#
# Examples of the Convex Hull of Surfaces.
#
#					Joon-Kyung Seong, November 2002
#

save_res = resolution;

##############################################################################
#
# The Convex hull of two surfaces
#

c = cbspline( 3, list( ctlpt( e2, -1, -1 ),
    		       ctlpt( e2, -1,  1 ),
    		       ctlpt( e2,  1,  1 ),
    		       ctlpt( e2,  1, -1 ) ), list ( kv_periodic ) );
c = coerce( c, kv_open );

ellip1 = sFromCrvs( list( c * sc( 0.001 ),
     			  c,
     			  c * tz( 2.4 ),
     			  c * sc( 0.001 ) * tz( 2.4 ) ) , 3, kv_open );

ellip2 = sFromCrvs( list( c * ry( 45 ) * sc( 0.001 ) * tz( 1.5 ) * tx( 2 ),
     			  c * ry( 45 ) * tz( 1.5 ) * tx( 2 ),
     			  c * ry( 45 ) * tz( 3.5 ) * tx( 4 ),
     			  c * ry( 45 ) * sc( 0.001 ) * tz( 3.5 ) * tx( 4 ) ) ,
     		    3, kv_open );

Srfs = list( ellip1, ellip2 );

ch = CNVXHULL( Srfs, 0.2 );
interact( list( Srfs, ch, axes ) );


#
# In two-surfaces-case, the following call gives you 
# the same results to that of the above.
#

attrib( Srfs, "tangency", true );
ch1 = CNVXHULL( Srfs, 0.2 );
interact( list( Srfs, ch1, axes ) );

#
# you can also get a more accurate result
#

ch2 = CNVXHULL( Srfs, 0.1 );

save( "scnvhul1", list( Srfs, ch, ch1, ch2 ) );

interact( list( Srfs, ch2, axes ) );


#
# Another simple example(two-surfaces-case)
#

c1 = cregion( pcircle( vector( 0, 0, 0 ), 1 ), 1, 3 );
view( list( c1, axes ), 1 );

s1 = surfPRev( c1 * ry( 90 ) );
view( list( s1, axes ), 1 );

s2 = s1 * sx( 0.7 ) * sx( 0.45 ) * tz( 3 ) * tx( 0.2 ) * ty( 0.1 );

Srfs = list( s1, s2 );
view( list( Srfs, axes ), 1 );

attrib( Srfs, "tangency", 1 );
ch3 = CNVXHULL( Srfs, 0.1 );
interact( list( Srfs, ch3, axes ) );


#####################################################################
#
# Example for three surfaces case
#

ellip3 = sFromCrvs( list( 
     c * ry( 70 ) * sc( 0.001 ) * tz( 3.5 ) * tx( -1 ),
     c * ry( 70 ) * tz( 3.5 ) * tx( -1 ),
     c * ry( 70 ) * tz( 6 ) * tx( 3 ),
     c * ry( 70 ) * sc( 0.001 ) * tz( 6 ) * tx( 3 ) ) , 3, kv_open )
     * rx( 180 ) * tz( 3 ) * tx( 1 );

Srfs = list( ellip1, ellip2, ellip3 );
view( list( Srfs, axes ), 1 );

attrib( Srfs, "tangency", 0 );
ch4 = CNVXHULL( Srfs, 0.2 );
interact( list( Srfs, ch4, axes ) );

###################################################################
#
#	more complex surface
#

s = sFromCrvs( list( 
	c * sc( 0.001 ),
     	c,
     	c * tz( 2 ),
     	c * sc( 0.1 ) * tz( 2.4 ) ,
     	c * sc( 1.6 ) * ry( 45 ) * tz( 3 ) * tx( 0.5 ),
     	c * sc( 1.21 ) * ry( 85 ) * tz( 3.2 ) * tx( 1.8 ),
     	c * ry( 86 ) * sc( 0.1 ) * tz( 3.5 ) * tx( 2 ),
     	c * sc( 1.5 ) * ry( 70 ) * tz( 3.7 ) * tx( 3.2 ),
     	c * sc( 1.2 ) * ry( 75 ) * tz( 4 ) * tx(4 ),
     	c * sc(0.7) * ry( 75 ) * tz( 4.4 ) * tx( 5 ),
     	c * sc( 0.001 ) * ry( 75 ) * tz( 4.4 ) * tx( 5 ) ), 3, kv_open );

view( list( s, axes ), 1 );

#
#  Let's seperate the surface into three patch.
#
s1 = sFromCrvs( list( c * sc( 0.001 ),
     		      c,
     		      c * tz( 2 ),
	 	      c * sc( 0.4 ) * tz( 2.2 ),
     		      c * sc( 0.1 ) * tz( 2.4 ) ), 3, kv_open );

s2 = sFromCrvs( list( 
	c * sc( 0.1 ) * tz( 2.4 ) ,
	c * sc( 0.53 ) * ry( 45 ) * tz( 2.55 ) * tx( 0.18 ), 
	c * sc( 1.56 ) * ry( 45 ) * tz( 3 ) * tx( 0.5 ),
	c * sc( 1.21 ) * ry( 85 ) * tz( 3.2 ) * tx( 1.8 ),
	c * sc( 0.5 ) * ry( 85 ) * tz( 3.3 ) * tx( 1.9 ),
     	c * ry( 86 ) * sc( 0.1 ) * tz( 3.5 ) * tx( 2 ) ), 3, kv_open );

s3  = sFromCrvs( list( 
	 c * ry( 86 ) * sc( 0.1 ) * tz( 3.5 ) * tx( 2 ),
	 c * sc( 1.55 ) * ry( 70 ) * tz( 3.7 ) * tx( 3.2 ),
     	 c * sc( 1.2 ) * ry( 75 ) * tz( 4 ) * tx(4 ),
     	 c * sc(0.7) * ry( 75 ) * tz( 4.4 ) * tx( 5 ),
     	 c * sc( 0.001 ) * ry( 75 ) * tz( 4.4 ) * tx( 5 ) ), 3, kv_open );

Srfs = list( s1, s2, s3 );
ch5 = CNVXHULL( Srfs, 0.2 );
interact( list( Srfs, ch5, axes ) );

#####################################################################
##  test for three-tangencies
ts1 = sFromCrvs( list( 
	c * sc( 0.001 ),
     	c,
     	c * tz( 2 ),
     	c * sc( 0.1 ) * tz( 2.4 ) ,
     	c * sc( 1.6 ) * ry( 45 ) * tz( 3 ) * tx( 0.5 ),
     	c * sc( 1.21 ) * ry( 85 ) * tz( 3.2 ) * tx( 1.8 ),
     	c * ry( 86 ) * sc( 0.1 ) * tz( 3.5 ) * tx( 2 ),
     	c * sc( 0.001 ) * ry( 86 ) * tz( 3.5 ) * tx( 2 ) ), 3, kv_open );

ts2 = ellip1 * tx( 4.0 ) * tz( 2.5 );
ts3 = ellip2 * tz( -2.0 );

Srfs = list( ts1, ts2, ts3 );
view( list( Srfs, axes ), 1 );

attrib( Srfs, "tangency", 1 );
ch6 = CNVXHULL( Srfs, 0.4 );
interact( list( Srfs, ch6, axes ) );

free( ts1 );
free( ts2 );
free( ts3 );
free( Srfs );
free( ellip1 );
free( ellip2 );
free( ellip3 );

free( c );
free( s );
free( c1 );
free( s1 );
free( s2 );
free( s3 );
free( ch );
free( ch1 );
free( ch2 );
free( ch3 );
free( ch4 );
free( ch5 );
free( ch6 );