geometric.h

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// =====================================================================================================================
//  fennec, a free and open source game engine
//  Copyright © 2025  Medusa Slockbower
//
//  This program is free software: you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation, either version 3 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program.  If not, see <https://www.gnu.org/licenses/>.
// =====================================================================================================================
 
 
 
#ifndef FENNEC_MATH_GEOMETRIC_H
#define FENNEC_MATH_GEOMETRIC_H
 
 
 
#include <fennec/math/vector.h>
#include <fennec/math/common.h>
#include <fennec/math/exponential.h>
 
namespace fennec
{
 
 
// dot -----------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr genType dot(const vector<genType, i...>& x, const vector<genType, i...>& y) {
    return ((x[i] * y[i]) + ...);
}
 
 
// length2 -------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr genType length2(const vector<genType, i...>& x) {
    return fennec::dot(x, x);
}
 
 
// length --------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr genType length(const vector<genType, i...>& x) {
    return fennec::sqrt(fennec::length2(x));
}
 
 
// distance ------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr genType distance(const vector<genType, i...>& p0, const vector<genType, i...>& p1) {
    return fennec::length(p1 - p0);
}
 
 
// cross ---------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i> requires(sizeof...(i) == 3)
constexpr vector<genType, i...> cross(const vector<genType, i...>& x, const vector<genType, i...>& y) {
    return vector<genType, i...>(x[1]*y[2]-y[1]*x[2], x[2]*y[0]-y[2]*x[0], x[0]*y[1]-y[0]*x[1]);
}
 
 
// normalize -----------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr vector<genType, i...> normalize(const vector<genType, i...>& x) {
    return x * fennec::inversesqrt(fennec::dot(x, x));
}
 
 
// faceforward ---------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr vector<genType, i...> faceforward(const vector<genType, i...>& N, const vector<genType, i...>& I, const vector<genType, i...>& Nref) {
    return fennec::sign(fennec::dot(Nref, I)) * N;
}
 
 
// reflect -------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr vector<genType, i...> reflect(const vector<genType, i...>& I, const vector<genType, i...>& N) {
    return I - genType(2.0) * fennec::dot(N, I) * N;
}
 
// refract -------------------------------------------------------------------------------------------------------------
 
template<typename genType, size_t...i>
constexpr vector<genType, i...> refract(const vector<genType, i...>& I, const vector<genType, i...>& N, genType eta) {
    genType ndi = fennec::dot(N, I);
    genType k = genType(1.0) - eta * eta * (genType(1.0) - ndi * ndi);
    if (k < 0) return vector<genType, i...>(0);
    return eta * I - N * (eta * ndi + fennec::sqrt(k));
}
 
}
 
#endif // FENNEC_MATH_GEOMETRIC_H