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543 lines
17 KiB
C++
543 lines
17 KiB
C++
/**************************************************************************/
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/* vector3.h */
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/**************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/**************************************************************************/
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#ifndef VECTOR3_H
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#define VECTOR3_H
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#include "core/error/error_macros.h"
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#include "core/math/math_funcs.h"
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#include "core/string/ustring.h"
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struct Basis;
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struct Vector2;
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struct Vector3i;
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struct _NO_DISCARD_ Vector3 {
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static const int AXIS_COUNT = 3;
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enum Axis {
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AXIS_X,
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AXIS_Y,
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AXIS_Z,
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};
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union {
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struct {
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real_t x;
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real_t y;
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real_t z;
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};
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real_t coord[3] = { 0 };
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};
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_FORCE_INLINE_ const real_t &operator[](int p_axis) const {
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DEV_ASSERT((unsigned int)p_axis < 3);
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return coord[p_axis];
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}
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_FORCE_INLINE_ real_t &operator[](int p_axis) {
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DEV_ASSERT((unsigned int)p_axis < 3);
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return coord[p_axis];
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}
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_FORCE_INLINE_ Vector3::Axis min_axis_index() const {
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return x < y ? (x < z ? Vector3::AXIS_X : Vector3::AXIS_Z) : (y < z ? Vector3::AXIS_Y : Vector3::AXIS_Z);
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}
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_FORCE_INLINE_ Vector3::Axis max_axis_index() const {
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return x < y ? (y < z ? Vector3::AXIS_Z : Vector3::AXIS_Y) : (x < z ? Vector3::AXIS_Z : Vector3::AXIS_X);
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}
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Vector3 min(const Vector3 &p_vector3) const {
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return Vector3(MIN(x, p_vector3.x), MIN(y, p_vector3.y), MIN(z, p_vector3.z));
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}
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Vector3 minf(real_t p_scalar) const {
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return Vector3(MIN(x, p_scalar), MIN(y, p_scalar), MIN(z, p_scalar));
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}
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Vector3 max(const Vector3 &p_vector3) const {
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return Vector3(MAX(x, p_vector3.x), MAX(y, p_vector3.y), MAX(z, p_vector3.z));
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}
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Vector3 maxf(real_t p_scalar) const {
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return Vector3(MAX(x, p_scalar), MAX(y, p_scalar), MAX(z, p_scalar));
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}
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_FORCE_INLINE_ real_t length() const;
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_FORCE_INLINE_ real_t length_squared() const;
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_FORCE_INLINE_ void normalize();
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_FORCE_INLINE_ Vector3 normalized() const;
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_FORCE_INLINE_ bool is_normalized() const;
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_FORCE_INLINE_ Vector3 inverse() const;
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Vector3 limit_length(real_t p_len = 1.0) const;
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_FORCE_INLINE_ void zero();
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void snap(const Vector3 &p_step);
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void snapf(real_t p_step);
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Vector3 snapped(const Vector3 &p_step) const;
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Vector3 snappedf(real_t p_step) const;
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void rotate(const Vector3 &p_axis, real_t p_angle);
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Vector3 rotated(const Vector3 &p_axis, real_t p_angle) const;
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/* Static Methods between 2 vector3s */
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_FORCE_INLINE_ Vector3 lerp(const Vector3 &p_to, real_t p_weight) const;
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_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, real_t p_weight) const;
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_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const;
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_FORCE_INLINE_ Vector3 cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const;
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_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const;
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_FORCE_INLINE_ Vector3 bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const;
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Vector3 move_toward(const Vector3 &p_to, real_t p_delta) const;
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Vector2 octahedron_encode() const;
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static Vector3 octahedron_decode(const Vector2 &p_oct);
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Vector2 octahedron_tangent_encode(float p_sign) const;
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static Vector3 octahedron_tangent_decode(const Vector2 &p_oct, float *r_sign);
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_FORCE_INLINE_ Vector3 cross(const Vector3 &p_with) const;
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_FORCE_INLINE_ real_t dot(const Vector3 &p_with) const;
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Basis outer(const Vector3 &p_with) const;
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_FORCE_INLINE_ Vector3 abs() const;
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_FORCE_INLINE_ Vector3 floor() const;
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_FORCE_INLINE_ Vector3 sign() const;
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_FORCE_INLINE_ Vector3 ceil() const;
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_FORCE_INLINE_ Vector3 round() const;
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Vector3 clamp(const Vector3 &p_min, const Vector3 &p_max) const;
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Vector3 clampf(real_t p_min, real_t p_max) const;
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_FORCE_INLINE_ real_t distance_to(const Vector3 &p_to) const;
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_FORCE_INLINE_ real_t distance_squared_to(const Vector3 &p_to) const;
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_FORCE_INLINE_ Vector3 posmod(real_t p_mod) const;
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_FORCE_INLINE_ Vector3 posmodv(const Vector3 &p_modv) const;
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_FORCE_INLINE_ Vector3 project(const Vector3 &p_to) const;
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_FORCE_INLINE_ real_t angle_to(const Vector3 &p_to) const;
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_FORCE_INLINE_ real_t signed_angle_to(const Vector3 &p_to, const Vector3 &p_axis) const;
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_FORCE_INLINE_ Vector3 direction_to(const Vector3 &p_to) const;
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_FORCE_INLINE_ Vector3 slide(const Vector3 &p_normal) const;
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_FORCE_INLINE_ Vector3 bounce(const Vector3 &p_normal) const;
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_FORCE_INLINE_ Vector3 reflect(const Vector3 &p_normal) const;
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bool is_equal_approx(const Vector3 &p_v) const;
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bool is_zero_approx() const;
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bool is_finite() const;
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/* Operators */
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_FORCE_INLINE_ Vector3 &operator+=(const Vector3 &p_v);
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_FORCE_INLINE_ Vector3 operator+(const Vector3 &p_v) const;
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_FORCE_INLINE_ Vector3 &operator-=(const Vector3 &p_v);
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_FORCE_INLINE_ Vector3 operator-(const Vector3 &p_v) const;
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_FORCE_INLINE_ Vector3 &operator*=(const Vector3 &p_v);
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_FORCE_INLINE_ Vector3 operator*(const Vector3 &p_v) const;
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_FORCE_INLINE_ Vector3 &operator/=(const Vector3 &p_v);
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_FORCE_INLINE_ Vector3 operator/(const Vector3 &p_v) const;
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_FORCE_INLINE_ Vector3 &operator*=(real_t p_scalar);
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_FORCE_INLINE_ Vector3 operator*(real_t p_scalar) const;
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_FORCE_INLINE_ Vector3 &operator/=(real_t p_scalar);
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_FORCE_INLINE_ Vector3 operator/(real_t p_scalar) const;
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_FORCE_INLINE_ Vector3 operator-() const;
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_FORCE_INLINE_ bool operator==(const Vector3 &p_v) const;
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_FORCE_INLINE_ bool operator!=(const Vector3 &p_v) const;
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_FORCE_INLINE_ bool operator<(const Vector3 &p_v) const;
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_FORCE_INLINE_ bool operator<=(const Vector3 &p_v) const;
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_FORCE_INLINE_ bool operator>(const Vector3 &p_v) const;
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_FORCE_INLINE_ bool operator>=(const Vector3 &p_v) const;
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operator String() const;
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operator Vector3i() const;
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_FORCE_INLINE_ Vector3() {}
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_FORCE_INLINE_ Vector3(real_t p_x, real_t p_y, real_t p_z) {
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x = p_x;
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y = p_y;
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z = p_z;
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}
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};
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Vector3 Vector3::cross(const Vector3 &p_with) const {
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Vector3 ret(
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(y * p_with.z) - (z * p_with.y),
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(z * p_with.x) - (x * p_with.z),
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(x * p_with.y) - (y * p_with.x));
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return ret;
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}
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real_t Vector3::dot(const Vector3 &p_with) const {
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return x * p_with.x + y * p_with.y + z * p_with.z;
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}
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Vector3 Vector3::abs() const {
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return Vector3(Math::abs(x), Math::abs(y), Math::abs(z));
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}
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Vector3 Vector3::sign() const {
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return Vector3(SIGN(x), SIGN(y), SIGN(z));
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}
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Vector3 Vector3::floor() const {
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return Vector3(Math::floor(x), Math::floor(y), Math::floor(z));
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}
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Vector3 Vector3::ceil() const {
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return Vector3(Math::ceil(x), Math::ceil(y), Math::ceil(z));
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}
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Vector3 Vector3::round() const {
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return Vector3(Math::round(x), Math::round(y), Math::round(z));
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}
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Vector3 Vector3::lerp(const Vector3 &p_to, real_t p_weight) const {
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Vector3 res = *this;
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res.x = Math::lerp(res.x, p_to.x, p_weight);
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res.y = Math::lerp(res.y, p_to.y, p_weight);
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res.z = Math::lerp(res.z, p_to.z, p_weight);
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return res;
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}
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Vector3 Vector3::slerp(const Vector3 &p_to, real_t p_weight) const {
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// This method seems more complicated than it really is, since we write out
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// the internals of some methods for efficiency (mainly, checking length).
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real_t start_length_sq = length_squared();
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real_t end_length_sq = p_to.length_squared();
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if (unlikely(start_length_sq == 0.0f || end_length_sq == 0.0f)) {
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// Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
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return lerp(p_to, p_weight);
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}
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Vector3 axis = cross(p_to);
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real_t axis_length_sq = axis.length_squared();
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if (unlikely(axis_length_sq == 0.0f)) {
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// Colinear vectors have no rotation axis or angle between them, so the best we can do is lerp.
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return lerp(p_to, p_weight);
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}
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axis /= Math::sqrt(axis_length_sq);
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real_t start_length = Math::sqrt(start_length_sq);
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real_t result_length = Math::lerp(start_length, Math::sqrt(end_length_sq), p_weight);
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real_t angle = angle_to(p_to);
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return rotated(axis, angle * p_weight) * (result_length / start_length);
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}
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Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const {
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Vector3 res = *this;
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res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
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res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
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res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
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return res;
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}
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Vector3 Vector3::cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const {
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Vector3 res = *this;
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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);
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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);
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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);
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return res;
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}
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Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const {
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Vector3 res = *this;
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res.x = Math::bezier_interpolate(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
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res.y = Math::bezier_interpolate(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
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res.z = Math::bezier_interpolate(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
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return res;
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}
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Vector3 Vector3::bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const {
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Vector3 res = *this;
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res.x = Math::bezier_derivative(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
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res.y = Math::bezier_derivative(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
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res.z = Math::bezier_derivative(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
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return res;
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}
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real_t Vector3::distance_to(const Vector3 &p_to) const {
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return (p_to - *this).length();
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}
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real_t Vector3::distance_squared_to(const Vector3 &p_to) const {
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return (p_to - *this).length_squared();
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}
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Vector3 Vector3::posmod(real_t p_mod) const {
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return Vector3(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod));
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}
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Vector3 Vector3::posmodv(const Vector3 &p_modv) const {
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return Vector3(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y), Math::fposmod(z, p_modv.z));
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}
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Vector3 Vector3::project(const Vector3 &p_to) const {
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return p_to * (dot(p_to) / p_to.length_squared());
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}
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real_t Vector3::angle_to(const Vector3 &p_to) const {
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return Math::atan2(cross(p_to).length(), dot(p_to));
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}
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real_t Vector3::signed_angle_to(const Vector3 &p_to, const Vector3 &p_axis) const {
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Vector3 cross_to = cross(p_to);
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real_t unsigned_angle = Math::atan2(cross_to.length(), dot(p_to));
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real_t sign = cross_to.dot(p_axis);
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return (sign < 0) ? -unsigned_angle : unsigned_angle;
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}
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Vector3 Vector3::direction_to(const Vector3 &p_to) const {
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Vector3 ret(p_to.x - x, p_to.y - y, p_to.z - z);
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ret.normalize();
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return ret;
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}
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/* Operators */
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Vector3 &Vector3::operator+=(const Vector3 &p_v) {
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x += p_v.x;
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y += p_v.y;
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z += p_v.z;
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return *this;
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}
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Vector3 Vector3::operator+(const Vector3 &p_v) const {
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return Vector3(x + p_v.x, y + p_v.y, z + p_v.z);
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}
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Vector3 &Vector3::operator-=(const Vector3 &p_v) {
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x -= p_v.x;
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y -= p_v.y;
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z -= p_v.z;
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return *this;
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}
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Vector3 Vector3::operator-(const Vector3 &p_v) const {
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return Vector3(x - p_v.x, y - p_v.y, z - p_v.z);
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}
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Vector3 &Vector3::operator*=(const Vector3 &p_v) {
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x *= p_v.x;
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y *= p_v.y;
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z *= p_v.z;
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return *this;
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}
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Vector3 Vector3::operator*(const Vector3 &p_v) const {
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return Vector3(x * p_v.x, y * p_v.y, z * p_v.z);
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}
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Vector3 &Vector3::operator/=(const Vector3 &p_v) {
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x /= p_v.x;
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y /= p_v.y;
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z /= p_v.z;
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return *this;
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}
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Vector3 Vector3::operator/(const Vector3 &p_v) const {
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return Vector3(x / p_v.x, y / p_v.y, z / p_v.z);
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}
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Vector3 &Vector3::operator*=(real_t p_scalar) {
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x *= p_scalar;
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y *= p_scalar;
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z *= p_scalar;
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return *this;
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}
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// Multiplication operators required to workaround issues with LLVM using implicit conversion
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// to Vector3i instead for integers where it should not.
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_FORCE_INLINE_ Vector3 operator*(float p_scalar, const Vector3 &p_vec) {
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return p_vec * p_scalar;
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}
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_FORCE_INLINE_ Vector3 operator*(double p_scalar, const Vector3 &p_vec) {
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return p_vec * p_scalar;
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}
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_FORCE_INLINE_ Vector3 operator*(int32_t p_scalar, const Vector3 &p_vec) {
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return p_vec * p_scalar;
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}
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_FORCE_INLINE_ Vector3 operator*(int64_t p_scalar, const Vector3 &p_vec) {
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return p_vec * p_scalar;
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}
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Vector3 Vector3::operator*(real_t p_scalar) const {
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return Vector3(x * p_scalar, y * p_scalar, z * p_scalar);
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}
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Vector3 &Vector3::operator/=(real_t p_scalar) {
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x /= p_scalar;
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y /= p_scalar;
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z /= p_scalar;
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return *this;
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}
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Vector3 Vector3::operator/(real_t p_scalar) const {
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return Vector3(x / p_scalar, y / p_scalar, z / p_scalar);
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}
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Vector3 Vector3::operator-() const {
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return Vector3(-x, -y, -z);
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}
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|
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bool Vector3::operator==(const Vector3 &p_v) const {
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return x == p_v.x && y == p_v.y && z == p_v.z;
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}
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|
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bool Vector3::operator!=(const Vector3 &p_v) const {
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return x != p_v.x || y != p_v.y || z != p_v.z;
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}
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|
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bool Vector3::operator<(const Vector3 &p_v) const {
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if (x == p_v.x) {
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if (y == p_v.y) {
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return z < p_v.z;
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}
|
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return y < p_v.y;
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}
|
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return x < p_v.x;
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|
}
|
|
|
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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;
|
|
}
|
|
|
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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 " + p_normal.operator String() + " must be normalized.");
|
|
#endif
|
|
return *this - p_normal * 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 " + p_normal.operator String() + " must be normalized.");
|
|
#endif
|
|
return 2.0f * p_normal * dot(p_normal) - *this;
|
|
}
|
|
|
|
#endif // VECTOR3_H
|