#include <cassert></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);

}