/**************************************************************************/ /* math.hpp */ /**************************************************************************/ /* 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 GODOT_MATH_HPP #define GODOT_MATH_HPP #include #include #include namespace godot { #define Math_SQRT12 0.7071067811865475244008443621048490 #define Math_SQRT2 1.4142135623730950488016887242 #define Math_LN2 0.6931471805599453094172321215 #define Math_PI 3.1415926535897932384626433833 #define Math_TAU 6.2831853071795864769252867666 #define Math_E 2.7182818284590452353602874714 #define Math_INF INFINITY #define Math_NAN NAN // Make room for our constexpr's below by overriding potential system-specific macros. #undef ABS #undef SIGN #undef MIN #undef MAX #undef CLAMP // Generic ABS function, for math uses please use Math::abs. template constexpr T ABS(T m_v) { return m_v < 0 ? -m_v : m_v; } template constexpr const T SIGN(const T m_v) { return m_v == 0 ? 0.0f : (m_v < 0 ? -1.0f : +1.0f); } template constexpr auto MIN(const T m_a, const T2 m_b) { return m_a < m_b ? m_a : m_b; } template constexpr auto MAX(const T m_a, const T2 m_b) { return m_a > m_b ? m_a : m_b; } template constexpr auto CLAMP(const T m_a, const T2 m_min, const T3 m_max) { return m_a < m_min ? m_min : (m_a > m_max ? m_max : m_a); } // Generic swap template. #ifndef SWAP #define SWAP(m_x, m_y) __swap_tmpl((m_x), (m_y)) template inline void __swap_tmpl(T &x, T &y) { T aux = x; x = y; y = aux; } #endif // SWAP /* Functions to handle powers of 2 and shifting. */ // Function to find the next power of 2 to an integer. static _FORCE_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; } // Function to find the previous power of 2 to an integer. static _FORCE_INLINE_ unsigned int previous_power_of_2(unsigned int x) { x |= x >> 1; x |= x >> 2; x |= x >> 4; x |= x >> 8; x |= x >> 16; return x - (x >> 1); } // Function to find the closest power of 2 to an integer. static _FORCE_INLINE_ unsigned int closest_power_of_2(unsigned int x) { unsigned int nx = next_power_of_2(x); unsigned int px = previous_power_of_2(x); return (nx - x) > (x - px) ? px : nx; } // Get a shift value from a power of 2. static inline int get_shift_from_power_of_2(unsigned int p_bits) { for (unsigned int i = 0; i < 32; i++) { if (p_bits == (unsigned int)(1 << i)) { return i; } } return -1; } template static _FORCE_INLINE_ T nearest_power_of_2_templated(T x) { --x; // The number of operations on x is the base two logarithm // of the number of bits in the type. Add three to account // for sizeof(T) being in bytes. size_t num = get_shift_from_power_of_2(sizeof(T)) + 3; // If the compiler is smart, it unrolls this loop. // If it's dumb, this is a bit slow. for (size_t i = 0; i < num; i++) { x |= x >> (1 << i); } return ++x; } // Function to find the nearest (bigger) power of 2 to an integer. static inline unsigned int nearest_shift(unsigned int p_number) { for (int i = 30; i >= 0; i--) { if (p_number & (1 << i)) { return i + 1; } } return 0; } // constexpr function to find the floored log2 of a number template constexpr T floor_log2(T x) { return x < 2 ? x : 1 + floor_log2(x >> 1); } // Get the number of bits needed to represent the number. // IE, if you pass in 8, you will get 4. // If you want to know how many bits are needed to store 8 values however, pass in (8 - 1). template constexpr T get_num_bits(T x) { return floor_log2(x); } // Swap 16, 32 and 64 bits value for endianness. #if defined(__GNUC__) #define BSWAP16(x) __builtin_bswap16(x) #define BSWAP32(x) __builtin_bswap32(x) #define BSWAP64(x) __builtin_bswap64(x) #else static inline uint16_t BSWAP16(uint16_t x) { return (x >> 8) | (x << 8); } static inline uint32_t BSWAP32(uint32_t x) { return ((x << 24) | ((x << 8) & 0x00FF0000) | ((x >> 8) & 0x0000FF00) | (x >> 24)); } static inline uint64_t BSWAP64(uint64_t x) { x = (x & 0x00000000FFFFFFFF) << 32 | (x & 0xFFFFFFFF00000000) >> 32; x = (x & 0x0000FFFF0000FFFF) << 16 | (x & 0xFFFF0000FFFF0000) >> 16; x = (x & 0x00FF00FF00FF00FF) << 8 | (x & 0xFF00FF00FF00FF00) >> 8; return x; } #endif namespace Math { // This epsilon should match the one used by Godot for consistency. // Using `f` when `real_t` is float. #define CMP_EPSILON 0.00001f #define CMP_EPSILON2 (CMP_EPSILON * CMP_EPSILON) // This epsilon is for values related to a unit size (scalar or vector len). #ifdef PRECISE_MATH_CHECKS #define UNIT_EPSILON 0.00001 #else // Tolerate some more floating point error normally. #define UNIT_EPSILON 0.001 #endif // Functions reproduced as in Godot's source code `math_funcs.h`. // Some are overloads to automatically support changing real_t into either double or float in the way Godot does. inline double fmod(double p_x, double p_y) { return ::fmod(p_x, p_y); } inline float fmod(float p_x, float p_y) { return ::fmodf(p_x, p_y); } inline double fposmod(double p_x, double p_y) { double value = Math::fmod(p_x, p_y); if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) { value += p_y; } value += 0.0; return value; } inline float fposmod(float p_x, float p_y) { float value = Math::fmod(p_x, p_y); if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) { value += p_y; } value += 0.0f; return value; } inline float fposmodp(float p_x, float p_y) { float value = Math::fmod(p_x, p_y); if (value < 0) { value += p_y; } value += 0.0f; return value; } inline double fposmodp(double p_x, double p_y) { double value = Math::fmod(p_x, p_y); if (value < 0) { value += p_y; } value += 0.0; return value; } inline int64_t posmod(int64_t p_x, int64_t p_y) { int64_t value = p_x % p_y; if ((value < 0 && p_y > 0) || (value > 0 && p_y < 0)) { value += p_y; } return value; } inline double floor(double p_x) { return ::floor(p_x); } inline float floor(float p_x) { return ::floorf(p_x); } inline double ceil(double p_x) { return ::ceil(p_x); } inline float ceil(float p_x) { return ::ceilf(p_x); } inline double exp(double p_x) { return ::exp(p_x); } inline float exp(float p_x) { return ::expf(p_x); } inline double sin(double p_x) { return ::sin(p_x); } inline float sin(float p_x) { return ::sinf(p_x); } inline double cos(double p_x) { return ::cos(p_x); } inline float cos(float p_x) { return ::cosf(p_x); } inline double tan(double p_x) { return ::tan(p_x); } inline float tan(float p_x) { return ::tanf(p_x); } inline double sinh(double p_x) { return ::sinh(p_x); } inline float sinh(float p_x) { return ::sinhf(p_x); } inline float sinc(float p_x) { return p_x == 0 ? 1 : ::sin(p_x) / p_x; } inline double sinc(double p_x) { return p_x == 0 ? 1 : ::sin(p_x) / p_x; } inline float sincn(float p_x) { return (float)sinc(Math_PI * p_x); } inline double sincn(double p_x) { return sinc(Math_PI * p_x); } inline double cosh(double p_x) { return ::cosh(p_x); } inline float cosh(float p_x) { return ::coshf(p_x); } inline double tanh(double p_x) { return ::tanh(p_x); } inline float tanh(float p_x) { return ::tanhf(p_x); } inline double asin(double p_x) { return ::asin(p_x); } inline float asin(float p_x) { return ::asinf(p_x); } inline double acos(double p_x) { return ::acos(p_x); } inline float acos(float p_x) { return ::acosf(p_x); } inline double atan(double p_x) { return ::atan(p_x); } inline float atan(float p_x) { return ::atanf(p_x); } inline double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); } inline float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); } inline double sqrt(double p_x) { return ::sqrt(p_x); } inline float sqrt(float p_x) { return ::sqrtf(p_x); } inline double pow(double p_x, double p_y) { return ::pow(p_x, p_y); } inline float pow(float p_x, float p_y) { return ::powf(p_x, p_y); } inline double log(double p_x) { return ::log(p_x); } inline float log(float p_x) { return ::logf(p_x); } inline float lerp(float minv, float maxv, float t) { return minv + t * (maxv - minv); } inline double lerp(double minv, double maxv, double t) { return minv + t * (maxv - minv); } inline double lerp_angle(double p_from, double p_to, double p_weight) { double difference = fmod(p_to - p_from, Math_TAU); double distance = fmod(2.0 * difference, Math_TAU) - difference; return p_from + distance * p_weight; } inline float lerp_angle(float p_from, float p_to, float p_weight) { float difference = fmod(p_to - p_from, (float)Math_TAU); float distance = fmod(2.0f * difference, (float)Math_TAU) - difference; return p_from + distance * p_weight; } inline double cubic_interpolate(double p_from, double p_to, double p_pre, double p_post, double p_weight) { return 0.5 * ((p_from * 2.0) + (-p_pre + p_to) * p_weight + (2.0 * p_pre - 5.0 * p_from + 4.0 * p_to - p_post) * (p_weight * p_weight) + (-p_pre + 3.0 * p_from - 3.0 * p_to + p_post) * (p_weight * p_weight * p_weight)); } inline float cubic_interpolate(float p_from, float p_to, float p_pre, float p_post, float p_weight) { return 0.5f * ((p_from * 2.0f) + (-p_pre + p_to) * p_weight + (2.0f * p_pre - 5.0f * p_from + 4.0f * p_to - p_post) * (p_weight * p_weight) + (-p_pre + 3.0f * p_from - 3.0f * p_to + p_post) * (p_weight * p_weight * p_weight)); } inline double cubic_interpolate_angle(double p_from, double p_to, double p_pre, double p_post, double p_weight) { double from_rot = fmod(p_from, Math_TAU); double pre_diff = fmod(p_pre - from_rot, Math_TAU); double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff; double to_diff = fmod(p_to - from_rot, Math_TAU); double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff; double post_diff = fmod(p_post - to_rot, Math_TAU); double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff; return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight); } inline float cubic_interpolate_angle(float p_from, float p_to, float p_pre, float p_post, float p_weight) { float from_rot = fmod(p_from, (float)Math_TAU); float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU); float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff; float to_diff = fmod(p_to - from_rot, (float)Math_TAU); float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff; float post_diff = fmod(p_post - to_rot, (float)Math_TAU); float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff; return cubic_interpolate(from_rot, to_rot, pre_rot, post_rot, p_weight); } inline double cubic_interpolate_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight, double p_to_t, double p_pre_t, double p_post_t) { /* Barry-Goldman method */ double t = Math::lerp(0.0, p_to_t, p_weight); double a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0 : (t - p_pre_t) / -p_pre_t); double a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5 : t / p_to_t); double a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0 : (t - p_to_t) / (p_post_t - p_to_t)); double b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0 : (t - p_pre_t) / (p_to_t - p_pre_t)); double b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0 : t / p_post_t); return Math::lerp(b1, b2, p_to_t == 0 ? 0.5 : t / p_to_t); } inline float cubic_interpolate_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight, float p_to_t, float p_pre_t, float p_post_t) { /* Barry-Goldman method */ float t = Math::lerp(0.0f, p_to_t, p_weight); float a1 = Math::lerp(p_pre, p_from, p_pre_t == 0 ? 0.0f : (t - p_pre_t) / -p_pre_t); float a2 = Math::lerp(p_from, p_to, p_to_t == 0 ? 0.5f : t / p_to_t); float a3 = Math::lerp(p_to, p_post, p_post_t - p_to_t == 0 ? 1.0f : (t - p_to_t) / (p_post_t - p_to_t)); float b1 = Math::lerp(a1, a2, p_to_t - p_pre_t == 0 ? 0.0f : (t - p_pre_t) / (p_to_t - p_pre_t)); float b2 = Math::lerp(a2, a3, p_post_t == 0 ? 1.0f : t / p_post_t); return Math::lerp(b1, b2, p_to_t == 0 ? 0.5f : t / p_to_t); } inline double cubic_interpolate_angle_in_time(double p_from, double p_to, double p_pre, double p_post, double p_weight, double p_to_t, double p_pre_t, double p_post_t) { double from_rot = fmod(p_from, Math_TAU); double pre_diff = fmod(p_pre - from_rot, Math_TAU); double pre_rot = from_rot + fmod(2.0 * pre_diff, Math_TAU) - pre_diff; double to_diff = fmod(p_to - from_rot, Math_TAU); double to_rot = from_rot + fmod(2.0 * to_diff, Math_TAU) - to_diff; double post_diff = fmod(p_post - to_rot, Math_TAU); double post_rot = to_rot + fmod(2.0 * post_diff, Math_TAU) - post_diff; return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t); } inline float cubic_interpolate_angle_in_time(float p_from, float p_to, float p_pre, float p_post, float p_weight, float p_to_t, float p_pre_t, float p_post_t) { float from_rot = fmod(p_from, (float)Math_TAU); float pre_diff = fmod(p_pre - from_rot, (float)Math_TAU); float pre_rot = from_rot + fmod(2.0f * pre_diff, (float)Math_TAU) - pre_diff; float to_diff = fmod(p_to - from_rot, (float)Math_TAU); float to_rot = from_rot + fmod(2.0f * to_diff, (float)Math_TAU) - to_diff; float post_diff = fmod(p_post - to_rot, (float)Math_TAU); float post_rot = to_rot + fmod(2.0f * post_diff, (float)Math_TAU) - post_diff; return cubic_interpolate_in_time(from_rot, to_rot, pre_rot, post_rot, p_weight, p_to_t, p_pre_t, p_post_t); } inline double bezier_interpolate(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) { /* Formula from Wikipedia article on Bezier curves. */ double omt = (1.0 - p_t); double omt2 = omt * omt; double omt3 = omt2 * omt; double t2 = p_t * p_t; double t3 = t2 * p_t; return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3; } inline float bezier_interpolate(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) { /* Formula from Wikipedia article on Bezier curves. */ float omt = (1.0f - p_t); float omt2 = omt * omt; float omt3 = omt2 * omt; float t2 = p_t * p_t; float t3 = t2 * p_t; return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3; } template inline T clamp(T x, T minv, T maxv) { if (x < minv) { return minv; } if (x > maxv) { return maxv; } return x; } template inline T min(T a, T b) { return a < b ? a : b; } template inline T max(T a, T b) { return a > b ? a : b; } template inline T sign(T x) { return static_cast(SIGN(x)); } template inline T abs(T x) { return std::abs(x); } inline double deg_to_rad(double p_y) { return p_y * Math_PI / 180.0; } inline float deg_to_rad(float p_y) { return p_y * static_cast(Math_PI) / 180.f; } inline double rad_to_deg(double p_y) { return p_y * 180.0 / Math_PI; } inline float rad_to_deg(float p_y) { return p_y * 180.f / static_cast(Math_PI); } inline double inverse_lerp(double p_from, double p_to, double p_value) { return (p_value - p_from) / (p_to - p_from); } inline float inverse_lerp(float p_from, float p_to, float p_value) { return (p_value - p_from) / (p_to - p_from); } inline double remap(double p_value, double p_istart, double p_istop, double p_ostart, double p_ostop) { return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value)); } inline float remap(float p_value, float p_istart, float p_istop, float p_ostart, float p_ostop) { return Math::lerp(p_ostart, p_ostop, Math::inverse_lerp(p_istart, p_istop, p_value)); } inline bool is_nan(float p_val) { return std::isnan(p_val); } inline bool is_nan(double p_val) { return std::isnan(p_val); } inline bool is_inf(float p_val) { return std::isinf(p_val); } inline bool is_inf(double p_val) { return std::isinf(p_val); } inline bool is_equal_approx(float a, float b) { // Check for exact equality first, required to handle "infinity" values. if (a == b) { return true; } // Then check for approximate equality. float tolerance = (float)CMP_EPSILON * abs(a); if (tolerance < (float)CMP_EPSILON) { tolerance = (float)CMP_EPSILON; } return abs(a - b) < tolerance; } inline bool is_equal_approx(float a, float b, float tolerance) { // Check for exact equality first, required to handle "infinity" values. if (a == b) { return true; } // Then check for approximate equality. return abs(a - b) < tolerance; } inline bool is_zero_approx(float s) { return abs(s) < (float)CMP_EPSILON; } inline bool is_equal_approx(double a, double b) { // Check for exact equality first, required to handle "infinity" values. if (a == b) { return true; } // Then check for approximate equality. double tolerance = CMP_EPSILON * abs(a); if (tolerance < CMP_EPSILON) { tolerance = CMP_EPSILON; } return abs(a - b) < tolerance; } inline bool is_equal_approx(double a, double b, double tolerance) { // Check for exact equality first, required to handle "infinity" values. if (a == b) { return true; } // Then check for approximate equality. return abs(a - b) < tolerance; } inline bool is_zero_approx(double s) { return abs(s) < CMP_EPSILON; } inline float absf(float g) { union { float f; uint32_t i; } u; u.f = g; u.i &= 2147483647u; return u.f; } inline double absd(double g) { union { double d; uint64_t i; } u; u.d = g; u.i &= (uint64_t)9223372036854775807ull; return u.d; } inline double smoothstep(double p_from, double p_to, double p_weight) { if (is_equal_approx(static_cast(p_from), static_cast(p_to))) { return p_from; } double x = clamp((p_weight - p_from) / (p_to - p_from), 0.0, 1.0); return x * x * (3.0 - 2.0 * x); } inline float smoothstep(float p_from, float p_to, float p_weight) { if (is_equal_approx(p_from, p_to)) { return p_from; } float x = clamp((p_weight - p_from) / (p_to - p_from), 0.0f, 1.0f); return x * x * (3.0f - 2.0f * x); } inline double move_toward(double p_from, double p_to, double p_delta) { return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta; } inline float move_toward(float p_from, float p_to, float p_delta) { return std::abs(p_to - p_from) <= p_delta ? p_to : p_from + sign(p_to - p_from) * p_delta; } 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 fract(float value) { return value - floor(value); } inline double fract(double value) { return value - floor(value); } inline float pingpong(float value, float length) { return (length != 0.0f) ? abs(fract((value - length) / (length * 2.0f)) * length * 2.0f - length) : 0.0f; } inline double pingpong(double value, double length) { return (length != 0.0) ? abs(fract((value - length) / (length * 2.0)) * length * 2.0 - length) : 0.0; } // 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 b = lrintf(a); // assuming everything but msvc 2012 or earlier has lrint #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; } inline float snap_scalar(float p_offset, float p_step, float p_target) { return p_step != 0 ? Math::snapped(p_target - p_offset, p_step) + p_offset : p_target; } inline float snap_scalar_separation(float p_offset, float p_step, float p_target, float p_separation) { if (p_step != 0) { float a = Math::snapped(p_target - p_offset, p_step + p_separation) + p_offset; float b = a; if (p_target >= 0) { b -= p_separation; } else { b += p_step; } return (Math::abs(p_target - a) < Math::abs(p_target - b)) ? a : b; } return p_target; } } // namespace Math } // namespace godot #endif // GODOT_MATH_HPP