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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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45
vcg/math/gen_normal.h
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@ -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) static void Uniform(int vn, std::vector<Point3<ScalarType > > &NN)
{ {