2021-09-08 18:11:12 +00:00
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/*************************************************************************/
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/* math.hpp */
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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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2022-03-15 09:17:53 +00:00
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/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md). */
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2021-09-08 18:11:12 +00:00
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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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2022-09-18 22:37:31 +00:00
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#ifndef GODOT_MATH_HPP
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#define GODOT_MATH_HPP
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2021-09-01 03:11:10 +00:00
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#include <godot_cpp/core/defs.hpp>
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#include <godot/gdnative_interface.h>
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#include <cmath>
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namespace godot {
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namespace Math {
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// This epsilon should match the one used by Godot for consistency.
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// Using `f` when `real_t` is float.
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#define CMP_EPSILON 0.00001f
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#define CMP_EPSILON2 (CMP_EPSILON * CMP_EPSILON)
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// This epsilon is for values related to a unit size (scalar or vector len).
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#ifdef PRECISE_MATH_CHECKS
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#define UNIT_EPSILON 0.00001
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#else
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// Tolerate some more floating point error normally.
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#define UNIT_EPSILON 0.001
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#endif
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#define Math_SQRT12 0.7071067811865475244008443621048490
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#define Math_SQRT2 1.4142135623730950488016887242
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#define Math_LN2 0.6931471805599453094172321215
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#define Math_PI 3.1415926535897932384626433833
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#define Math_TAU 6.2831853071795864769252867666
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#define Math_E 2.7182818284590452353602874714
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#define Math_INF INFINITY
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#define Math_NAN NAN
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2022-02-15 10:58:28 +00:00
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// Windows badly defines a lot of stuff we'll never use. Undefine it.
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#ifdef _WIN32
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#undef MIN // override standard definition
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#undef MAX // override standard definition
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#undef CLAMP // override standard definition
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#endif
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// Generic ABS function, for math uses please use Math::abs.
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#ifndef ABS
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#define ABS(m_v) (((m_v) < 0) ? (-(m_v)) : (m_v))
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#endif
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#ifndef SIGN
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#define SIGN(m_v) (((m_v) == 0) ? (0.0) : (((m_v) < 0) ? (-1.0) : (+1.0)))
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#endif
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#ifndef MIN
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#define MIN(m_a, m_b) (((m_a) < (m_b)) ? (m_a) : (m_b))
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#endif
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#ifndef MAX
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#define MAX(m_a, m_b) (((m_a) > (m_b)) ? (m_a) : (m_b))
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#endif
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#ifndef CLAMP
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#define CLAMP(m_a, m_min, m_max) (((m_a) < (m_min)) ? (m_min) : (((m_a) > (m_max)) ? m_max : m_a))
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#endif
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2021-09-01 03:11:10 +00:00
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// Functions reproduced as in Godot's source code `math_funcs.h`.
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// Some are overloads to automatically support changing real_t into either double or float in the way Godot does.
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inline double fmod(double p_x, double p_y) {
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return ::fmod(p_x, p_y);
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}
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inline float fmod(float p_x, float p_y) {
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return ::fmodf(p_x, p_y);
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}
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inline double fposmod(double p_x, double p_y) {
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double value = Math::fmod(p_x, p_y);
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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value += 0.0;
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return value;
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}
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inline float fposmod(float p_x, float p_y) {
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float value = Math::fmod(p_x, p_y);
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if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) {
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value += p_y;
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}
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value += 0.0;
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return value;
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}
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inline float fposmodp(float p_x, float p_y) {
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float value = Math::fmod(p_x, p_y);
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if (value < 0) {
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value += p_y;
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}
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value += 0.0;
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return value;
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}
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inline double fposmodp(double p_x, double p_y) {
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double value = Math::fmod(p_x, p_y);
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if (value < 0) {
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value += p_y;
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}
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value += 0.0;
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return value;
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}
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inline double floor(double p_x) {
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return ::floor(p_x);
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}
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inline float floor(float p_x) {
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return ::floorf(p_x);
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}
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inline double ceil(double p_x) {
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return ::ceil(p_x);
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}
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inline float ceil(float p_x) {
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return ::ceilf(p_x);
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}
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inline double exp(double p_x) {
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return ::exp(p_x);
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}
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inline float exp(float p_x) {
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return ::expf(p_x);
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}
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inline double sin(double p_x) {
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return ::sin(p_x);
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}
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inline float sin(float p_x) {
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return ::sinf(p_x);
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}
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inline double cos(double p_x) {
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return ::cos(p_x);
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}
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inline float cos(float p_x) {
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return ::cosf(p_x);
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}
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inline double tan(double p_x) {
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return ::tan(p_x);
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}
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inline float tan(float p_x) {
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return ::tanf(p_x);
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}
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inline double sinh(double p_x) {
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return ::sinh(p_x);
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}
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inline float sinh(float p_x) {
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return ::sinhf(p_x);
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}
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inline float sinc(float p_x) {
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return p_x == 0 ? 1 : ::sin(p_x) / p_x;
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}
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inline double sinc(double p_x) {
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return p_x == 0 ? 1 : ::sin(p_x) / p_x;
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}
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inline float sincn(float p_x) {
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2021-11-12 10:03:29 +00:00
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return (float)sinc(Math_PI * p_x);
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2021-09-01 03:11:10 +00:00
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}
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inline double sincn(double p_x) {
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return sinc(Math_PI * p_x);
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}
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inline double cosh(double p_x) {
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return ::cosh(p_x);
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}
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inline float cosh(float p_x) {
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return ::coshf(p_x);
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}
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inline double tanh(double p_x) {
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return ::tanh(p_x);
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}
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inline float tanh(float p_x) {
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return ::tanhf(p_x);
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}
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inline double asin(double p_x) {
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return ::asin(p_x);
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}
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inline float asin(float p_x) {
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return ::asinf(p_x);
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}
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inline double acos(double p_x) {
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return ::acos(p_x);
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}
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inline float acos(float p_x) {
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return ::acosf(p_x);
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}
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inline double atan(double p_x) {
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return ::atan(p_x);
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}
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inline float atan(float p_x) {
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return ::atanf(p_x);
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}
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inline double atan2(double p_y, double p_x) {
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return ::atan2(p_y, p_x);
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}
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inline float atan2(float p_y, float p_x) {
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return ::atan2f(p_y, p_x);
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}
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inline double sqrt(double p_x) {
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return ::sqrt(p_x);
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}
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inline float sqrt(float p_x) {
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return ::sqrtf(p_x);
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}
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inline double pow(double p_x, double p_y) {
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return ::pow(p_x, p_y);
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}
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inline float pow(float p_x, float p_y) {
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return ::powf(p_x, p_y);
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}
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inline double log(double p_x) {
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return ::log(p_x);
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}
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inline float log(float p_x) {
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return ::logf(p_x);
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}
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inline float lerp(float minv, float maxv, float t) {
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return minv + t * (maxv - minv);
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}
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inline double lerp(double minv, double maxv, double t) {
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return minv + t * (maxv - minv);
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}
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inline double lerp_angle(double p_from, double p_to, double p_weight) {
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double difference = fmod(p_to - p_from, Math_TAU);
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double distance = fmod(2.0 * difference, Math_TAU) - difference;
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return p_from + distance * p_weight;
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}
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inline float lerp_angle(float p_from, float p_to, float p_weight) {
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float difference = fmod(p_to - p_from, (float)Math_TAU);
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float distance = fmod(2.0f * difference, (float)Math_TAU) - difference;
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return p_from + distance * p_weight;
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}
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2022-07-20 20:49:08 +00:00
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inline double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) {
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return 0.5 *
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((p_from * 2.0) +
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(-p_pre + p_to) * p_weight +
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(2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) +
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(-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight));
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}
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inline float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) {
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return 0.5f *
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((p_from * 2.0f) +
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(-p_pre + p_to) * p_weight +
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(2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) +
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(-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight));
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}
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2021-09-01 03:11:10 +00:00
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template <typename T>
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inline T clamp(T x, T minv, T maxv) {
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if (x < minv) {
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return minv;
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}
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if (x > maxv) {
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return maxv;
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}
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return x;
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}
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template <typename T>
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inline T min(T a, T b) {
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return a < b ? a : b;
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}
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template <typename T>
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inline T max(T a, T b) {
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return a > b ? a : b;
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}
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template <typename T>
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inline T sign(T x) {
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return static_cast<T>(x < 0 ? -1 : 1);
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}
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template <typename T>
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inline T abs(T x) {
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return std::abs(x);
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}
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inline double deg2rad(double p_y) {
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return p_y * Math_PI / 180.0;
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}
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inline float deg2rad(float p_y) {
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return p_y * static_cast<float>(Math_PI) / 180.f;
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}
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inline double rad2deg(double p_y) {
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return p_y * 180.0 / Math_PI;
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}
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inline float rad2deg(float p_y) {
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return p_y * 180.f / static_cast<float>(Math_PI);
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}
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inline double inverse_lerp(double p_from, double p_to, double p_value) {
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return (p_value - p_from) / (p_to - p_from);
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}
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inline float inverse_lerp(float p_from, float p_to, float p_value) {
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return (p_value - p_from) / (p_to - p_from);
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}
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inline double range_lerp(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) {
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return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
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}
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inline float range_lerp(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) {
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return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value));
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}
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2022-08-24 12:28:44 +00:00
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inline bool is_nan(float p_val) {
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return std::isnan(p_val);
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}
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inline bool is_nan(double p_val) {
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return std::isnan(p_val);
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}
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inline bool is_inf(float p_val) {
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return std::isinf(p_val);
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}
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inline bool is_inf(double p_val) {
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return std::isinf(p_val);
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}
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2022-09-18 22:37:31 +00:00
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inline bool is_equal_approx(float a, float b) {
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2021-09-01 03:11:10 +00:00
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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2022-09-18 22:37:31 +00:00
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float tolerance = (float)CMP_EPSILON * abs(a);
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if (tolerance < (float)CMP_EPSILON) {
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tolerance = (float)CMP_EPSILON;
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}
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return abs(a - b) < tolerance;
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}
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inline bool is_equal_approx(float a, float b, float tolerance) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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return abs(a - b) < tolerance;
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}
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inline bool is_zero_approx(float s) {
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return abs(s) < (float)CMP_EPSILON;
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}
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inline bool is_equal_approx(double a, double b) {
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// Check for exact equality first, required to handle "infinity" values.
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if (a == b) {
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return true;
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}
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// Then check for approximate equality.
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double tolerance = CMP_EPSILON * abs(a);
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2021-09-01 03:11:10 +00:00
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if (tolerance < CMP_EPSILON) {
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tolerance = CMP_EPSILON;
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}
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2022-09-18 22:37:31 +00:00
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return abs(a - b) < tolerance;
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2021-09-01 03:11:10 +00:00
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}
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|
2022-09-18 22:37:31 +00:00
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inline bool is_equal_approx(double a, double b, double tolerance) {
|
2021-09-01 03:11:10 +00:00
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// Check for exact equality first, required to handle "infinity" values.
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|
if (a == b) {
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return true;
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}
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// Then check for approximate equality.
|
2022-09-18 22:37:31 +00:00
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return abs(a - b) < tolerance;
|
2021-09-01 03:11:10 +00:00
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}
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|
2022-09-18 22:37:31 +00:00
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inline bool is_zero_approx(double s) {
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return abs(s) < CMP_EPSILON;
|
2021-09-01 03:11:10 +00:00
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|
}
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inline double smoothstep(double p_from, double p_to, double p_weight) {
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if (is_equal_approx(static_cast<real_t>(p_from), static_cast<real_t>(p_to))) {
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|
return p_from;
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|
}
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double x = clamp((p_weight - p_from) / (p_to - p_from), 0.0, 1.0);
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return x * x * (3.0 - 2.0 * x);
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}
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|
inline float smoothstep(float p_from, float p_to, float p_weight) {
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|
|
if (is_equal_approx(p_from, p_to)) {
|
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|
|
return p_from;
|
|
|
|
}
|
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|
|
float x = clamp((p_weight - p_from) / (p_to - p_from), 0.0f, 1.0f);
|
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|
|
return x * x * (3.0f - 2.0f * x);
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|
}
|
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|
inline double move_toward(double p_from, double p_to, double p_delta) {
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|
return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta;
|
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|
}
|
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|
|
inline float move_toward(float p_from, float p_to, float p_delta) {
|
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|
|
return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta;
|
|
|
|
}
|
|
|
|
|
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|
|
inline double linear2db(double p_linear) {
|
|
|
|
return log(p_linear) * 8.6858896380650365530225783783321;
|
|
|
|
}
|
|
|
|
inline float linear2db(float p_linear) {
|
|
|
|
return log(p_linear) * 8.6858896380650365530225783783321f;
|
|
|
|
}
|
|
|
|
|
|
|
|
inline double db2linear(double p_db) {
|
|
|
|
return exp(p_db * 0.11512925464970228420089957273422);
|
|
|
|
}
|
|
|
|
inline float db2linear(float p_db) {
|
|
|
|
return exp(p_db * 0.11512925464970228420089957273422f);
|
|
|
|
}
|
|
|
|
|
|
|
|
inline double round(double p_val) {
|
|
|
|
return (p_val >= 0) ? floor(p_val + 0.5) : -floor(-p_val + 0.5);
|
|
|
|
}
|
|
|
|
inline float round(float p_val) {
|
|
|
|
return (p_val >= 0) ? floor(p_val + 0.5f) : -floor(-p_val + 0.5f);
|
|
|
|
}
|
|
|
|
|
|
|
|
inline int64_t wrapi(int64_t value, int64_t min, int64_t max) {
|
|
|
|
int64_t range = max - min;
|
|
|
|
return range == 0 ? min : min + ((((value - min) % range) + range) % range);
|
|
|
|
}
|
|
|
|
|
|
|
|
inline float wrapf(real_t value, real_t min, real_t max) {
|
|
|
|
const real_t range = max - min;
|
|
|
|
return is_zero_approx(range) ? min : value - (range * floor((value - min) / range));
|
|
|
|
}
|
|
|
|
|
|
|
|
inline float stepify(float p_value, float p_step) {
|
|
|
|
if (p_step != 0) {
|
|
|
|
p_value = floor(p_value / p_step + 0.5f) * p_step;
|
|
|
|
}
|
|
|
|
return p_value;
|
|
|
|
}
|
|
|
|
inline double stepify(double p_value, double p_step) {
|
|
|
|
if (p_step != 0) {
|
|
|
|
p_value = floor(p_value / p_step + 0.5) * p_step;
|
|
|
|
}
|
|
|
|
return p_value;
|
|
|
|
}
|
|
|
|
|
|
|
|
inline unsigned int next_power_of_2(unsigned int x) {
|
|
|
|
if (x == 0)
|
|
|
|
return 0;
|
|
|
|
|
|
|
|
--x;
|
|
|
|
x |= x >> 1;
|
|
|
|
x |= x >> 2;
|
|
|
|
x |= x >> 4;
|
|
|
|
x |= x >> 8;
|
|
|
|
x |= x >> 16;
|
|
|
|
|
|
|
|
return ++x;
|
|
|
|
}
|
|
|
|
|
|
|
|
// This function should be as fast as possible and rounding mode should not matter.
|
|
|
|
inline int fast_ftoi(float a) {
|
|
|
|
static int b;
|
|
|
|
|
|
|
|
#if (defined(_WIN32_WINNT) && _WIN32_WINNT >= 0x0603) || WINAPI_FAMILY == WINAPI_FAMILY_PHONE_APP // windows 8 phone?
|
|
|
|
b = (int)((a > 0.0) ? (a + 0.5) : (a - 0.5));
|
|
|
|
|
|
|
|
#elif defined(_MSC_VER) && _MSC_VER < 1800
|
|
|
|
__asm fld a __asm fistp b
|
|
|
|
/*#elif defined( __GNUC__ ) && ( defined( __i386__ ) || defined( __x86_64__ ) )
|
|
|
|
// use AT&T inline assembly style, document that
|
|
|
|
// we use memory as output (=m) and input (m)
|
|
|
|
__asm__ __volatile__ (
|
|
|
|
"flds %1 \n\t"
|
|
|
|
"fistpl %0 \n\t"
|
|
|
|
: "=m" (b)
|
|
|
|
: "m" (a));*/
|
|
|
|
|
|
|
|
#else
|
2022-02-15 10:58:28 +00:00
|
|
|
b = lrintf(a); // assuming everything but msvc 2012 or earlier has lrint
|
2021-09-01 03:11:10 +00:00
|
|
|
#endif
|
|
|
|
return b;
|
|
|
|
}
|
|
|
|
|
|
|
|
inline double snapped(double p_value, double p_step) {
|
|
|
|
if (p_step != 0) {
|
|
|
|
p_value = Math::floor(p_value / p_step + 0.5) * p_step;
|
|
|
|
}
|
|
|
|
return p_value;
|
|
|
|
}
|
|
|
|
|
|
|
|
} // namespace Math
|
|
|
|
} // namespace godot
|
|
|
|
|
2022-09-18 22:37:31 +00:00
|
|
|
#endif // GODOT_MATH_HPP
|