#
# Moments of freeform surfaces
#

sp = surfPRev( cregion( pcircle( vector( 0, 0, 0 ), 1 ), 1, 3 ) * ry( 90 ) );
interact( list( axes, sp ) );

# SVolume( Srf, Method, Eval )
# Srf - surface to use
# Method - 1 for projection onto XY plane, 2 through the origin.
# Eval - false for returning integral surface, true for returning volume.

Vol1 = list( svolume( sp, 1, 1 ) * 3 / 4,
	     svolume( sp, 2, 1 ) * 3 / 4 );
printf( "Volume1 = %f  %f\\n", Vol1 );

# SMoments( Srf, Moment, Axis1, Axis2, Eval )
# Srf - surface to use
# Moment - 1 for first moment, 2 for second moment.
# Axis1, Axis2 - the two axes of moment computation, 1 for X, 2 for Y, 3 for Z.
# Eval - false for returning integral surface, true for returning volume.

Mom1 = list( smoments( sp, 1, 1, 1, 1 ),
	     smoments( sp, 2, 1, 1, 1 ),
	     smoments( sp, 2, 2, 2, 1 ),
	     smoments( sp, 2, 3, 3, 1 ) );
printf( "Moments1 = %f  %f  %f  %f\\n", Mom1 );

#############################################################################

sp = sp * sx( 0.1 ) * sy( 0.1 );
interact( list( axes, sp ) );

Vol2 = list( svolume( sp, 1, 1 ) * 3 / 4,
	     svolume( sp, 2, 1 ) * 3 / 4 );
printf( "Volume2 = %f  %f\\n", Vol2 );

Mom2 = list( smoments( sp, 2, 1, 1, 1 ),
	     smoments( sp, 2, 2, 2, 1 ),
	     smoments( sp, 2, 3, 3, 1 ) );

printf( "Moments2 = %f  %f  %f\\n", Mom2 );

#############################################################################

save( "moments", list( Vol1, Mom1, Vol2, Mom2 ) );

#############################################################################

free( Vol1 );
free( Vol2 );
free( Mom1 );
free( Mom2 );
free( sp );