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godot/core/math/vector3.h
Rémi Verschelde d95794ec8a
One Copyright Update to rule them all 
As many open source projects have started doing it, we're removing the
current year from the copyright notice, so that we don't need to bump
it every year.

It seems like only the first year of publication is technically
relevant for copyright notices, and even that seems to be something
that many companies stopped listing altogether (in a version controlled
codebase, the commits are a much better source of date of publication
than a hardcoded copyright statement).

We also now list Godot Engine contributors first as we're collectively
the current maintainers of the project, and we clarify that the
"exclusive" copyright of the co-founders covers the timespan before
opensourcing (their further contributions are included as part of Godot
Engine contributors).

Also fixed "cf." Frenchism - it's meant as "refer to / see".
2023-01-05 13:25:55 +01:00

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/**************************************************************************/
/* vector3.h */
/**************************************************************************/
/* This file is part of: */
/* GODOT ENGINE */
/* https://godotengine.org */
/**************************************************************************/
/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
/* */
/* 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;
_FORCE_INLINE_ Vector3 bezier_derivative(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 {
Vector3 res = *this;
res.x = Math::lerp(res.x, p_to.x, p_weight);
res.y = Math::lerp(res.y, p_to.y, p_weight);
res.z = Math::lerp(res.z, p_to.z, p_weight);
return res;
}
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;
res.x = Math::bezier_interpolate(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
res.y = Math::bezier_interpolate(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
res.z = Math::bezier_interpolate(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
return res;
}
Vector3 Vector3::bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
Vector3 res = *this;
res.x = Math::bezier_derivative(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
res.y = Math::bezier_derivative(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
res.z = Math::bezier_derivative(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
return res;
}
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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