CartesianToTriangleTransform.h

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/*
    This source file is part of Rigs of Rods
    Copyright 2016 Fabian Killus
 
    For more information, see http://www.rigsofrods.org/
 
    Rigs of Rods is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License version 3, as
    published by the Free Software Foundation.
 
    Rigs of Rods 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 Rigs of Rods. If not, see <http://www.gnu.org/licenses/>.
*/
 
#pragma once
 
#include "Triangle.h"
 
#include <OgreMatrix3.h>
#include <OgreVector3.h>
 
 
 
 
class CartesianToTriangleTransform
{
public:
 
    struct TriangleCoord {
        const struct {
            Ogre::Real alpha,  
                       beta,   
                       gamma;  
        } barycentric;
        const Ogre::Real distance;  
    };
 
    explicit CartesianToTriangleTransform(const Triangle &triangle) : m_triangle{triangle}, m_initialized{false} {}
 
 
    TriangleCoord operator() (const Ogre::Vector3 &p) const
    {
        // lazy initialization of transformation matrix
        if (!m_initialized) {
            InitMatrix();
            m_initialized = true;
        }
 
        // apply transformation matrix and extract alpha, beta, gamma and perpendicular offset
        const Ogre::Vector3 result = m_matrix * (p - m_triangle.c);
        return {result[0], result[1], (1.f - result[0] - result[1]), result[2]};
    }
 
private:
    void InitMatrix() const {
        // determine span and normal vectors
        const Ogre::Vector3 u = m_triangle.u;
        const Ogre::Vector3 v = m_triangle.v;
        const Ogre::Vector3 n = m_triangle.normal();
        
        // construct and invert matrix
        m_matrix = Ogre::Matrix3{ u[0], v[0], n[0],
                                  u[1], v[1], n[1],
                                  u[2], v[2], n[2] }.Inverse();
    }
 
    const Triangle m_triangle;       
    mutable bool m_initialized;
    mutable Ogre::Matrix3 m_matrix;  
};