void PMCone::createPoints( PMPointArray& points, const PMVector& end1,
const PMVector& end2, double radius1, double radius2, int steps )
{
double angle = ( 2.0 * M_PI ) / (double) steps;
PMVector pointAt = end2 - end1;
double pl = pointAt.abs( );
if( approxZero( pl ) )
pointAt = PMVector( 0.0, 1.0, 0.0 );
else
pointAt /= pl;
PMMatrix rotation = PMMatrix::rotation( pointAt, angle );
PMVector endPoint1 = pointAt.orthogonal( );
endPoint1 *= radius1;
PMVector endPoint2 = pointAt.orthogonal( );
endPoint2 *= radius2;
int i;
for( i = 0; i < steps; i++ )
{
points[i] = PMPoint( endPoint1 + end1 );
points[i + steps] = PMPoint( endPoint2 + end2 );
endPoint1 = rotation * endPoint1;
endPoint2 = rotation * endPoint2;
}
}
void PMTorus::createPoints( PMPointArray& points, double minor_radius,
double major_radius, int uStep, int vStep )
{
double l_UradStep = ( 2.0 * M_PI ) / uStep;
double l_VradStep = ( 2.0 * M_PI ) / vStep;
double l_u = l_UradStep;
int u, v;
for( u = 0; u < uStep; ++u )
{
double l_v = 0.0;
double y = minor_radius * sin ( l_u );
double l_rcosu = major_radius + minor_radius * cos( l_u );
for( v = 0; v < vStep; ++v )
{
double x = l_rcosu * cos( l_v );
double z = l_rcosu * sin( l_v );
points[u * vStep + v ] = PMPoint( x, y, z );
l_v = l_v + l_VradStep;
}
l_u = l_u + l_UradStep;
}
}
void PMSuperquadricEllipsoid::createPoints( PMPointArray& points,
double e, double n, int uStep, int vStep )
{
int u, v;
int zi;
int pbase = 0, pref = 0;
if( e <= 0.001 )
e = 0.001;
if( n <= 0.001 )
n = 0.001;
double c2_e = 2.0 / e;
double c2_n = 2.0 / n;
double cn_2 = n / 2.0;
double ce_2 = e / 2.0;
double cn_e = n / e;
// double ce_n = e / n;
double z = 0.0, c = 0.0, a = 0.0, a2 = 0.0, x = 0.0, y = 0.0;
double k = 0.0, k2 = 0.0, du = 0.0, dv = 0.0;
PMPoint p;
points[0] = PMPoint( 0, 0, 1 );
pbase++;
for( zi = 0; zi < 2; zi++ )
{
for( u = 0; u < uStep; u++ )
{
du = ( double ) ( u + 1 ) / ( double ) uStep;
if( zi == 1 )
du = 1.0 - du;
k = tan( M_PI / 4.0 * pow( du, n < 1.0 ? n : sqrt( n ) ) );
k2 = 1 / ( pow( k, c2_n ) + 1 );
z = pow( k2, cn_2 );
if( zi == 1 )
z *= k;
c = pow( 1 - pow( z, c2_n ), cn_e );
for( v = 0; v < ( vStep + 1 ); v++ )
{
dv = ( double ) v / ( double ) vStep;
a = tan( M_PI / 4.0 * pow( dv, e < 1.0 ? e : sqrt( e ) ) );
a2 = 1 + pow( a, c2_e );
x = pow( c / a2, ce_2 );
y = x * a;
points[pbase+v] = PMPoint( x, y, z );
}
// 1/8
pref = pbase + 2 * vStep;
for( v = 0; v < vStep; v++, pref-- )
{
p = points[pbase+v];
x = p[0];
p[0] = p[1];
p[1] = x;
points[pref] = p;
}
// 1/4
pref = pbase + 4 * vStep;
for( v = 0; v < ( 2 * vStep ); v++, pref-- )
{
p = points[pbase+v];
p[0] = -p[0];
points[pref] = p;
}
// 1/2
pref = pbase + 8 * vStep - 1;
for( v = 1; v < ( 4 * vStep ); v++, pref-- )
{
p = points[pbase+v];
p[1] = -p[1];
points[pref] = p;
}
pbase += 8 * vStep;
}
}
for( u = 0; u < ( uStep * 2 - 1 ); u++ )
{
pbase = 1 + u * vStep * 8;
pref = 1 + ( uStep * 4 - 2 - u ) * vStep * 8;
for( v = 0; v < ( vStep * 8 ); v++, pref++ )
{
p = points[pbase + v];
p[2] = -p[2];
points[pref] = p;
}
}
points[ vStep * 8 * ( uStep * 4 - 1 ) + 1 ] = PMPoint( 0, 0, -1 );
}