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/* ----------------------------------------------------------------------- *

 * This file is part of GEL, http://www.imm.dtu.dk/GEL

 * Copyright (C) the authors and DTU Informatics

 * For license and list of authors, see ../../doc/intro.pdf

 * ----------------------------------------------------------------------- */

#include "curvature.h"

#include <iostream>

#include "../CGLA/eigensolution.h"

#include "../CGLA/Vec2d.h"

#include "../CGLA/Vec3d.h"

#include "../CGLA/Mat3x3d.h"

#include "../CGLA/Mat2x2d.h"

#include "../CGLA/Mat2x3d.h"

#include "Manifold.h"

#include "AttributeVector.h"

#include "x3d_save.h"

#include "x3d_load.h"

#include "obj_load.h"

#include "mesh_optimization.h"

#include "../LinAlg/Matrix.h"

#include "../LinAlg/Vector.h"

#include "../LinAlg/LapackFunc.h"

using namespace std;

using namespace LinAlg;

using namespace CGLA;

using namespace HMesh;

namespace HMesh

{

    namespace 

    {

        //double scal = 0.001;

        //double vector_scal = 0.001;

        template<class T> 

        void smooth_something_on_mesh(const Manifold& m, VertexAttributeVector<T>& vec, int smooth_steps)

        {

            for(int iter=0;iter<smooth_steps;++iter){

                VertexAttributeVector<T> new_vec(m.allocated_vertices());

                for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v){

                    new_vec[*v] = vec[*v];

                    for(Walker w = m.walker(*v); !w.full_circle(); w = w.circulate_vertex_cw()){

                        new_vec[*v] += vec[w.vertex()];

                    }

                    new_vec[*v] /= (valency(m, *v) + 1.0);

                }

                swap(vec,new_vec);

            }		

        }

    }

    double mixed_area(const Manifold& m, VertexID v)

    {

        double area_mixed = 0;

        //For each triangle T from the 1-ring neighborhood of x

        for(Walker w = m.walker(v); !w.full_circle(); w = w.circulate_vertex_cw()){

            double f_area = area(m, w.face());

            Vec3d v0(m.pos(v));

            Vec3d v1(m.pos(w.vertex()));

            Vec3d v2(m.pos(w.next().vertex()));

            double a0 = acos(dot(v1-v0, v2-v0)/(length(v1-v0)*length(v2-v0)));

            double a1 = acos(dot(v2-v1, v0-v1)/(length(v2-v1)*length(v0-v1)));

            double a2 = acos(dot(v0-v2, v1-v2)/(length(v0-v2)*length(v1-v2)));

            if(a0>(M_PI/2.0) && a1>(M_PI/2.0) && a2>(M_PI/2.0)) // f is non-obtuse

            {

                // Add Voronoi formula (see Section 3.3)

                area_mixed += (1.0/8) * 

                    ((1.0/tan(a1)) * sqr_length(v2-v0) + 

                    (1.0/tan(a2)) * sqr_length(v1-v0));

            }

            else // Voronoi inappropriate

            {

                // Add either area(f)/4 or area(f)/2

                area_mixed += f_area/3;

            }

        }

        return area_mixed;

    }

    double barycentric_area(const Manifold& m, VertexID v)

    {

        double barea = 0;

        //For each triangle T from the 1-ring neighborhood of x

        for(Walker w = m.walker(v); !w.full_circle(); w = w.circulate_vertex_cw()){

            barea += area(m, w.face())/3.0;

        }

        return barea;

    }

    void unnormalized_mean_curvature_normal(const Manifold& m, VertexID v, Vec3d& curv_normal, double& w_sum)

    {

        if(boundary(m, v))

            return;

        Vec3d vertex(m.pos(v));

        curv_normal = Vec3d(0);

        w_sum = 0;

        for(Walker walker = m.walker(v); !walker.full_circle(); walker = walker.circulate_vertex_ccw()){

            Vec3d nbr(m.pos(walker.vertex()));

            Vec3d left(m.pos(walker.next().vertex()));

            Vec3d right(m.pos(walker.opp().next().vertex()));

            double d_left = dot(cond_normalize(nbr-left),cond_normalize(vertex-left));

            double d_right = dot(cond_normalize(nbr-right),cond_normalize(vertex-right));

            double a_left  = acos(min(1.0, max(-1.0, d_left)));

            double a_right = acos(min(1.0, max(-1.0, d_right)));

//            double w = 1.0/(1e-300+tan(a_left));

//            w += 1.0/(1e-300+tan(a_right));

            double w = sin(a_left + a_right) / (1e-300 + sin(a_left)*sin(a_right));

            curv_normal += w * (nbr-vertex);

            w_sum += w;

        }

    }

    Vec3d mean_curvature_normal(const Manifold& m, VertexID v)

    {

        Vec3d curv_normal;

        double w_sum;

        unnormalized_mean_curvature_normal(m, v, curv_normal, w_sum);

        return curv_normal / (4*mixed_area(m, v));

    }

    double sum_curvatures(const Manifold& m, VertexAttributeVector<double>& curvature)

    {

        double sum = 0;

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v){

            if(boundary(m, *v))

                continue;	

            sum += curvature[*v] * mixed_area(m, *v);

        }

        return sum;

    }

    double gaussian_curvature_angle_defect(const Manifold& m, VertexID v)

    {

        if(boundary(m, v))

            return 0;

        Vec3d vertex(m.pos(v));

        vector<Vec3d> edges;

        for(Walker w = m.walker(v); !w.full_circle(); w = w.circulate_vertex_cw()){

            Vec3d e(normalize(m.pos(w.vertex()) - vertex));

            edges.push_back(e);

        }

        size_t N=edges.size();

        double angle_sum = 0;

        for(size_t i = 0; i < N; ++i)

        {

            double dot_prod = 

                std::max(-1.0, std::min(1.0, dot(edges[i],edges[(i+1)%N])));

            angle_sum += acos(dot_prod);

        }

        return (2*M_PI - angle_sum)/mixed_area(m, v);

    }

    Mat3x3d curvature_tensor(const Manifold& m, HalfEdgeID h)

    {

        if(boundary(m, h))

            return Mat3x3d(0);

        Walker w = m.walker(h);

        Vec3d edge(m.pos(w.vertex()) - m.pos(w.opp().vertex()));

        double edge_len = length(edge);

        edge /= edge_len;

        Vec3d h_norm(normal(m, w.face()));

        Vec3d h_opp_norm(normal(m, w.opp().face()));

        Vec3d nc = cross(h_norm, h_opp_norm);

        double sign = (dot(nc, edge) >= 0) ? 1 : -1;

        double beta = asin(nc.length());

        Mat3x3d mat;

        outer_product(edge, edge, mat);

        return sign * edge_len * beta * mat;

    }

    Mat3x3d curvature_tensor_from_edges(const Manifold& m, VertexID v)

    {

        Mat3x3d curv_tensor(0);

        if(boundary(m, v))

            return curv_tensor;

        for(Walker w = m.walker(v); !w.full_circle(); w = w.circulate_vertex_cw())

            curv_tensor += 0.5*curvature_tensor(m, w.halfedge());

        curv_tensor /= mixed_area(m, v);

        return curv_tensor;

    }

    void curvature_tensor_paraboloid(const Manifold& m, VertexID v, Mat2x2d& curv_tensor, Mat3x3d& frame)

    {

        if(boundary(m, v))

            return;

        // First estimate the normal and compute a transformation matrix

        // which takes us into tangent plane coordinates.

        Vec3d Norm = Vec3d(normal(m, v));

        Vec3d X,Y;

        orthogonal(Norm,X,Y);

        frame = Mat3x3d(X,Y,Norm);

        Vec3d centre(m.pos(v));

        vector<Vec3d> points;

        for(Walker w = m.walker(v); !w.full_circle(); w = w.circulate_vertex_cw())

            points.push_back(Vec3d(m.pos(w.vertex())));

        int N = int(points.size());

        CVector b(N);

        // Compute the matrix of parameter values

        CMatrix PMat(N, 3);

        for(int i = 0; i < N; ++i){

            Vec3d p = frame * (points[i]-centre);

            b[i] = p[2];

            PMat.set(i,0,0.5*sqr(p[0]));

            PMat.set(i,1,p[0]*p[1]);

            PMat.set(i,2,0.5*sqr(p[1]));

        }

        // Compute the coefficients of the polynomial surface

        CVector x(3);

        x = LinearLSSolve(PMat,b);

        if(isnan(x[0])) cout << __LINE__ << " " << PMat << b << endl ;

        // Finally compute the shape tensor from the coefficients

        // using the first and second fundamental forms.

        curv_tensor = - Mat2x2d(x[0],x[1],x[1],x[2]);

    }

    void curvature_tensors_from_edges(const Manifold& m, VertexAttributeVector<Mat3x3d>& curvature_tensors)

    {

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v)

            curvature_tensors[*v] = curvature_tensor_from_edges(m, *v);

    }

    void smooth_curvature_tensors(const Manifold& m, VertexAttributeVector<Mat3x3d>& curvature_tensors)

    {

        assert(curvature_tensors.size() == m.allocated_vertices());

        VertexAttributeVector<Mat3x3d> tmp_curvature_tensors(m.allocated_vertices());

        double tmp_area;

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v){

            if(boundary(m, *v))

                continue;

            double a = mixed_area(m, *v);

            tmp_curvature_tensors[*v] = curvature_tensors[*v] * a;

            tmp_area = a;

            for(Walker w = m.walker(*v); !w.full_circle(); w = w.circulate_vertex_cw()){

                if(!boundary(m, w.vertex())){

                    double a = mixed_area(m, w.vertex());

                    tmp_curvature_tensors[*v] += curvature_tensors[w.vertex()]*a;

                    tmp_area += a;

                }

                tmp_curvature_tensors[*v] /= tmp_area;

            }

        }

        curvature_tensors = move(tmp_curvature_tensors);

    }

    void gaussian_curvature_angle_defects(const Manifold& m, VertexAttributeVector<double>& curvature, int smooth_steps)

    {

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v)

            curvature[*v] = gaussian_curvature_angle_defect(m, *v);

        smooth_something_on_mesh(m, curvature, smooth_steps);

    }

    void mean_curvatures(const Manifold& m, VertexAttributeVector<double>& curvature, int smooth_steps)

    {

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v)

			if(!boundary(m,*v))

			{

				Vec3d N = -mean_curvature_normal(m, *v);

				curvature[*v] = length(N) * sign(dot(N,Vec3d(normal(m, *v))));

			}	

        smooth_something_on_mesh(m, curvature, smooth_steps);	

    }

    void curvature_paraboloids( const Manifold& m, 

                                VertexAttributeVector<Vec3d>& min_curv_direction, 

                                VertexAttributeVector<Vec3d>& max_curv_direction,

                                VertexAttributeVector<Vec2d>& curvature)

    {

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v){

            Mat2x2d tensor;

            Mat3x3d frame;

            curvature_tensor_paraboloid(m, *v, tensor, frame);

            Mat2x2d Q,L;

            int s = power_eigensolution(tensor, Q, L);

            if(s < 2)	

                cout << tensor << Q << L << endl;

            int max_idx = 0;

            int min_idx = 1;

            if(L[max_idx][max_idx]<L[min_idx][min_idx]) swap(max_idx, min_idx);

            Mat3x3d frame_t = transpose(frame);

            max_curv_direction[*v] = cond_normalize(frame_t * Vec3d(Q[max_idx][0], Q[max_idx][1], 0));

            min_curv_direction[*v] = cond_normalize(frame_t * Vec3d(Q[min_idx][0], Q[min_idx][1], 0));

            curvature[*v][0] = L[min_idx][min_idx];

            curvature[*v][1] = L[max_idx][max_idx];

        }

    }

    void curvature_from_tensors(const Manifold& m,

                                const VertexAttributeVector<Mat3x3d>& curvature_tensors,

                                VertexAttributeVector<Vec3d>& min_curv_direction,

                                VertexAttributeVector<Vec3d>& max_curv_direction,

                                VertexAttributeVector<Vec2d>& curvature)

    {

        assert(curvature_tensors.size() == m.allocated_vertices());

        double max_val = -1e30;

        for(VertexIDIterator v = m.vertices_begin(); v != m.vertices_end(); ++v){

            Mat3x3d C,Q,L;

            C = curvature_tensors[*v];

            int s = power_eigensolution(C, Q, L);

            Vec3d dmin, dmax;

            if(s == 0)

            {

                Vec3d n(normal(m, *v));

                orthogonal(n, dmin, dmax);

                curvature[*v] = Vec2d(0);

                cout << " rank 0 " << endl;

            }

            else if(s == 1)

            {

                Vec3d n(normal(m, *v));

                dmin = normalize(Q[0]);

                dmax = cross(n, dmin);

                curvature[*v] = Vec2d(0);

                cout << " rank 1 " << endl;

            }

            else

            {

                Vec2d l(fabs(L[0][0]), fabs(L[1][1]));

                int max_idx = 0;

                int min_idx = 1;

                if(l[max_idx] < l[min_idx]) swap(max_idx, min_idx);

                // Yes - the biggest eigenvalue corresponds to the min direction

                // and vice versa.

                dmin = normalize(Q[max_idx]);

                dmax = normalize(Q[min_idx]);

                curvature[*v][0] = L[min_idx][min_idx];

                curvature[*v][1] = L[max_idx][max_idx];

            }

            min_curv_direction[*v] = dmin;

            max_curv_direction[*v] = dmax;

            max_val = max(fabs(curvature[*v][1]), max_val);

        }

        //scal = 1.0/max_val;

    }

}