#include <cassert>

#include "shape.h"


PointShape::PointShape(const Vector3 &pos, const Vector3 &dir) {
    Vector3 vx = dir.perp().norm();
    Vector3 vy = vx.cross(dir);
    matrix = Matrix4(
        vx.x , vx.y , vx.z , 0,
        vy.x , vy.y , vy.z , 0,
        dir.x, dir.y, dir.z, 0,
        pos.x, pos.y, pos.z, 1 ).inv();
}

Real PointShape::base_distance_to_triangle(const Vector3 *v) {
    Real dist = INFINITY;
    
    Vector3 d[3] = {
        v[1] - v[0],
        v[2] - v[1],
        v[0] - v[2] };
    
    // collision with plane
    Vector3 perp = d[1].cross(d[2]);
    if (fabs(perp.z) > precision) {
        // nearest plane touch point
        Vector3 p(0, 0, perp*v[0]/perp.z);
        
        // is touch point inside tringle
        Real s =  sign( perp.cross(d[0])*(p - v[0]), 0.1*precision );
        if ( s
          && s == sign( perp.cross(d[1])*(p - v[1]), 0.1*precision )
          && s == sign( perp.cross(d[2])*(p - v[2]), 0.1*precision ) )
            dist = std::min(dist, p.z);
    }
    
    return dist;
}


Real PointShape::distance_to_triangle(const Triangle &triangle) const {
    Vector3 v[3] = {
        matrix.transform( triangle.vertices[0] ),
        matrix.transform( triangle.vertices[1] ),
        matrix.transform( triangle.vertices[2] ) };
    return base_distance_to_triangle(v);
}



CilinderShape::CilinderShape(const Vector3 &pos, const Vector3 &dir, Real radius) {
    Vector3 vx = dir.perp().norm();
    Vector3 vy = vx.cross(dir);
    matrix = Matrix4(
        vx.x*radius, vx.y*radius, vx.z*radius, 0,
        vy.x*radius, vy.y*radius, vy.z*radius, 0,
        dir.x      , dir.y      , dir.z      , 0,
        pos.x      , pos.y      , pos.z      , 1 ).inv();
}

Real CilinderShape::base_distance_to_triangle(const Vector3 *v) {
    Real dist = INFINITY;
    
    Vector3 d[3];
    Real A[3], B[3], C[3];
    for(int i = 0; i < 3; ++i) {
        C[i] = v[i].x*v[i].x + v[i].y*v[i].y - 1;
        
        // collision with vertex
        if (C[i] <= precision)
            dist = std::min(dist, v[i].z);
    }

    for(int i = 0; i < 3; ++i) {
        d[i] = v[(i+1)%3] - v[i];
        A[i] = d[i].x*d[i].x + d[i].y*d[i].y;
        B[i] = 2*(d[i].x*v[i].x + d[i].y*v[i].y);
        
        // collision with edge
        Real roots[2];
        int count = solve(roots, C[i], B[i], A[i]);
        for(int j = 0; j < count; ++j)
            if (roots[j] >= -precision && roots[j] <= 1 + precision)
                dist = std::min(dist, d[i].z*roots[j] + v[i].z);
    }
    
    // collision with plane
    Vector3 perp = d[1].cross(d[2]);
    if (perp.z < 0) perp = Vector3(-perp.x, -perp.y, -perp.z);
    if (perp.z > precision) {
        // nearest plane touch point
        Vector3 p(0, 0, perp*v[0]/perp.z);
        Real xy = sqrt(perp.x*perp.x + perp.y*perp.y);
        if (xy > precision) {
            Real dxy = 1/xy;
            p.x = perp.x*dxy;
            p.y = perp.y*dxy;
            p.z -= xy/perp.z;
        }
        
        // is touch point inside tringle
        Real s =  sign( perp.cross(d[0])*(p - v[0]), 0.1*precision );
        if ( s
          && s == sign( perp.cross(d[1])*(p - v[1]), 0.1*precision )
          && s == sign( perp.cross(d[2])*(p - v[2]), 0.1*precision ) )
            dist = std::min(dist, p.z);
    }
    
    return dist;
}


Real CilinderShape::distance_to_triangle(const Triangle &triangle) const {
    Vector3 v[3] = {
        matrix.transform( triangle.vertices[0] ),
        matrix.transform( triangle.vertices[1] ),
        matrix.transform( triangle.vertices[2] ) };
    return base_distance_to_triangle(v);
}


ConeShape::ConeShape(const Vector3 &pos, const Vector3 &dir, Real radius, Real height, Real cut_radius) {
    Vector3 vx = dir.perp().norm();
    Vector3 vy = vx.cross(dir);
    matrix = Matrix4(
        vx.x*radius, vx.y*radius, vx.z*radius, 0,
        vy.x*radius, vy.y*radius, vy.z*radius, 0,
        dir.x      , dir.y      , dir.z      , 0,
        pos.x      , pos.y      , pos.z      , 1 ).inv();
    this->cut_radius = fabs(radius) > precision ? fabs(cut_radius/radius) : 0;
    this->height = fabs(height);
}

Real ConeShape::base_distance_to_triangle(const Vector3 *v, Real height, Real cut_radius) {
    Real dist = INFINITY;
    
    height = fabs(height);
    cut_radius = fabs(cut_radius);
    
    dist = std::min(dist, CilinderShape::base_distance_to_triangle(v) + height);
    if (cut_radius <= precision)
        dist = std::min(dist, PointShape::base_distance_to_triangle(v));
    if (cut_radius >= 1 - precision || height <= precision)
        return dist;
    
    Real kz = (1 - cut_radius)/height;
    Real dkz = 1/kz;
    Real d_cut_radius = 1/cut_radius;

    Vector3 v_cut[3] = {
        Vector3(v[0].x*d_cut_radius, v[0].y*d_cut_radius, v[0].z),
        Vector3(v[1].x*d_cut_radius, v[1].y*d_cut_radius, v[1].z),
        Vector3(v[2].x*d_cut_radius, v[2].y*d_cut_radius, v[2].z) };
    dist = std::min(dist, CilinderShape::base_distance_to_triangle(v_cut));
    
    
    Real xy2[3];
    for(int i = 0; i < 3; ++i) {
        xy2[i] = v[i].x*v[i].x + v[i].y*v[i].y;
        
        // collision with vertex
        if (xy2[i] < 1 && xy2[i] >= cut_radius*cut_radius) {
            Real dz = (sqrt(xy2[i]) - cut_radius)*dkz;
            dist = std::min(dist, v[i].z + dz);
        }
    }
    
    // collision with edge
    Real kz2 = kz*kz;
    Real cut_z = cut_radius*dkz;
    for(int i = 0; i < 3; ++i) {
        Vector3 d = v[(i+1)%3] - v[i];
        
        Real A = d.x*d.x + d.y*d.y - d.z*d.z*kz2;
        if (A > precision) {
            // B = oB + kB*z
            Real oB = 2*(d.x*v[i].x + d.y*v[i].y);
            Real kB = -2*d.z*kz2;

            // C = oC + kC*z*z
            Real oC = xy2[i];
            Real kC = -kz2;
            
            // B*B - 4AC = 0
            Real a = kB*kB - 4*A*kC;
            Real b = 2*oB*kB;
            Real c = oB*oB - 4*A*oC;
            
            Real roots[2];
            int count = solve(roots, c, b, a);
            for(int j = 0; j < count; ++j) {
                Real B = oB + kB*roots[j];
                Real l = -0.5*B/A;
                
                //Vector3 pp = d*l + Vector3(v[i].x, v[i].y, roots[j]);
                //assert(fabs(pp.x*pp.x + pp.y*pp.y - kz2*pp.z*pp.z) < precision);
                
                if (l >= -precision && l <= 1 + precision) {
                    Real z = d.z*l + roots[j];
                    if (z < 0) {
                        Vector3 p = d*l + v[i];
                        Real r2 = p.x*p.x + p.y*p.y;
                        if (r2 <= 1 + precision && r2 >= cut_radius*cut_radius)
                            dist = std::min(dist, p.z - cut_z - z);
                    }
                }
            }
        }
    }

    return dist;
}

Real ConeShape::distance_to_triangle(const Triangle &triangle) const {
    Vector3 v[3] = {
        matrix.transform( triangle.vertices[0] ),
        matrix.transform( triangle.vertices[1] ),
        matrix.transform( triangle.vertices[2] ) };
    return base_distance_to_triangle(v, height, cut_radius);
}