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Added an implementation of the Dave Rusin’s Disco Ball algorithm for the generation of regular points on a sphere.

This commit is contained in:
Paolo Cignoni 2014-06-17 14:51:20 +00:00
parent a90b2a79ef
commit e6e7999c6c
1 changed files with 74 additions and 29 deletions
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103
vcg/math/gen_normal.h
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@ -8,7 +8,7 @@
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* 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. *
@ -34,7 +34,7 @@ $Log: gen_normal.h,v $
namespace vcg {
template <class ScalarType>
class GenNormal
class GenNormal
{
public:
typedef Point3<ScalarType> Point3x;
@ -45,8 +45,8 @@ static void Random(int vn, std::vector<Point3<ScalarType > > &NN)
while(NN.size()<vn)
{
Point3x pp(((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX);
((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX);
pp=pp*2.0-Point3x(1,1,1);
if(pp.SquaredNorm()<1)
{
@ -69,7 +69,7 @@ static void UniformCone(int vn, std::vector<Point3<ScalarType > > &NN, ScalarTyp
Uniform(vn/Ratio,NNT);
printf("asked %i got %i (expecting %i instead of %i)\n", int(vn/Ratio), NNT.size(), int(NNT.size()*Ratio), vn);
typename std::vector<Point3<ScalarType> >::iterator vi;
ScalarType DotProd = cos(AngleRad);
for(vi=NNT.begin();vi!=NNT.end();++vi)
{
@ -77,6 +77,51 @@ static void UniformCone(int vn, std::vector<Point3<ScalarType > > &NN, ScalarTyp
}
}
// 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 Regular(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));
qDebug("N %f -> %f",N,expectedPoints);
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 Uniform(int vn, std::vector<Point3<ScalarType > > &NN)
{
@ -99,11 +144,11 @@ 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)
for(vi=NN.begin(); vi!=NN.end();++vi)
{
Point3x pp(((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX);
((float)rand())/RAND_MAX,
((float)rand())/RAND_MAX);
pp=pp*2.0-Point3x(1,1,1);
pp*=width;
(*vi)+=pp;
@ -118,20 +163,20 @@ 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();
}
}
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;
return ret;
}
@ -156,7 +201,7 @@ class OctaLevel
if(lev==0)
{
Val(0,0)=Point3x( 0, 0,-1); Val(0,1)=Point3x( 0, 1, 0); Val(0,2)=Point3x( 0, 0,-1);
Val(1,0)=Point3x(-1, 0, 0); Val(1,1)=Point3x( 0, 0, 1); Val(1,2)=Point3x( 1, 0, 0);
Val(2,0)=Point3x( 0, 0,-1); Val(2,1)=Point3x( 0,-1, 0); Val(2,2)=Point3x( 0, 0,-1);
@ -169,19 +214,19 @@ class OctaLevel
for(i=0;i<sz;++i)
for(j=0;j<sz;++j)
{
if((i%2)==0 && (j%2)==0)
if((i%2)==0 && (j%2)==0)
Val(i,j)=tmp.Val(i/2,j/2);
if((i%2)!=0 && (j%2)==0)
if((i%2)!=0 && (j%2)==0)
Val(i,j)=(tmp.Val(i/2+0,j/2)+tmp.Val(i/2+1,j/2))/2.0;
if((i%2)==0 && (j%2)!=0)
if((i%2)==0 && (j%2)!=0)
Val(i,j)=(tmp.Val(i/2,j/2+0)+tmp.Val(i/2,j/2+1))/2.0;
if((i%2)!=0 && (j%2)!=0)
if((i%2)!=0 && (j%2)!=0)
Val(i,j)=(tmp.Val(i/2+0,j/2+0)+tmp.Val(i/2+0,j/2+1)+tmp.Val(i/2+1,j/2+0)+tmp.Val(i/2+1,j/2+1))/4.0;
}
typename std::vector<Point3<ScalarType> >::iterator vi;
for(vi=v.begin(); vi!=v.end();++vi)
typename std::vector<Point3<ScalarType> >::iterator vi;
for(vi=v.begin(); vi!=v.end();++vi)
(*vi).Normalize();
}
}
};