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openMVS/vcglib/vcg/math/gen_normal.h

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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004-2016 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program 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 (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/****************************************************************************
History
$Log: gen_normal.h,v $
****************************************************************************/
#ifndef __VCG_GEN_NORMAL
#define __VCG_GEN_NORMAL
namespace vcg {
template <class ScalarType>
class GenNormal
{
public:
typedef Point3<ScalarType> Point3x;
static void Random(int vn, std::vector<Point3<ScalarType > > &NN)
{
NN.clear();
while(NN.size()<vn)
{
Point3x pp(((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX);
pp=pp*2.0-Point3x(1,1,1);
if(pp.SquaredNorm()<1)
{
Normalize(pp);
NN.push_back(pp);
}
}
}
static Point3x FibonacciPt(int i, int n)
{
const ScalarType Phi = ScalarType(std::sqrt(ScalarType(5))*0.5 + 0.5);
const ScalarType phi = 2.0*M_PI* (i/Phi - floor(i/Phi));
ScalarType cosTheta = 1.0 - (2*i + 1.0)/ScalarType(n);
ScalarType sinTheta = 1 - cosTheta*cosTheta;
sinTheta = std::sqrt(std::min(ScalarType(1),std::max(ScalarType(0),sinTheta)));
return Point3x(
cos(phi)*sinTheta,
sin(phi)*sinTheta,
cosTheta);
}
// Implementation of the Spherical Fibonacci Point Sets
// according to the description of
// Spherical Fibonacci Mapping
// Benjamin Keinert, Matthias Innmann, Michael Sanger, Marc Stamminger
// TOG 2015
static void Fibonacci(int n, std::vector<Point3x > &NN)
{
NN.resize(n);
for(int i=0;i<n;++i)
NN[i]=FibonacciPt(i,n);
}
static void UniformCone(int vn, std::vector<Point3<ScalarType > > &NN, ScalarType AngleRad, Point3x dir=Point3x(0,1,0))
{
assert(AngleRad>0 && AngleRad<M_PI);
std::vector<Point3<ScalarType > > NNT;
NN.clear();
// To compute the number of points we need to know the area of
// the spherical cap and then use the ratio with the total surface of the sphere
ScalarType Height= 1.0 - cos(AngleRad); // height is measured from top...
ScalarType CapArea = 2.0*M_PI*Height; // Surface is the one of the tangent cylinder
ScalarType Ratio = CapArea / (4.0*M_PI);
// printf("----------AngleRad %f Angledeg %f ratio %f vn %i vn2 %i \n",AngleRad,math::ToDeg(AngleRad),Ratio,vn,int(vn/Ratio));
Fibonacci(vn/Ratio,NNT);
// printf("asked %i got %i (expecting %i instead of %i)\n", int(vn/Ratio), int(NNT.size()), int(NNT.size()*Ratio), vn);
ScalarType cosAngle = cos(AngleRad);
for(auto ni : NNT)
{
if(dir.dot(ni) >= cosAngle) NN.push_back(ni);
}
}
// This is an Implementation of the Dave Rusin’s Disco Ball algorithm
// You can spread the points as follows:
// Put N+1 points on the meridian from north to south poles, equally spaced.
// If you swing this meridian around the sphere, you'll sweep out the entire
// surface; in the process, each of the points will sweep out a circle. You
// can show that the ith point will sweep out a circle of radius sin(pi i/N).
// If you space points equally far apart on this circle, keeping the
// displacement roughly the same as on that original meridian, you'll be
// able to fit about 2N sin(pi i/N) points here. This process will put points
// pretty evenly spaced on the sphere; the number of such points is about
// 2+ 2N*Sum(i=1 to N-1) sin(pi i/N).
// The closed form of this summation
// 2.0 - ( (2.0*N * sin (M_PI/N))/(cos(M_PI/N) - 1.0));
static void DiscoBall(int vn, std::vector<Point3<ScalarType > > &NN)
{
// Guess the right N
ScalarType N=0;
for(N=1;N<vn;++N)
{
ScalarType expectedPoints = 2.0 - ( (2.0*N * sin (M_PI/N))/(cos(M_PI/N) - 1.0));
if(expectedPoints >= vn) break;
}
ScalarType VerticalAngle = M_PI / N;
NN.push_back(Point3<ScalarType>(0,0,1.0));
for (int i =1; i<N; ++i)
{
// Z is the north/south axis
ScalarType HorizRadius = sin(i*VerticalAngle);
ScalarType CircleLength = 2.0 * M_PI * HorizRadius;
ScalarType Z = cos(i*VerticalAngle);
ScalarType PointNumPerCircle = floor( CircleLength / VerticalAngle);
ScalarType HorizontalAngle = 2.0*M_PI/PointNumPerCircle;
for(ScalarType j=0;j<PointNumPerCircle;++j)
{
ScalarType X = cos(j*HorizontalAngle)*HorizRadius;
ScalarType Y = sin(j*HorizontalAngle)*HorizRadius;
NN.push_back(Point3<ScalarType>(X,Y,Z));
}
}
NN.push_back(Point3<ScalarType>(0,0,-1.0));
}
static void RecursiveOctahedron(int vn, std::vector<Point3<ScalarType > > &NN)
{
OctaLevel pp;
int ll=10;
while(pow(4.0f,ll)+2>vn) ll--;
pp.Init(ll);
sort(pp.v.begin(),pp.v.end());
int newsize = unique(pp.v.begin(),pp.v.end())-pp.v.begin();
pp.v.resize(newsize);
NN=pp.v;
//Perturb(NN);
}
static void Perturb(std::vector<Point3<ScalarType > > &NN)
{
float width=0.2f/sqrt(float(NN.size()));
typename std::vector<Point3<ScalarType> >::iterator vi;
for(vi=NN.begin(); vi!=NN.end();++vi)
{
Point3x pp(((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX);
pp=pp*2.0-Point3x(1,1,1);
pp*=width;
(*vi)+=pp;
(*vi).Normalize();
}
}
/*
Trova la normale piu vicina a quella data.
Assume che tutte normale in ingresso sia normalizzata;
*/
static int BestMatchingNormal(const Point3x &n, std::vector<Point3x> &nv)
{
int ret=-1;
ScalarType bestang=-1;
ScalarType cosang;
typename std::vector<Point3x>::iterator ni;
for(ni=nv.begin();ni!=nv.end();++ni)
{
cosang=(*ni).dot(n);
if(cosang>bestang) {
bestang=cosang;
ret=ni-nv.begin();
}
}
assert(ret>=0 && ret <int(nv.size()));
return ret;
}
private :
class OctaLevel
{
public:
std::vector<Point3x> v;
int level;
int sz;
int sz2;
Point3x &Val(int i, int j) {
assert(i>=-sz2 && i<=sz2);
assert(j>=-sz2 && j<=sz2);
return v[i+sz2 +(j+sz2)*sz];
}
/*
* Only the first quadrant is generated and replicated onto the other ones.
*
* o lev == 1
* | \ sz2 = 2^lev = 2
* o - o sz = 5 (eg. all the points lie in a 5x5 squre)
* | \ | \
* o - o - o
*
* |
* V
*
* o
* | \ lev == 1
* o - o sz2 = 4
* | \ | \ sz = 9 (eg. all the points lie in a 9x9 squre)
* o - o - o
* | \ | \ | \
* o - o - o - o
* | \ | \ | \ | \
* o - o - o - o - o
*
*
*/
void Init(int lev)
{
sz2=pow(2.0f,lev);
sz=sz2*2+1;
v.resize(sz*sz,Point3x(0,0,0));
if(lev==0)
{
Val( 0,0)=Point3x( 0, 0, 1);
Val( 1,0)=Point3x( 1, 0, 0);
Val( 0,1)=Point3x( 0, 1, 0);
}
else
{
OctaLevel tmp;
tmp.Init(lev-1);
int i,j;
for(i=0;i<=sz2;++i)
for(j=0;j<=(sz2-i);++j)
{
if((i%2)==0 && (j%2)==0)
Val(i,j)=tmp.Val(i/2,j/2);
if((i%2)!=0 && (j%2)==0)
Val(i,j)=(tmp.Val((i-1)/2,j/2)+tmp.Val((i+1)/2,j/2))/2.0;
if((i%2)==0 && (j%2)!=0)
Val(i,j)=(tmp.Val(i/2,(j-1)/2)+tmp.Val(i/2,(j+1)/2))/2.0;
if((i%2)!=0 && (j%2)!=0)
Val(i,j)=(tmp.Val((i-1)/2,(j+1)/2)+tmp.Val((i+1)/2,(j-1)/2))/2.0;
Val( sz2-j, sz2-i)[0] = Val(i,j)[0]; Val( sz2-j, sz2-i)[1] = Val(i,j)[1]; Val( sz2-j, sz2-i)[2] = -Val(i,j)[2];
Val(-sz2+j, sz2-i)[0] =-Val(i,j)[0]; Val(-sz2+j, sz2-i)[1] = Val(i,j)[1]; Val(-sz2+j, sz2-i)[2] = -Val(i,j)[2];
Val( sz2-j,-sz2+i)[0] = Val(i,j)[0]; Val( sz2-j,-sz2+i)[1] =-Val(i,j)[1]; Val( sz2-j,-sz2+i)[2] = -Val(i,j)[2];
Val(-sz2+j,-sz2+i)[0] =-Val(i,j)[0]; Val(-sz2+j,-sz2+i)[1] =-Val(i,j)[1]; Val(-sz2+j,-sz2+i)[2] = -Val(i,j)[2];
Val(-i,-j)[0] = -Val(i,j)[0]; Val(-i,-j)[1] = -Val(i,j)[1]; Val(-i,-j)[2] = Val(i,j)[2];
Val( i,-j)[0] = Val(i,j)[0]; Val( i,-j)[1] = -Val(i,j)[1]; Val( i,-j)[2] = Val(i,j)[2];
Val(-i, j)[0] = -Val(i,j)[0]; Val(-i, j)[1] = Val(i,j)[1]; Val(-i, j)[2] = Val(i,j)[2];
}
typename std::vector<Point3<ScalarType> >::iterator vi;
for(vi=v.begin(); vi!=v.end();++vi)
(*vi).Normalize();
}
}
};
};
}
#endif