💿🐜 Antkeeper source code
https://antkeeper.com
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119 lines
3.3 KiB
119 lines
3.3 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_SPRING_HPP
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#define ANTKEEPER_SPRING_HPP
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/**
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* Contains the variables required for numeric springing.
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*
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* @tparam T Value type.
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* @tparam S Scalar type.
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*
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* @see spring()
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* @see solve_numeric_spring()
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*/
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template <typename T, typename S>
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struct numeric_spring
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{
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T x0; ///< Start value
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T x1; ///< End value
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T v; ///< Velocity
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S z; ///< Damping ratio, which can be undamped (z = 0), underdamped (z < 1), critically damped (z = 1), or overdamped (z > 1).
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S w; ///< Angular frequency of the oscillation, in radians per second (2pi = 1Hz).
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};
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/**
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* Performs numeric, damped springing on a value and velocity.
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*
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* @tparam T Value type.
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* @tparam S Scalar type.
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*
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* @param[in,out] x0 Start value, which will be oscillated by this function.
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* @param[in,out] v Velocity, which will be modified by this function.
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* @param[in] x1 End value.
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* @param[in] z Damping ratio, which can be undamped (z = 0), underdamped (z < 1), critically damped (z = 1), or overdamped (z > 1).
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* @param[in] w Angular frequency of the oscillation, in radians per second (2pi = 1Hz).
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* @param[in] dt Delta time, in seconds.
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*/
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template <typename T, typename S>
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void spring(T& x0, T& v, const T& x1, S z, S w, S dt);
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/**
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* Solves a numeric spring using the spring() function.
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*
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* @param[in,out] ns Numeric spring to be sovled.
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* @param dt Delta time, in seconds.
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*
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* @see spring()
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*/
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template <typename T, typename S>
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void solve_numeric_spring(numeric_spring<T, S>& ns, S dt);
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/**
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* Converts a frequency from hertz to radians per second.
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*
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* @param hz Frequency in hertz.
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* @return Frequency in radians per second.
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*/
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template <typename T>
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T hz_to_rads(T hz);
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/**
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* Converts a frequency from radians per second to hertz.
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*
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* @param rads Frequency in radians per second.
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* @return Frequency in hertz.
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*/
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template <typename T>
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T rads_to_hz(T rads);
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template <typename T, typename S>
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void spring(T& x0, T& v, const T& x1, S z, S w, S dt)
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{
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const S w2_dt = w * w * dt;
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const S w2_dt2 = w2_dt * dt;
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const S f = z * w * dt * S(2) + S(1);
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const T det_x = x0 * f + v * dt + x1 * w2_dt2;
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const T det_v = v + (x1 - x0) * w2_dt;
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const S inv_det = S(1) / (f + w2_dt2);
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x0 = det_x * inv_det;
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v = det_v * inv_det;
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}
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template <typename T, typename S>
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void solve_numeric_spring(numeric_spring<T, S>& ns, S dt)
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{
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spring(ns.x0, ns.v, ns.x1, ns.z, ns.w, dt);
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}
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template <typename T>
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inline T hz_to_rads(T hz)
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{
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return hz * math::two_pi<T>;
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}
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template <typename T>
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inline T rads_to_hz(T rads)
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{
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return rads / math::two_pi<T>;
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}
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#endif // ANTKEEPER_SPRING_HPP
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