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godot/core/math/vector3.h

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/*************************************************************************/
/* vector3.h */
/*************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/*************************************************************************/
/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
/* */
/* Permission is hereby granted, free of charge, to any person obtaining */
/* a copy of this software and associated documentation files (the */
/* "Software"), to deal in the Software without restriction, including */
/* without limitation the rights to use, copy, modify, merge, publish, */
/* distribute, sublicense, and/or sell copies of the Software, and to */
/* permit persons to whom the Software is furnished to do so, subject to */
/* the following conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
/*************************************************************************/
#ifndef VECTOR3_H
#define VECTOR3_H
#include "core/error/error_macros.h"
#include "core/math/math_funcs.h"
class String;
struct Basis;
struct Vector2;
struct Vector3i;
struct _NO_DISCARD_ Vector3 {
static const int AXIS_COUNT = 3;
enum Axis {
AXIS_X,
AXIS_Y,
AXIS_Z,
};
union {
struct {
real_t x;
real_t y;
real_t z;
};
real_t coord[3] = { 0 };
};
_FORCE_INLINE_ const real_t &operator[](const int p_axis) const {
DEV_ASSERT((unsigned int)p_axis < 3);
return coord[p_axis];
}
_FORCE_INLINE_ real_t &operator[](const int p_axis) {
DEV_ASSERT((unsigned int)p_axis < 3);
return coord[p_axis];
}
_FORCE_INLINE_ Vector3::Axis min_axis_index() const {
return x < y ? (x < z ? Vector3::AXIS_X : Vector3::AXIS_Z) : (y < z ? Vector3::AXIS_Y : Vector3::AXIS_Z);
}
_FORCE_INLINE_ Vector3::Axis max_axis_index() const {
return x < y ? (y < z ? Vector3::AXIS_Z : Vector3::AXIS_Y) : (x < z ? Vector3::AXIS_Z : Vector3::AXIS_X);
}
_FORCE_INLINE_ real_t length() const;
_FORCE_INLINE_ real_t length_squared() const;
_FORCE_INLINE_ void normalize();
_FORCE_INLINE_ Vector3 normalized() const;
_FORCE_INLINE_ bool is_normalized() const;
_FORCE_INLINE_ Vector3 inverse() const;
Vector3 limit_length(const real_t p_len = 1.0) const;
_FORCE_INLINE_ void zero();
void snap(const Vector3 p_val);
Vector3 snapped(const Vector3 p_val) const;
void rotate(const Vector3 &p_axis, const real_t p_angle);
Vector3 rotated(const Vector3 &p_axis, const real_t p_angle) const;
/* Static Methods between 2 vector3s */
_FORCE_INLINE_ Vector3 lerp(const Vector3 &p_to, const real_t p_weight) const;
_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, const real_t p_weight) const;
_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const;
_FORCE_INLINE_ Vector3 cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
Vector2 octahedron_encode() const;
static Vector3 octahedron_decode(const Vector2 &p_oct);
Vector2 octahedron_tangent_encode(const float sign) const;
static Vector3 octahedron_tangent_decode(const Vector2 &p_oct, float *sign);
_FORCE_INLINE_ Vector3 cross(const Vector3 &p_with) const;
_FORCE_INLINE_ real_t dot(const Vector3 &p_with) const;
Basis outer(const Vector3 &p_with) const;
_FORCE_INLINE_ Vector3 abs() const;
_FORCE_INLINE_ Vector3 floor() const;
_FORCE_INLINE_ Vector3 sign() const;
_FORCE_INLINE_ Vector3 ceil() const;
_FORCE_INLINE_ Vector3 round() const;
Vector3 clamp(const Vector3 &p_min, const Vector3 &p_max) const;
_FORCE_INLINE_ real_t distance_to(const Vector3 &p_to) const;
_FORCE_INLINE_ real_t distance_squared_to(const Vector3 &p_to) const;
_FORCE_INLINE_ Vector3 posmod(const real_t p_mod) const;
_FORCE_INLINE_ Vector3 posmodv(const Vector3 &p_modv) const;
_FORCE_INLINE_ Vector3 project(const Vector3 &p_to) const;
_FORCE_INLINE_ real_t angle_to(const Vector3 &p_to) const;
_FORCE_INLINE_ real_t signed_angle_to(const Vector3 &p_to, const Vector3 &p_axis) const;
_FORCE_INLINE_ Vector3 direction_to(const Vector3 &p_to) const;
_FORCE_INLINE_ Vector3 slide(const Vector3 &p_normal) const;
_FORCE_INLINE_ Vector3 bounce(const Vector3 &p_normal) const;
_FORCE_INLINE_ Vector3 reflect(const Vector3 &p_normal) const;
bool is_equal_approx(const Vector3 &p_v) const;
bool is_zero_approx() const;
bool is_finite() const;
/* Operators */
_FORCE_INLINE_ Vector3 &operator+=(const Vector3 &p_v);
_FORCE_INLINE_ Vector3 operator+(const Vector3 &p_v) const;
_FORCE_INLINE_ Vector3 &operator-=(const Vector3 &p_v);
_FORCE_INLINE_ Vector3 operator-(const Vector3 &p_v) const;
_FORCE_INLINE_ Vector3 &operator*=(const Vector3 &p_v);
_FORCE_INLINE_ Vector3 operator*(const Vector3 &p_v) const;
_FORCE_INLINE_ Vector3 &operator/=(const Vector3 &p_v);
_FORCE_INLINE_ Vector3 operator/(const Vector3 &p_v) const;
_FORCE_INLINE_ Vector3 &operator*=(const real_t p_scalar);
_FORCE_INLINE_ Vector3 operator*(const real_t p_scalar) const;
_FORCE_INLINE_ Vector3 &operator/=(const real_t p_scalar);
_FORCE_INLINE_ Vector3 operator/(const real_t p_scalar) const;
_FORCE_INLINE_ Vector3 operator-() const;
_FORCE_INLINE_ bool operator==(const Vector3 &p_v) const;
_FORCE_INLINE_ bool operator!=(const Vector3 &p_v) const;
_FORCE_INLINE_ bool operator<(const Vector3 &p_v) const;
_FORCE_INLINE_ bool operator<=(const Vector3 &p_v) const;
_FORCE_INLINE_ bool operator>(const Vector3 &p_v) const;
_FORCE_INLINE_ bool operator>=(const Vector3 &p_v) const;
operator String() const;
operator Vector3i() const;
_FORCE_INLINE_ Vector3() {}
_FORCE_INLINE_ Vector3(const real_t p_x, const real_t p_y, const real_t p_z) {
x = p_x;
y = p_y;
z = p_z;
}
};
Vector3 Vector3::cross(const Vector3 &p_with) const {
Vector3 ret(
(y * p_with.z) - (z * p_with.y),
(z * p_with.x) - (x * p_with.z),
(x * p_with.y) - (y * p_with.x));
return ret;
}
real_t Vector3::dot(const Vector3 &p_with) const {
return x * p_with.x + y * p_with.y + z * p_with.z;
}
Vector3 Vector3::abs() const {
return Vector3(Math::abs(x), Math::abs(y), Math::abs(z));
}
Vector3 Vector3::sign() const {
return Vector3(SIGN(x), SIGN(y), SIGN(z));
}
Vector3 Vector3::floor() const {
return Vector3(Math::floor(x), Math::floor(y), Math::floor(z));
}
Vector3 Vector3::ceil() const {
return Vector3(Math::ceil(x), Math::ceil(y), Math::ceil(z));
}
Vector3 Vector3::round() const {
return Vector3(Math::round(x), Math::round(y), Math::round(z));
}
Vector3 Vector3::lerp(const Vector3 &p_to, const real_t p_weight) const {
return Vector3(
x + (p_weight * (p_to.x - x)),
y + (p_weight * (p_to.y - y)),
z + (p_weight * (p_to.z - z)));
}
Vector3 Vector3::slerp(const Vector3 &p_to, const real_t p_weight) const {
// This method seems more complicated than it really is, since we write out
// the internals of some methods for efficiency (mainly, checking length).
real_t start_length_sq = length_squared();
real_t end_length_sq = p_to.length_squared();
if (unlikely(start_length_sq == 0.0f || end_length_sq == 0.0f)) {
// Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
return lerp(p_to, p_weight);
}
Vector3 axis = cross(p_to);
real_t axis_length_sq = axis.length_squared();
if (unlikely(axis_length_sq == 0.0f)) {
// Colinear vectors have no rotation axis or angle between them, so the best we can do is lerp.
return lerp(p_to, p_weight);
}
axis /= Math::sqrt(axis_length_sq);
real_t start_length = Math::sqrt(start_length_sq);
real_t result_length = Math::lerp(start_length, Math::sqrt(end_length_sq), p_weight);
real_t angle = angle_to(p_to);
return rotated(axis, angle * p_weight) * (result_length / start_length);
}
Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const {
Vector3 res = *this;
res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
return res;
}
Vector3 Vector3::cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
Vector3 res = *this;
res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
res.z = Math::cubic_interpolate_in_time(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
return res;
}
Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
Vector3 res = *this;
/* Formula from Wikipedia article on Bezier curves. */
real_t omt = (1.0 - p_t);
real_t omt2 = omt * omt;
real_t omt3 = omt2 * omt;
real_t t2 = p_t * p_t;
real_t t3 = t2 * p_t;
return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
}
real_t Vector3::distance_to(const Vector3 &p_to) const {
return (p_to - *this).length();
}
real_t Vector3::distance_squared_to(const Vector3 &p_to) const {
return (p_to - *this).length_squared();
}
Vector3 Vector3::posmod(const real_t p_mod) const {
return Vector3(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod));
}
Vector3 Vector3::posmodv(const Vector3 &p_modv) const {
return Vector3(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y), Math::fposmod(z, p_modv.z));
}
Vector3 Vector3::project(const Vector3 &p_to) const {
return p_to * (dot(p_to) / p_to.length_squared());
}
real_t Vector3::angle_to(const Vector3 &p_to) const {
return Math::atan2(cross(p_to).length(), dot(p_to));
}
real_t Vector3::signed_angle_to(const Vector3 &p_to, const Vector3 &p_axis) const {
Vector3 cross_to = cross(p_to);
real_t unsigned_angle = Math::atan2(cross_to.length(), dot(p_to));
real_t sign = cross_to.dot(p_axis);
return (sign < 0) ? -unsigned_angle : unsigned_angle;
}
Vector3 Vector3::direction_to(const Vector3 &p_to) const {
Vector3 ret(p_to.x - x, p_to.y - y, p_to.z - z);
ret.normalize();
return ret;
}
/* Operators */
Vector3 &Vector3::operator+=(const Vector3 &p_v) {
x += p_v.x;
y += p_v.y;
z += p_v.z;
return *this;
}
Vector3 Vector3::operator+(const Vector3 &p_v) const {
return Vector3(x + p_v.x, y + p_v.y, z + p_v.z);
}
Vector3 &Vector3::operator-=(const Vector3 &p_v) {
x -= p_v.x;
y -= p_v.y;
z -= p_v.z;
return *this;
}
Vector3 Vector3::operator-(const Vector3 &p_v) const {
return Vector3(x - p_v.x, y - p_v.y, z - p_v.z);
}
Vector3 &Vector3::operator*=(const Vector3 &p_v) {
x *= p_v.x;
y *= p_v.y;
z *= p_v.z;
return *this;
}
Vector3 Vector3::operator*(const Vector3 &p_v) const {
return Vector3(x * p_v.x, y * p_v.y, z * p_v.z);
}
Vector3 &Vector3::operator/=(const Vector3 &p_v) {
x /= p_v.x;
y /= p_v.y;
z /= p_v.z;
return *this;
}
Vector3 Vector3::operator/(const Vector3 &p_v) const {
return Vector3(x / p_v.x, y / p_v.y, z / p_v.z);
}
Vector3 &Vector3::operator*=(const real_t p_scalar) {
x *= p_scalar;
y *= p_scalar;
z *= p_scalar;
return *this;
}
// Multiplication operators required to workaround issues with LLVM using implicit conversion
// to Vector3i instead for integers where it should not.
_FORCE_INLINE_ Vector3 operator*(const float p_scalar, const Vector3 &p_vec) {
return p_vec * p_scalar;
}
_FORCE_INLINE_ Vector3 operator*(const double p_scalar, const Vector3 &p_vec) {
return p_vec * p_scalar;
}
_FORCE_INLINE_ Vector3 operator*(const int32_t p_scalar, const Vector3 &p_vec) {
return p_vec * p_scalar;
}
_FORCE_INLINE_ Vector3 operator*(const int64_t p_scalar, const Vector3 &p_vec) {
return p_vec * p_scalar;
}
Vector3 Vector3::operator*(const real_t p_scalar) const {
return Vector3(x * p_scalar, y * p_scalar, z * p_scalar);
}
Vector3 &Vector3::operator/=(const real_t p_scalar) {
x /= p_scalar;
y /= p_scalar;
z /= p_scalar;
return *this;
}
Vector3 Vector3::operator/(const real_t p_scalar) const {
return Vector3(x / p_scalar, y / p_scalar, z / p_scalar);
}
Vector3 Vector3::operator-() const {
return Vector3(-x, -y, -z);
}
bool Vector3::operator==(const Vector3 &p_v) const {
return x == p_v.x && y == p_v.y && z == p_v.z;
}
bool Vector3::operator!=(const Vector3 &p_v) const {
return x != p_v.x || y != p_v.y || z != p_v.z;
}
bool Vector3::operator<(const Vector3 &p_v) const {
if (x == p_v.x) {
if (y == p_v.y) {
return z < p_v.z;
}
return y < p_v.y;
}
return x < p_v.x;
}
bool Vector3::operator>(const Vector3 &p_v) const {
if (x == p_v.x) {
if (y == p_v.y) {
return z > p_v.z;
}
return y > p_v.y;
}
return x > p_v.x;
}
bool Vector3::operator<=(const Vector3 &p_v) const {
if (x == p_v.x) {
if (y == p_v.y) {
return z <= p_v.z;
}
return y < p_v.y;
}
return x < p_v.x;
}
bool Vector3::operator>=(const Vector3 &p_v) const {
if (x == p_v.x) {
if (y == p_v.y) {
return z >= p_v.z;
}
return y > p_v.y;
}
return x > p_v.x;
}
_FORCE_INLINE_ Vector3 vec3_cross(const Vector3 &p_a, const Vector3 &p_b) {
return p_a.cross(p_b);
}
_FORCE_INLINE_ real_t vec3_dot(const Vector3 &p_a, const Vector3 &p_b) {
return p_a.dot(p_b);
}
real_t Vector3::length() const {
real_t x2 = x * x;
real_t y2 = y * y;
real_t z2 = z * z;
return Math::sqrt(x2 + y2 + z2);
}
real_t Vector3::length_squared() const {
real_t x2 = x * x;
real_t y2 = y * y;
real_t z2 = z * z;
return x2 + y2 + z2;
}
void Vector3::normalize() {
real_t lengthsq = length_squared();
if (lengthsq == 0) {
x = y = z = 0;
} else {
real_t length = Math::sqrt(lengthsq);
x /= length;
y /= length;
z /= length;
}
}
Vector3 Vector3::normalized() const {
Vector3 v = *this;
v.normalize();
return v;
}
bool Vector3::is_normalized() const {
// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON);
}
Vector3 Vector3::inverse() const {
return Vector3(1.0f / x, 1.0f / y, 1.0f / z);
}
void Vector3::zero() {
x = y = z = 0;
}
// slide returns the component of the vector along the given plane, specified by its normal vector.
Vector3 Vector3::slide(const Vector3 &p_normal) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 must be normalized.");
#endif
return *this - p_normal * this->dot(p_normal);
}
Vector3 Vector3::bounce(const Vector3 &p_normal) const {
return -reflect(p_normal);
}
Vector3 Vector3::reflect(const Vector3 &p_normal) const {
#ifdef MATH_CHECKS
ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 must be normalized.");
#endif
return 2.0f * p_normal * this->dot(p_normal) - *this;
}
#endif // VECTOR3_H
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