cup_edit/macos/include/math/quat.h

/*
 * Copyright (C) 2013 The Android Open Source Project
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#ifndef TNT_MATH_QUAT_H
#define TNT_MATH_QUAT_H

#include <math/TQuatHelpers.h>
#include <math/compiler.h>
#include <math/half.h>
#include <math/vec3.h>
#include <math/vec4.h>

#include <stdint.h>
#include <sys/types.h>

namespace filament {
namespace math {
// -------------------------------------------------------------------------------------

namespace details {

template<typename T>
class MATH_EMPTY_BASES TQuaternion :
        public TVecAddOperators<TQuaternion, T>,
        public TVecUnaryOperators<TQuaternion, T>,
        public TVecComparisonOperators<TQuaternion, T>,
        public TQuatProductOperators<TQuaternion, T>,
        public TQuatFunctions<TQuaternion, T> {
public:
    enum no_init {
        NO_INIT
    };
    typedef T value_type;
    typedef T& reference;
    typedef T const& const_reference;
    typedef size_t size_type;

    /*
     * quaternion internals stored as:
     *
     * q = w + xi + yj + zk
     *
     *  q[0] = x;
     *  q[1] = y;
     *  q[2] = z;
     *  q[3] = w;
     *
     */
    union {
        struct { T x, y, z, w; };
        TVec4<T> xyzw;
        TVec3<T> xyz;
        TVec2<T> xy;
    };

    enum { SIZE = 4 };
    inline constexpr static size_type size() { return SIZE; }

    // array access
    inline constexpr T const& operator[](size_t i) const {
        // only possible in C++0x14 with constexpr
        assert(i < SIZE);
        return (&x)[i];
    }

    inline constexpr T& operator[](size_t i) {
        assert(i < SIZE);
        return (&x)[i];
    }

    // -----------------------------------------------------------------------
    // we want the compiler generated versions for these...
    TQuaternion(const TQuaternion&) = default;
    ~TQuaternion() = default;
    TQuaternion& operator=(const TQuaternion&) = default;

    // constructors

    // leaves object uninitialized. use with caution.
    explicit constexpr TQuaternion(no_init) {}

    // default constructor. sets all values to zero.
    constexpr TQuaternion() : x(0), y(0), z(0), w(0) {}

    // handles implicit conversion to a quat. must not be explicit.
    template<typename A, typename = enable_if_arithmetic_t<A>>
    constexpr TQuaternion(A w) : x(0), y(0), z(0), w(w) {}

    // initialize from 4 values to w + xi + yj + zk
    template<typename A, typename B, typename C, typename D,
            typename = enable_if_arithmetic_t<A, B, C, D>>
    constexpr TQuaternion(A w, B x, C y, D z) : x(x), y(y), z(z), w(w) {}

    // initialize from a vec3 + a value to : v.xi + v.yj + v.zk + w
    template<typename A, typename B, typename = enable_if_arithmetic_t<A, B>>
    constexpr TQuaternion(const TVec3<A>& v, B w) : x(v.x), y(v.y), z(v.z), w(w) {}

    // initialize from a vec4
    template<typename A, typename = enable_if_arithmetic_t<A>>
    constexpr explicit TQuaternion(const TVec4<A>& v) : x(v.x), y(v.y), z(v.z), w(v.w) {}

    // initialize from a quaternion of a different type
    template<typename A, typename = enable_if_arithmetic_t<A>>
    constexpr explicit TQuaternion(const TQuaternion<A>& v) : x(v.x), y(v.y), z(v.z), w(v.w) {}

    // conjugate operator
    constexpr TQuaternion operator~() const {
        return conj(*this);
    }

    // constructs a quaternion from an axis and angle
    template<typename A, typename B, typename = enable_if_arithmetic_t<A, B>>
    constexpr static TQuaternion MATH_PURE fromAxisAngle(const TVec3<A>& axis, B angle) {
        return TQuaternion(std::sin(angle * 0.5) * normalize(axis), std::cos(angle * 0.5));
    }

    // constructs a quaternion from orig to dest.
    // it returns the shortest arc and `from` and `to` must be normalized.
    template<typename A, typename B, typename = enable_if_arithmetic_t<A, B>>
    constexpr static TQuaternion MATH_PURE fromDirectedRotation(const TVec3<A>& from, const TVec3<B>& to) {
        // see the implementation of glm/gtx/quaternion.hpp
        T cosTheta = dot(from, to);
        TVec3<T> rotationAxis;

        if (cosTheta >= T(1) - std::numeric_limits<T>::epsilon()) {
            // orig and dest point in the same direction
            return TQuaternion(1, 0, 0, 0);
        }

        if (cosTheta < T(-1) + std::numeric_limits<T>::epsilon()) {
            // special case when vectors in opposite directions :
            // there is no "ideal" rotation axis
            // So guess one; any will do as long as it's perpendicular to start
            // This implementation favors a rotation around the Up axis (Y),
            // since it's often what you want to do.
            rotationAxis = cross(TVec3<T>(0, 0, 1), from);

            if (length2(rotationAxis) < std::numeric_limits<T>::epsilon()) {
                 // bad luck, they were parallel, try again!
                 rotationAxis = cross(TVec3<T>(1, 0, 0), from);
            }

            rotationAxis = normalize(rotationAxis);
            return fromAxisAngle(rotationAxis, F_PI);
        }

        // implementation from Stan Melax's Game Programming Gems 1 article
        rotationAxis = cross(from, to);

        const T s = std::sqrt((T(1) + cosTheta) * T(2));
        return TQuaternion(s * T(0.5),
                rotationAxis.x / s, rotationAxis.y / s, rotationAxis.z / s);
    }
};

}  // namespace details

// ----------------------------------------------------------------------------------------

typedef details::TQuaternion<double> quat;
typedef details::TQuaternion<float> quatf;
typedef details::TQuaternion<half> quath;

constexpr inline quat operator "" _i(long double v) {
    return quat(0.0, double(v), 0.0, 0.0);
}

constexpr inline quat operator "" _j(long double v) {
    return quat(0.0, 0.0, double(v), 0.0);
}

constexpr inline quat operator "" _k(long double v) {
    return quat(0.0, 0.0, 0.0, double(v));
}

constexpr inline quat operator "" _i(unsigned long long v) {
    return quat(0.0, double(v), 0.0, 0.0);
}

constexpr inline quat operator "" _j(unsigned long long v) {
    return quat(0.0, 0.0, double(v), 0.0);
}

constexpr inline quat operator "" _k(unsigned long long v) {
    return quat(0.0, 0.0, 0.0, double(v));
}

// ----------------------------------------------------------------------------------------
}  // namespace math
}  // namespace filament

#endif  // TNT_MATH_QUAT_H