plane.h

#pragma once
#include <cgv/math/vec.h>
#include <cgv/math/point_operations.h>
#include <cgv/math/eig.h>
#include <algorithm>
 
namespace cgv{
    namespace math{
 
template <typename T>
T plane_val(const vec<T>& plane,const vec<T>& x)
{
 
    assert(plane.size()-1  == x.size());
 
    T val=0;
    for(unsigned i = 0;i< x.size(); i++)
        val += plane(i)*x(i);
 
    return val+plane(plane.size()-1);
}
 
template <typename T>
vec<T> plane_val(const vec<T>& plane,const mat<T>& xs)
{
 
    assert(plane.size()-1  == xs.nrows());
 
    vec<T> vals(xs.ncols());
    for(unsigned i = 0;i< xs.ncols(); i++)
        vals(i) = plane_val(plane,xs.col(i));
        
 
    return vals;
}
 
 
//construct implicit plane from 3 points
template <typename T>
vec<T> plane_fit(const vec<T>& p1,const vec<T>& p2,const vec<T>& p3)
{
    vec<T> plane(4);
    double l_nml;
    
    vec<T> nml = cross(normalize(p2-p1),normalize(p3-p1));
    l_nml = length(nml);
    assert(l_nml != 0);
            
    nml/=l_nml;
    plane.set(nml(0),nml(1),nml(2),-dot(p1,nml));
    return plane;
}
 
//fit implicit plane into multiple points (total least squares)
template <typename T>
vec<T> tls_plane_fit(const mat<T>& points)
{
    vec<T> plane(4);
    mat<T> covmat,v;
    diag_mat<T> d;
    vec<T> mean;
    
    covmat_and_mean(points,covmat, mean);
    eig_sym(covmat,v,d);
 
//  T l_nml;
    
    vec<T> nml = normalize(v.col(2));
        
    plane.set(nml(0),nml(1),nml(2),-dot(mean,nml));
    return plane;
}
 
 
 
 
template <typename T>
vec<T> ransac_plane_fit(const mat<T>& points,const T p_out=0.8, const T d_max=0.001, const T p_surety = 0.99, bool msac=true)
{
    assert(points.nrows == 3);
    vec<T> plane(4);
 
    vec<unsigned int> ind;
    vec<T> p1,p2,p3,dists(points.ncols());
    cgv::math::random rg;
    unsigned n = points.ncols;
    unsigned max_iter = num_ransac_iterations(3,p_out,psurety);
    unsigned num_inlier = (unsigned)::ceil((1-p_out)*points.ncols());
    
    T error = std::numeric_limits<T>::max();
    
    for(unsigned i = 0; i < max_iter; i++)
    {
        //random sample
        do
        {
            rg.uniform_nchoosek(n,3,ind);
            p1 = points.col(ind(0));
            p2 = points.col(ind(1));
            p3 = points.col(ind(2));
        }
        while(fabs(length(cross(q2-q1,q3-q1)))<0.001);
        
        //fit
        vec<T> pl = plane_fit(p1,p2,p3);
        
        //consensus
        int n_inlier=0;
        T e = 0;
        
        for(unsigned i = 0; i < points.ncols(); i++)
        {
            dists(i) = std::abs(plane_val(pl,points.col(i)));   
            if(dists(i) < d_max)
            {
                n_inlier++;
                if(msac)
                    e += dists(i);
            }
            else
            {
                e += dmax;
            }
        }
 
        //local reoptimize 
        if(loransac && n_inlier > 3)
        {
            mat<T> inliers(3,n_inlier);
            int j=0;
            n_inlier=0;
            for(unsigned i = 0; i < points.ncols(); i++)
            {
                if(dists(i) < d_max)
                { 
                    n_inlier++;
                    inliers.set_col(j,points.col(i));
                    j++;
                }
            }
            pl = plane_fit(inliers)
 
            //recompute error
            for(unsigned i = 0; i < points.ncols(); i++)
            {
                dists(i) = std::abs(plane_val(pl,points.col(i)));   
                if(dists(i) < d_max)
                {
                
                    if(msac)
                        e += dists(i);
                }
                else
                {
                    e += dmax;
                }
            }
        }
 
        //remember best plane
        if(error > e)
        {
            error = e;
            plane = pl;
        }
        
        if(n_inlier >= num_inlier)
        {
            p_out = (T)1-(T)n_inlier/(T)points.ncols();
            max_iter = num_ransac_iterations(3,p_out,psurety);  
        }
    }
    return plane;
}
 
 
 
 
 
 
 
 
    }
}