545 lines
18 KiB
C
545 lines
18 KiB
C
#ifndef _BASIC_GEOMETRY_VECTOR3_H_
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#define _BASIC_GEOMETRY_VECTOR3_H_
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#include "basis.h"
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#include "angle.h"
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#include <math.h>
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// ================== Vector3 =================== //
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typedef struct
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{
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float x1, x2, x3;
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} vector3_fp32_t;
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typedef struct
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{
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double x1, x2, x3;
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} vector3_fp64_t;
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// ================ Declarations ================ //
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/*
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extern inline void vector3_reset_fp32(vector3_fp32_t* vector);
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extern inline void vector3_set_fp32(const float x1, const float x2, const float x3, vector3_fp32_t* to);
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extern inline void vector3_copy_fp32(const vector3_fp32_t* from, vector3_fp32_t* to);
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extern inline void vector3_fp32_convert(const vector3_fp64_t* from, vector3_fp32_t* to);
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extern inline void vector3_swap_fp32(vector3_fp32_t* vector1, vector3_fp32_t* vector2);
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extern inline void vector3_invert_fp32(vector3_fp32_t* vector);
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extern inline void vector3_fp32_make_inverted(const vector3_fp32_t* vector, vector3_fp32_t* result);
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extern inline void vector3_fp32_make_inverted_fp64(const vector3_fp64_t* vector, vector3_fp32_t* result);
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extern inline float vector3_get_square_modulus_fp32(const vector3_fp32_t* vector);
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extern inline float vector3_get_modulus_fp32(const vector3_fp32_t* vector);
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extern inline void vector3_reset_fp64(vector3_fp64_t* vector);
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extern inline void vector3_set_fp64(const double x1, const double x2, const double x3, vector3_fp64_t* to);
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extern inline void vector3_copy_fp64(const vector3_fp64_t* from, vector3_fp64_t* to);
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extern inline void vector3_fp64_convert(const vector3_fp32_t* from, vector3_fp64_t* to);
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extern inline void vector3_swap_fp64(vector3_fp64_t* vector1, vector3_fp64_t* vector2);
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extern inline void vector3_invert_fp64(vector3_fp64_t* vector);
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extern inline void vector3_fp64_make_inverted(const vector3_fp64_t* vector, vector3_fp64_t* result);
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extern inline void vector3_fp64_make_inverted_fp32(const vector3_fp32_t* vector, vector3_fp64_t* result);
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extern inline double vector3_get_square_modulus_fp64(const vector3_fp64_t* vector);
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extern inline double vector3_get_modulus_fp64(const vector3_fp64_t* vector);
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*/
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// =================== Reset ==================== //
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inline void vector3_reset_fp32(vector3_fp32_t* vector)
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{
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vector->x1 = 0.0f;
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vector->x2 = 0.0f;
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vector->x3 = 0.0f;
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}
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inline void vector3_reset_fp64(vector3_fp64_t* vector)
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{
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vector->x1 = 0.0;
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vector->x2 = 0.0;
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vector->x3 = 0.0;
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}
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// ==================== Set ===================== //
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inline void vector3_set_fp32(const float x1, const float x2, const float x3, vector3_fp32_t* to)
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{
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to->x1 = x1;
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to->x2 = x2;
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to->x3 = x3;
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}
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inline void vector3_set_fp64(const double x1, const double x2, const double x3, vector3_fp64_t* to)
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{
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to->x1 = x1;
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to->x2 = x2;
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to->x3 = x3;
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}
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// ==================== Copy ==================== //
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inline void vector3_copy_fp32(const vector3_fp32_t* from, vector3_fp32_t* to)
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{
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to->x1 = from->x1;
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to->x2 = from->x2;
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to->x3 = from->x3;
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}
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inline void vector3_copy_fp64(const vector3_fp64_t* from, vector3_fp64_t* to)
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{
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to->x1 = from->x1;
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to->x2 = from->x2;
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to->x3 = from->x3;
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}
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// ================== Convert =================== //
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inline void vector3_fp32_convert(const vector3_fp64_t* from, vector3_fp32_t* to)
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{
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to->x1 = (float) from->x1;
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to->x2 = (float) from->x2;
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to->x3 = (float) from->x3;
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}
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inline void vector3_fp64_convert(const vector3_fp32_t* from, vector3_fp64_t* to)
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{
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to->x1 = from->x1;
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to->x2 = from->x2;
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to->x3 = from->x3;
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}
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// ==================== Swap ==================== //
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inline void vector3_swap_fp32(vector3_fp32_t* vector1, vector3_fp32_t* vector2)
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{
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const float x1 = vector2->x1;
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const float x2 = vector2->x2;
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const float x3 = vector2->x3;
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vector2->x1 = vector1->x1;
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vector2->x2 = vector1->x2;
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vector2->x3 = vector1->x3;
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vector1->x1 = x1;
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vector1->x2 = x2;
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vector1->x3 = x3;
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}
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inline void vector3_swap_fp64(vector3_fp64_t* vector1, vector3_fp64_t* vector2)
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{
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const double x1 = vector2->x1;
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const double x2 = vector2->x2;
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const double x3 = vector2->x3;
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vector2->x1 = vector1->x1;
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vector2->x2 = vector1->x2;
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vector2->x3 = vector1->x3;
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vector1->x1 = x1;
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vector1->x2 = x2;
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vector1->x3 = x3;
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}
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// ==================== Invert ================== //
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inline void vector3_invert_fp32(vector3_fp32_t* vector)
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{
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vector->x1 = -vector->x1;
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vector->x2 = -vector->x2;
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vector->x3 = -vector->x3;
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}
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inline void vector3_invert_fp64(vector3_fp64_t* vector)
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{
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vector->x1 = -vector->x1;
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vector->x2 = -vector->x2;
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vector->x3 = -vector->x3;
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}
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// ================ Make Inverted =============== //
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inline void vector3_fp32_make_inverted(const vector3_fp32_t* vector, vector3_fp32_t* result)
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{
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result->x1 = -vector->x1;
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result->x2 = -vector->x2;
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result->x3 = -vector->x3;
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}
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inline void vector3_fp64_make_inverted(const vector3_fp64_t* vector, vector3_fp64_t* result)
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{
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result->x1 = -vector->x1;
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result->x2 = -vector->x2;
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result->x3 = -vector->x3;
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}
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// ============== Make Inverted Twin ============ //
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inline void vector3_fp32_make_inverted_fp64(const vector3_fp32_t* vector, vector3_fp64_t* result)
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{
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result->x1 = -vector->x1;
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result->x2 = -vector->x2;
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result->x3 = -vector->x3;
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}
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inline void vector3_fp64_make_inverted_fp32(const vector3_fp64_t* vector, vector3_fp32_t* result)
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{
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result->x1 = (float) -vector->x1;
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result->x2 = (float) -vector->x2;
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result->x3 = (float) -vector->x3;
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}
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// =================== Module =================== //
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inline float vector3_get_square_modulus_fp32(const vector3_fp32_t* vector)
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{
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return vector->x1 * vector->x1 + vector->x2 * vector->x2 + vector->x3 * vector->x3;
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}
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inline double vector3_get_square_modulus_fp64(const vector3_fp64_t* vector)
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{
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return vector->x1 * vector->x1 + vector->x2 * vector->x2 + vector->x3 * vector->x3;
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}
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inline float vector3_get_modulus_fp32(const vector3_fp32_t* vector)
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{
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return sqrtf(vector3_get_square_modulus_fp32(vector));
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}
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inline double vector3_get_modulus_fp64(const vector3_fp64_t* vector)
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{
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return sqrt(vector3_get_square_modulus_fp64(vector));
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}
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// ================= Comparison ================= //
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inline int vector3_fp32_is_zero(const vector3_fp32_t* vector)
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{
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return vector3_get_square_modulus_fp32(vector) <= FP32_SQUARE_EPSYLON;
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}
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inline int vector3_fp64_is_zero(const vector3_fp64_t* vector)
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{
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return vector3_get_square_modulus_fp64(vector) <= FP64_SQUARE_EPSYLON;
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}
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inline int vector3_fp32_is_unit(const vector3_fp32_t* vector)
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{
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const float square_modulus = vector3_get_square_modulus_fp32(vector);
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return 1.0f - FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + FP32_TWO_EPSYLON;
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}
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inline int vector3_fp64_is_unit(const vector3_fp64_t* vector)
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{
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const double square_modulus = vector3_get_square_modulus_fp64(vector);
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return 1.0f - FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + FP64_TWO_EPSYLON;
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}
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// ==================== Add ===================== //
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inline void vector3_fp32_add(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, vector3_fp32_t* sum)
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{
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sum->x1 = vector1->x1 + vector2->x1;
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sum->x2 = vector1->x2 + vector2->x2;
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sum->x3 = vector1->x3 + vector2->x3;
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}
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inline void vector3_fp64_add(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, vector3_fp64_t* sum)
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{
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sum->x1 = vector1->x1 + vector2->x1;
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sum->x2 = vector1->x2 + vector2->x2;
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sum->x3 = vector1->x3 + vector2->x3;
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}
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// ================ Subtraction ================= //
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inline void vector3_fp32_subtract(const vector3_fp32_t* minuend, const vector3_fp32_t* subtrahend, vector3_fp32_t* difference)
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{
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difference->x1 = minuend->x1 - subtrahend->x1;
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difference->x2 = minuend->x2 - subtrahend->x2;
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difference->x3 = minuend->x3 - subtrahend->x3;
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}
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inline void vector3_fp64_subtract(const vector3_fp64_t* minuend, const vector3_fp64_t* subtrahend, vector3_fp64_t* difference)
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{
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difference->x1 = minuend->x1 - subtrahend->x1;
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difference->x2 = minuend->x2 - subtrahend->x2;
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difference->x3 = minuend->x3 - subtrahend->x3;
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}
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// =============== Multiplication =============== //
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inline void vector3_fp32_multiply(const vector3_fp32_t* multiplicand, const float multiplier, vector3_fp32_t* product)
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{
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product->x1 = multiplicand->x1 * multiplier;
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product->x2 = multiplicand->x2 * multiplier;
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product->x3 = multiplicand->x3 * multiplier;
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}
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inline void vector3_fp64_multiply(const vector3_fp64_t* multiplicand, const double multiplier, vector3_fp64_t* product)
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{
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product->x1 = multiplicand->x1 * multiplier;
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product->x2 = multiplicand->x2 * multiplier;
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product->x3 = multiplicand->x3 * multiplier;
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}
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// ================== Division ================== //
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inline void vector3_fp32_divide(const vector3_fp32_t* dividend, const float divisor, vector3_fp32_t* quotient)
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{
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vector3_fp32_multiply(dividend, 1.0f / divisor, quotient);
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}
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inline void vector3_fp64_divide(const vector3_fp64_t* dividend, const double divisor, vector3_fp64_t* quotient)
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{
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vector3_fp64_multiply(dividend, 1.0 / divisor, quotient);
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}
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// ================ Append scaled =============== //
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inline void vector3_fp32_append_scaled(vector3_fp32_t* basic_vector, const vector3_fp32_t* scalable_vector, const float scale)
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{
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basic_vector->x1 += scalable_vector->x1 * scale;
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basic_vector->x2 += scalable_vector->x2 * scale;
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basic_vector->x3 += scalable_vector->x3 * scale;
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}
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inline void vector3_fp64_append_scaled(vector3_fp64_t* basic_vector, const vector3_fp64_t* scalable_vector, const double scale)
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{
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basic_vector->x1 += scalable_vector->x1 * scale;
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basic_vector->x2 += scalable_vector->x2 * scale;
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basic_vector->x3 += scalable_vector->x3 * scale;
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}
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// ================== Average2 ================== //
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inline void vector3_fp32_get_mean2(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, vector3_fp32_t* result)
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{
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result->x1 = (vector1->x1 + vector2->x1) * 0.5f;
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result->x2 = (vector1->x2 + vector2->x2) * 0.5f;
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result->x3 = (vector1->x3 + vector2->x3) * 0.5f;
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}
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inline void vector3_fp64_get_mean2(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, vector3_fp64_t* result)
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{
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result->x1 = (vector1->x1 + vector2->x1) * 0.5;
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result->x2 = (vector1->x2 + vector2->x2) * 0.5;
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result->x3 = (vector1->x3 + vector2->x3) * 0.5;
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}
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// ================== Average3 ================== //
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inline void vector3_fp32_get_mean3(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, const vector3_fp32_t* vector3, vector3_fp32_t* result)
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{
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result->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * FP32_ONE_THIRD;
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result->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * FP32_ONE_THIRD;
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result->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * FP32_ONE_THIRD;
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}
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inline void vector3_fp64_get_mean3(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, const vector3_fp64_t* vector3, vector3_fp64_t* result)
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{
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result->x1 = (vector1->x1 + vector2->x1 + vector3->x1) * FP64_ONE_THIRD;
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result->x2 = (vector1->x2 + vector2->x2 + vector3->x2) * FP64_ONE_THIRD;
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result->x3 = (vector1->x3 + vector2->x3 + vector3->x3) * FP64_ONE_THIRD;
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}
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// =============== Scalar Product =============== //
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inline float vector3_fp32_scalar_product(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2)
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{
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return vector1->x1 * vector2->x1 + vector1->x2 * vector2->x2 + vector1->x3 * vector2->x3;
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}
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inline double vector3_fp64_scalar_product(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2)
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{
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return vector1->x1 * vector2->x1 + vector1->x2 * vector2->x2 + vector1->x3 * vector2->x3;
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}
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// =============== Triple Product =============== //
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inline float vector3_fp32_triple_product(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, const vector3_fp32_t* vector3)
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{
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return vector1->x1 * (vector2->x2 * vector3->x3 - vector2->x3 * vector3->x2)
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+ vector1->x2 * (vector2->x3 * vector3->x1 - vector2->x1 * vector3->x3)
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+ vector1->x3 * (vector2->x1 * vector3->x2 - vector2->x2 * vector3->x1);
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}
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inline double vector3_fp64_triple_product(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, const vector3_fp64_t* vector3)
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{
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return vector1->x1 * (vector2->x2 * vector3->x3 - vector2->x3 * vector3->x2)
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+ vector1->x2 * (vector2->x3 * vector3->x1 - vector2->x1 * vector3->x3)
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+ vector1->x3 * (vector2->x1 * vector3->x2 - vector2->x2 * vector3->x1);
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}
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// =============== Cross Product ================ //
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inline void vector3_fp32_cross_product(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, vector3_fp32_t* result)
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{
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const float x1 = vector1->x2 * vector2->x3 - vector1->x3 * vector2->x2;
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const float x2 = vector1->x3 * vector2->x1 - vector1->x1 * vector2->x3;
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const float x3 = vector1->x1 * vector2->x2 - vector1->x2 * vector2->x1;
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result->x1 = x1;
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result->x2 = x2;
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result->x3 = x3;
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}
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inline void vector3_fp64_cross_product(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, vector3_fp64_t* result)
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{
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const double x1 = vector1->x2 * vector2->x3 - vector1->x3 * vector2->x2;
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const double x2 = vector1->x3 * vector2->x1 - vector1->x1 * vector2->x3;
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const double x3 = vector1->x1 * vector2->x2 - vector1->x2 * vector2->x1;
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result->x1 = x1;
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result->x2 = x2;
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result->x3 = x3;
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}
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// ============ Double Cross Product ============ //
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inline void vector3_fp32_double_cross_product(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, const vector3_fp32_t* vector3, vector3_fp32_t* result)
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{
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const float ac = vector3_fp32_scalar_product(vector1, vector3);
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const float ab = vector3_fp32_scalar_product(vector1, vector2);
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result->x1 = vector2->x1 * ac - vector3->x1 * ab;
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result->x2 = vector2->x2 * ac - vector3->x2 * ab;
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result->x3 = vector2->x3 * ac - vector3->x3 * ab;
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}
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inline void vector3_fp64_double_cross(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, const vector3_fp64_t* vector3, vector3_fp64_t* result)
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{
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const double ac = vector3_fp64_scalar_product(vector1, vector3);
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const double ab = vector3_fp64_scalar_product(vector1, vector2);
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result->x1 = vector2->x1 * ac - vector3->x1 * ab;
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result->x2 = vector2->x2 * ac - vector3->x2 * ab;
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result->x3 = vector2->x3 * ac - vector3->x3 * ab;
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}
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// =============== Normalization ================ //
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inline int vector3_fp32_normalize(vector3_fp32_t* vector)
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{
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const float square_modulus = vector3_get_square_modulus_fp32(vector);
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|
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if (1.0f - FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + FP32_TWO_EPSYLON) {
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return 1;
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}
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|
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if (square_modulus <= FP32_SQUARE_EPSYLON) {
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vector3_reset_fp32(vector);
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return 0;
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}
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|
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vector3_fp32_multiply(vector, sqrtf(1.0f / square_modulus), vector);
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return 1;
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}
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|
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inline int vector3_fp64_normalize(vector3_fp64_t* vector)
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|
{
|
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const double square_modulus = vector3_get_square_modulus_fp64(vector);
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|
|
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if (1.0 - FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + FP64_TWO_EPSYLON) {
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return 1;
|
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}
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|
|
|
if (square_modulus <= FP64_SQUARE_EPSYLON) {
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|
vector3_reset_fp64(vector);
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return 0;
|
|
}
|
|
|
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vector3_fp64_multiply(vector, sqrt(1.0 / square_modulus), vector);
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return 1;
|
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}
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|
|
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// =============== Get Normalized =============== //
|
|
|
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inline int vector3_fp32_set_normalized(const vector3_fp32_t* vector, vector3_fp32_t* result)
|
|
{
|
|
vector3_copy_fp32(vector, result);
|
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return vector3_fp32_normalize(result);
|
|
}
|
|
|
|
inline int vector3_fp64_set_normalized(const vector3_fp64_t* vector, vector3_fp64_t* result)
|
|
{
|
|
vector3_copy_fp64(vector, result);
|
|
return vector3_fp64_normalize(result);
|
|
}
|
|
|
|
// =================== Angle ==================== //
|
|
|
|
float vector3_fp32_get_angle(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2, const angle_unit_t unit);
|
|
|
|
double vector3_fp64_get_angle(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2, const angle_unit_t unit);
|
|
|
|
// =============== Square Distance ============== //
|
|
|
|
inline float vector3_fp32_get_square_distance(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2)
|
|
{
|
|
const float dx1 = (vector1->x1 - vector2->x1);
|
|
const float dx2 = (vector1->x2 - vector2->x2);
|
|
const float dx3 = (vector1->x3 - vector2->x3);
|
|
|
|
return dx1 * dx1 + dx2 * dx2 + dx3 * dx3;
|
|
}
|
|
|
|
inline double vector3_fp64_get_square_distance(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2)
|
|
{
|
|
const double dx1 = (vector1->x1 - vector2->x1);
|
|
const double dx2 = (vector1->x2 - vector2->x2);
|
|
const double dx3 = (vector1->x3 - vector2->x3);
|
|
|
|
return dx1 * dx1 + dx2 * dx2 + dx3 * dx3;
|
|
}
|
|
|
|
// ================== Distance ================== //
|
|
|
|
inline float vector3_fp32_get_distance(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2)
|
|
{
|
|
return sqrtf(vector3_fp32_get_square_distance(vector1, vector2));
|
|
}
|
|
|
|
inline double vector3_fp64_get_distance(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2)
|
|
{
|
|
return sqrt(vector3_fp64_get_square_distance(vector1, vector2));
|
|
}
|
|
|
|
// ================== Are Equal ================= //
|
|
|
|
inline int vector3_fp32_are_equal(const vector3_fp32_t* vector1, const vector3_fp32_t* vector2)
|
|
{
|
|
const float square_modulus1 = vector3_get_square_modulus_fp32(vector1);
|
|
const float square_modulus2 = vector3_get_square_modulus_fp32(vector2);
|
|
const float square_modulus3 = vector3_fp32_get_square_distance(vector1, vector2);
|
|
|
|
// 3.0f means dimension amount
|
|
if (square_modulus1 < FP32_EPSYLON_EFFECTIVENESS_LIMIT || square_modulus2 < FP32_EPSYLON_EFFECTIVENESS_LIMIT) {
|
|
return square_modulus3 < (3.0f * FP32_SQUARE_EPSYLON);
|
|
}
|
|
|
|
if (square_modulus1 <= square_modulus2) {
|
|
return square_modulus3 <= (3.0f * FP32_SQUARE_EPSYLON) * square_modulus2;
|
|
}
|
|
|
|
return square_modulus3 <= (3.0f * FP32_SQUARE_EPSYLON) * square_modulus1;
|
|
}
|
|
|
|
inline int vector3_fp64_are_equal(const vector3_fp64_t* vector1, const vector3_fp64_t* vector2)
|
|
{
|
|
const double square_modulus1 = vector3_get_square_modulus_fp64(vector1);
|
|
const double square_modulus2 = vector3_get_square_modulus_fp64(vector2);
|
|
const double square_modulus3 = vector3_fp64_get_square_distance(vector1, vector2);
|
|
|
|
// 3.0 means dimension amount
|
|
if (square_modulus1 < FP64_EPSYLON_EFFECTIVENESS_LIMIT || square_modulus2 < FP64_EPSYLON_EFFECTIVENESS_LIMIT) {
|
|
return square_modulus3 < (3.0 * FP64_SQUARE_EPSYLON);
|
|
}
|
|
|
|
if (square_modulus1 <= square_modulus2) {
|
|
return square_modulus3 <= (3.0 * FP64_SQUARE_EPSYLON) * square_modulus2;
|
|
}
|
|
|
|
return square_modulus3 <= (3.0 * FP64_SQUARE_EPSYLON) * square_modulus1;
|
|
}
|
|
|
|
#endif
|