sin;
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} BgFP32Tangent;
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typedef struct
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{
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double _cos, _sin;
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} BgFP64Tangent;
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extern const BgFP32Tangent BG_FP32_IDLE_TANGENT;
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extern const BgFP64Tangent BG_FP64_IDLE_TANGENT;
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// =================== Reset ==================== //
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static inline void bg_fp32_tangent_reset(BgFP32Tangent* tangent)
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{
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tangent->_cos = 1.0f;
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tangent->_sin = 0.0f;
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}
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static inline void bg_fp64_tangent_reset(BgFP64Tangent* tangent)
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{
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tangent->_cos = 1.0;
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tangent->_sin = 0.0;
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}
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// ==================== Copy ==================== //
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static inline void bg_fp32_tangent_copy(const BgFP32Tangent* from, BgFP32Tangent* to)
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{
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to->_cos = from->_cos;
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to->_sin = from->_sin;
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}
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static inline void bg_fp64_tangent_copy(const BgFP64Tangent* from, BgFP64Tangent* to)
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{
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to->_cos = from->_cos;
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to->_sin = from->_sin;
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}
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// ==================== Make ==================== //
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static inline void bg_fp32_tangent_set_values(const float x1, const float x2, BgFP32Tangent* tangent)
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{
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const float square_module = x1 * x1 + x2 * x2;
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tangent->_cos = x1;
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tangent->_sin = x2;
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if (1.0f - BG_FP32_TWO_EPSYLON <= square_module && square_module <= 1.0f + BG_FP32_TWO_EPSYLON) {
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return;
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}
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if (square_module <= BG_FP32_SQUARE_EPSYLON) {
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tangent->_cos = 1.0f;
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tangent->_sin = 0.0f;
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return;
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}
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const float multiplier = sqrtf(1.0f / square_module);
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tangent->_cos = x1 * multiplier;
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tangent->_sin = x2 * multiplier;
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}
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static inline void bg_fp64_tangent_set_values(const double x1, const double x2, BgFP64Tangent* tangent)
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{
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const double square_module = x1 * x1 + x2 * x2;
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tangent->_cos = x1;
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tangent->_sin = x2;
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if (1.0 - BG_FP64_TWO_EPSYLON <= square_module && square_module <= 1.0 + BG_FP64_TWO_EPSYLON) {
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return;
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}
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if (square_module <= BG_FP64_SQUARE_EPSYLON) {
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tangent->_cos = 1.0;
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tangent->_sin = 0.0;
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return;
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}
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const double multiplier = sqrt(1.0 / square_module);
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tangent->_cos = x1 * multiplier;
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tangent->_sin = x2 * multiplier;
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}
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// ================== Set Angle ================= //
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static inline void bg_fp32_tangent_set_angle(const float angle, const angle_unit_t unit, BgFP32Tangent* tangent)
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{
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const float radians = bg_fp32_angle_to_radians(angle, unit);
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tangent->_cos = cosf(radians);
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tangent->_sin = sinf(radians);
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}
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static inline void bg_fp64_tangent_set_angle(const double angle, const angle_unit_t unit, BgFP64Tangent* tangent)
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{
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const double radians = bg_fp64_angle_to_radians(angle, unit);
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tangent->_cos = cos(radians);
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tangent->_sin = sin(radians);
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}
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// ============= Copy to twin type ============== //
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static inline void bg_fp32_tangent_copy_to_double(const BgFP32Tangent* from, BgFP64Tangent* to)
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{
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bg_fp64_tangent_set_values((double)from->_cos, (double)from->_sin, to);
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}
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static inline void bg_fp64_tangent_copy_to_single(const BgFP64Tangent* from, BgFP32Tangent* to)
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{
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bg_fp32_tangent_set_values((float)from->_cos, (float)from->_sin, to);
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}
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// ================= Inversion ================== //
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static inline void bg_fp32_tangent_invert(BgFP32Tangent* tangent)
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{
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tangent->_sin = -tangent->_sin;
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}
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static inline void bg_fp64_tangent_invert(BgFP64Tangent* tangent)
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{
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tangent->_sin = -tangent->_sin;
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}
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// ================ Set Inverted ================ //
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static inline void bg_fp32_tangent_set_inverted(const BgFP32Tangent* tangent, BgFP32Tangent* result)
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{
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result->_cos = tangent->_cos;
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result->_sin = -tangent->_sin;
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}
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static inline void bg_fp64_tangent_set_inverted(const BgFP64Tangent* tangent, BgFP64Tangent* result)
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{
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result->_cos = tangent->_cos;
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result->_sin = -tangent->_sin;
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}
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// ============== Rotation Matrix =============== //
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static inline void bg_fp32_tangent_make_rotation_matrix(const BgFP32Tangent* tangent, BgFP32Matrix2x2* matrix)
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{
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matrix->r1c1 = tangent->_cos;
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matrix->r1c2 = -tangent->_sin;
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matrix->r2c1 = tangent->_sin;
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matrix->r2c2 = tangent->_cos;
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}
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static inline void bg_fp64_tangent_make_rotation_matrix(const BgFP64Tangent* tangent, BgFP64Matrix2x2* matrix)
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{
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matrix->r1c1 = tangent->_cos;
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matrix->r1c2 = -tangent->_sin;
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matrix->r2c1 = tangent->_sin;
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matrix->r2c2 = tangent->_cos;
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}
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// ============== Reverse Matrix ================ //
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static inline void bg_fp32_tangent_make_reverse_matrix(const BgFP32Tangent* tangent, BgFP32Matrix2x2* matrix)
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{
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matrix->r1c1 = tangent->_cos;
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matrix->r1c2 = tangent->_sin;
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matrix->r2c1 = -tangent->_sin;
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matrix->r2c2 = tangent->_cos;
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}
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static inline void bg_fp64_tangent_make_reverse_matrix(const BgFP64Tangent* tangent, BgFP64Matrix2x2* matrix)
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{
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matrix->r1c1 = tangent->_cos;
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matrix->r1c2 = tangent->_sin;
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matrix->r2c1 = -tangent->_sin;
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matrix->r2c2 = tangent->_cos;
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}
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// =================== Angle =================== //
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static inline float bg_fp32_tangent_get_angle(const BgFP32Tangent* tangent, const angle_unit_t unit)
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{
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if (tangent->_cos >= 1.0f - BG_FP32_TWO_EPSYLON) {
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return 0.0f;
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}
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if (tangent->_cos <= -1.0f + BG_FP32_TWO_EPSYLON) {
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return bg_fp32_angle_get_half_circle(unit);
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}
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if (tangent->_sin >= 1.0f - BG_FP32_TWO_EPSYLON) {
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return bg_fp32_angle_get_quater_circle(unit);
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}
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if (tangent->_sin <= -1.0f + BG_FP32_TWO_EPSYLON) {
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return 0.75f * bg_fp32_angle_get_full_circle(unit);
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}
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return bg_fp32_radians_to_units(atan2f(tangent->_cos, tangent->_sin), unit);
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}
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static inline double bg_fp64_tangent_get_angle(const BgFP64Tangent* tangent, const angle_unit_t unit)
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{
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if (tangent->_cos >= 1.0 - BG_FP64_TWO_EPSYLON) {
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return 0.0;
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}
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if (tangent->_cos <= -1.0 + BG_FP64_TWO_EPSYLON) {
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return bg_fp64_angle_get_half_circle(unit);
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}
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if (tangent->_sin >= 1.0 - BG_FP64_TWO_EPSYLON) {
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return bg_fp64_angle_get_quater_circle(unit);
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}
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if (tangent->_sin <= -1.0 + BG_FP64_TWO_EPSYLON) {
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return 0.75 * bg_fp64_angle_get_full_circle(unit);
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}
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return bg_fp64_radians_to_units(atan2(tangent->_cos, tangent->_sin), unit);
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}
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// ================ Combination ================= //
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static inline void bg_fp32_tangent_combine(const BgFP32Tangent* tangent1, const BgFP32Tangent* tangent2, BgFP32Tangent* result)
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{
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bg_fp32_tangent_set_values(
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tangent1->_cos * tangent2->_cos - tangent1->_sin * tangent2->_sin,
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tangent1->_cos * tangent2->_sin + tangent1->_sin * tangent2->_cos,
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result
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);
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}
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static inline void bg_fp64_tangent_combine(const BgFP64Tangent* tangent1, const BgFP64Tangent* tangent2, BgFP64Tangent* result)
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{
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bg_fp64_tangent_set_values(
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tangent1->_cos * tangent2->_cos - tangent1->_sin * tangent2->_sin,
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tangent1->_cos * tangent2->_sin + tangent1->_sin * tangent2->_cos,
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result
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);
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}
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// ================ Turn Vector ================= //
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static inline void bg_fp32_tangent_turn(const BgFP32Tangent* tangent, const BgFP32Vector2* vector, BgFP32Vector2* result)
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{
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const float x1 = tangent->_cos * vector->x1 - tangent->_sin * vector->x2;
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const float x2 = tangent->_sin * vector->x1 + tangent->_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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static inline void bg_fp64_tangent_turn(const BgFP64Tangent* tangent, const BgFP64Vector2* vector, BgFP64Vector2* result)
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{
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const double x1 = tangent->_cos * vector->x1 - tangent->_sin * vector->x2;
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const double x2 = tangent->_sin * vector->x1 + tangent->_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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static inline void bg_fp32_tangent_turn_back(const BgFP32Tangent* tangent, const BgFP32Vector2* vector, BgFP32Vector2* result)
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{
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const float x1 = tangent->_sin * vector->x2 + tangent->_cos * vector->x1;
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const float x2 = tangent->_cos * vector->x2 - tangent->_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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static inline void bg_fp64_tangent_turn_back(const BgFP64Tangent* tangent, const BgFP64Vector2* vector, BgFP64Vector2* result)
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{
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const double x1 = tangent->_sin * vector->x2 + tangent->_cos * vector->x1;
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const double x2 = tangent->_cos * vector->x2 - tangent->_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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#endif
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