ON_BOOL32 ON_Surface::FrameAt( double u, double v, ON_Plane& frame) const
{
ON_BOOL32 rc = false;
ON_3dPoint origin;
ON_3dVector udir, vdir, normal;
if( EvNormal( u, v, origin, udir, vdir, normal))
{
if ( udir.Unitize() )
vdir = ON_CrossProduct( normal, udir);
else if ( vdir.Unitize() )
udir = ON_CrossProduct( vdir, normal);
frame.CreateFromFrame( origin, udir, vdir);
rc = frame.IsValid();
}
return rc;
}
bool ON_Line::InPlane( ON_Plane& plane, double tolerance ) const
{
const ON_3dVector v = to-from;
const bool bTinyX = fabs(v.x) <= tolerance;
const bool bTinyY = fabs(v.y) <= tolerance;
const bool bTinyZ = fabs(v.z) <= tolerance;
bool rc = true;
ON_3dVector X;
ON_3dVector Y;
if ( bTinyZ && ( !bTinyX || !bTinyY ) )
{
X = ON_xaxis;
Y = ON_yaxis;
}
else if ( bTinyX && ( !bTinyY || !bTinyZ ) )
{
X = ON_yaxis;
Y = ON_zaxis;
}
else if ( bTinyY && ( !bTinyZ || !bTinyX ) )
{
X = ON_zaxis;
Y = ON_xaxis;
}
else
{
X = v;
X.Unitize();
Y.PerpendicularTo(X);
if ( bTinyX && bTinyY && bTinyZ )
{
rc = false;
if ( X.IsZero() )
{
X = ON_xaxis;
Y = ON_yaxis;
}
}
}
plane.CreateFromFrame( from, X, Y );
return rc;
}
bool ON_Plane::Morph( const ON_SpaceMorph& morph )
{
ON_Plane mp;
double s = sqrt( fabs(origin.MaximumCoordinate())*ON_SQRT_EPSILON + ON_ZERO_TOLERANCE );
mp.xaxis = morph.MorphVector(origin,s*xaxis);
mp.yaxis = morph.MorphVector(origin,s*yaxis);
mp.zaxis = morph.MorphVector(origin,s*zaxis);
origin = morph.MorphPoint(origin);
UpdateEquation();
bool bx = mp.xaxis.Unitize();
bool by = mp.yaxis.Unitize();
bool bz = mp.zaxis.Unitize();
if (!bx)
{
mp.xaxis = ON_CrossProduct(mp.yaxis,mp.zaxis);
bx = mp.xaxis.Unitize();
}
if (!by)
{
mp.yaxis = ON_CrossProduct(mp.zaxis,mp.xaxis);
by = mp.yaxis.Unitize();
}
if (!bz)
{
mp.zaxis = ON_CrossProduct(mp.xaxis,mp.yaxis);
bz = mp.zaxis.Unitize();
}
mp.origin.Set(0.0,0.0,0.0);
mp.UpdateEquation();
bool rc = mp.IsValid();
ON_3dVector x, y, z;
if ( rc )
{
x = mp.xaxis;
y = mp.yaxis;
z = mp.zaxis;
}
else
{
x = ON_CrossProduct(mp.yaxis,mp.zaxis);
y = ON_CrossProduct(mp.zaxis,mp.xaxis);
z = ON_CrossProduct(mp.xaxis,mp.yaxis);
x.Unitize();
y.Unitize();
z.Unitize();
x = mp.xaxis + x;
y = mp.yaxis + y;
z = mp.zaxis + z;
x.Unitize();
y.Unitize();
z.Unitize();
rc = mp.CreateFromFrame(ON_origin,x,y);
if (rc)
{
x = mp.xaxis;
y = mp.yaxis;
z = mp.zaxis;
}
else
{
rc = mp.CreateFromFrame(ON_origin,y,z);
if ( rc )
{
y = mp.xaxis;
z = mp.yaxis;
x = mp.zaxis;
}
else
{
rc = mp.CreateFromFrame(ON_origin,z,x);
if (rc)
{
z = mp.xaxis;
x = mp.yaxis;
y = mp.zaxis;
}
else
{
rc = mp.CreateFromNormal(ON_origin,z);
if (rc)
{
x = mp.xaxis;
y = mp.yaxis;
z = mp.zaxis;
}
}
}
}
}
if (rc)
{
xaxis = x;
yaxis = y;
zaxis = z;
UpdateEquation();
}
return rc;
}