kopia lustrzana https://github.com/jameshball/osci-render
88 wiersze
2.9 KiB
C++
88 wiersze
2.9 KiB
C++
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// L=============================================================================
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// L This software is distributed under the MIT license.
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// L Copyright 2021 Péter Kardos
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// L=============================================================================
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#pragma once
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#include "QuaternionImpl.hpp"
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namespace mathter {
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/// <summary> The euclidean length of the vector of the 4 elements of the quaternion. </summary>
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template <class T, bool Packed>
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T Abs(const Quaternion<T, Packed>& q) {
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return Length(q.vec);
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}
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/// <summary> Negates the imaginary values of the quaternion. </summary>
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template <class T, bool Packed>
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Quaternion<T, Packed> Conjugate(const Quaternion<T, Packed>& q) {
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return Quaternion<T, Packed>{ q.vec * Vector<T, 4, Packed>{ T(1), T(-1), T(-1), T(-1) } };
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}
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/// <summary> Natural quaternion exponentiation, base e. </summary>
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template <class T, bool Packed>
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Quaternion<T, Packed> Exp(const Quaternion<T, Packed>& q) {
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auto a = q.ScalarPart();
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auto v = q.VectorPart();
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T mag = Length(v);
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T es = exp(a);
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Quaternion<T, Packed> ret = { std::cos(mag), v * (std::sin(mag) / mag) };
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ret *= es;
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return ret;
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}
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/// <summary> Natural quaternion logarithm, base e. </summary>
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template <class T, bool Packed>
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Quaternion<T, Packed> Log(const Quaternion<T, Packed>& q) {
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auto magq = Length(q);
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auto vn = Normalize(q.VectorPart());
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Quaternion ret = { std::log(magq), vn * std::acos(q.s / magq) };
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return ret;
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}
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/// <summary> Raises <paramref name="q"/> to the power of <paramref name="a"/>. </summary>
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template <class T, bool Packed>
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Quaternion<T, Packed> Pow(const Quaternion<T, Packed>& q, T a) {
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return Exp(a * Log(q));
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}
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/// <summary> Returns the square of the absolute value. </summary>
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/// <remarks> Just like complex numbers, it's the square of the length of the vector formed by the coefficients.
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/// This is much faster than <see cref="Length">. </remarks>
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template <class T, bool Packed>
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T LengthSquared(const Quaternion<T, Packed>& q) {
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return LengthSquared(q.vec);
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}
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/// <summary> Returns the absolute value of the quaternion. </summary>
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/// <remarks> Just like complex numbers, it's the length of the vector formed by the coefficients. </remarks>
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template <class T, bool Packed>
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T Length(const Quaternion<T, Packed>& q) {
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return Abs(q);
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}
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/// <summary> Returns the unit quaternion of the same direction. Does not change this object. </summary>
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template <class T, bool Packed>
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Quaternion<T, Packed> Normalize(const Quaternion<T, Packed>& q) {
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return Quaternion<T, Packed>{ Normalize(q.vec) };
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}
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/// <summary> Returns the quaternion of opposite rotation. </summary>
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template <class T, bool Packed>
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Quaternion<T, Packed> Inverse(const Quaternion<T, Packed>& q) {
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return Conjugate(q);
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}
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/// <summary> Check if the quaternion is a unit quaternion, with some tolerance for floats. </summary>
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template <class T, bool Packed>
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bool IsNormalized(const Quaternion<T, Packed>& q) {
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return IsNormalized(q.vec);
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}
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} // namespace mathter
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