#
# Examples of ruled ruled surface intersection approximations.
#
#					Gershon Elber, February 1998
#

GenAxes = list( ctlpt( E3, 0, 0, 0 )+ ctlpt( E3, 0.0, 0.0, 0.4 ),
		ctlpt( E3, 0, 0, 0 )+ ctlpt( E3, 0.0, 1.1, 0.0 ),
		ctlpt( E3, 0, 0, 0 )+ ctlpt( E3, 1.1, 0.0, 0.0 ) );
awidth( GenAxes, 0.005 );
color( GenAxes, green );

EvalUVtoE3 = function( Srf, UVs, clr ): UV: i:
    return = nil():
    for ( i = 1, 1, sizeof( UVs ),
	UV = nth( UVs, i ):
	snoc( seval( Srf, coord( UV, 1 ), coord( UV, 2 ) ), return ) ):
    color( return, clr );

#############################################################################
#
# Case 1
#

c1 = cbezier( list( ctlpt( E3, -1.0, 0.0, -1.0 ),
	            ctlpt( E3,  0.0, 1.0, -1.0 ),
		    ctlpt( E3,  0.3, 0.0, -1.0 ),
		    ctlpt( E3,  1.0, 0.0, -1.0 ) ) );

c2 = cbezier( list( ctlpt( E3, -1.0, 0.0,  1.0 ),
		    ctlpt( E3,  0.0, 1.0,  1.0 ),
		    ctlpt( E3,  0.3, 1.0,  1.0 ),
		    ctlpt( E3,  1.0, 0.0,  1.0 ) ) );

r1 = ruledSrf( c1, c2 );

r2 = r1 * rx( 90 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1);

color( c, red );
adwidth( c, 3 );

interact( list( r1, r2, c ) );

zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      10, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 0.1 );
zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 0.00001 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );

interact( list( axes, zeroSetSrfE3, zeroSet ) );

#############################################################################
#
# Case 2
#

c1 = cbezier( list( ctlpt( E3, -1.0, 0.0, -1.0 ),
	            ctlpt( E3,  0.0, 1.0, -1.0 ),
		    ctlpt( E3,  0.3, 0.0, -1.0 ),
		    ctlpt( E3,  1.0, 0.0, -1.0 ) ) );

c2 = cbezier( list( ctlpt( E3, -1.0, 0.0,  1.0 ),
		    ctlpt( E3,  0.0, 1.0,  1.0 ),
		    ctlpt( E3,  0.3, 1.0,  1.0 ),
		    ctlpt( E3,  1.0, 0.0,  1.0 ) ) );

r1 = ruledSrf( c1, c2 );

r2 = r1 * rx( 90 ) * sc( 0.9 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1 );
color( c, red );
adwidth( c, 3 );

interact( list( r1, r2, c ) );


zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      10, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 0.1 );
zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 0.00001 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );

interact( list( axes, zeroSetSrfE3, zeroSet ) );

#############################################################################
#
# Case 3
#

c1 = cbezier( list( ctlpt( E3, -1.0, -1.0, -1.0 ),
	            ctlpt( E3, -0.5,  1.0, -1.0 ),
		    ctlpt( E3,  0.3, -2.0, -1.0 ),
		    ctlpt( E3,  0.5,  1.0, -1.0 ),
		    ctlpt( E3,  1.0, -1.0, -1.0 ) ) );

c2 = c1 * sc( 0.7 ) * tz( 1.7 );

r1 = ruledSrf( c1, c2 );

c1 = cbezier( list( ctlpt( E3, -1.0, 0.0, -1.0 ),
	            ctlpt( E3,  0.0, 1.0, -1.0 ),
		    ctlpt( E3,  0.3, 0.0, -1.0 ),
		    ctlpt( E3,  1.0, 0.0, -1.0 ) ) );

c2 = cbezier( list( ctlpt( E3, -1.0, 0.0,  1.0 ),
		    ctlpt( E3,  0.0, 1.0,  1.0 ),
		    ctlpt( E3,  0.3, 1.0,  1.0 ),
		    ctlpt( E3,  1.0, 0.0,  1.0 ) ) );

r2 = ruledSrf( c1, c2 ) * rx( 90 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1 );
color( c, red );
adwidth( c, 3 );

interact( list( r1, r2, c ) );


zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      10, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 0.1 );
zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 0.00001 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );

interact( list( axes, zeroSetSrfE3, zeroSet ) );

#############################################################################
#
# Case 4
#

c1 = cbezier( list( ctlpt( E3, -1.0,  -1.0, -1.0 ),
	            ctlpt( E3, -0.5,   8.0, -1.0 ),
		    ctlpt( E3,  0.3, -15.0, -1.0 ),
		    ctlpt( E3,  0.5,   8.0, -1.0 ),
		    ctlpt( E3,  1.0,  -1.0, -1.0 ) ) );

c2 = c1 * sc( 0.7 ) * tz( 1.7 );

r1 = ruledSrf( c1, c2 );

c1 = cbezier( list( ctlpt( E3, -1.0, 0.0, -1.0 ),
	            ctlpt( E3,  0.0, 1.0, -1.0 ),
		    ctlpt( E3,  0.3, 0.0, -1.0 ),
		    ctlpt( E3,  1.0, 0.0, -1.0 ) ) );

c2 = cbezier( list( ctlpt( E3, -1.0, 0.0,  1.0 ),
		    ctlpt( E3,  0.0, 1.0,  1.0 ),
		    ctlpt( E3,  0.3, 1.0,  1.0 ),
		    ctlpt( E3,  1.0, 0.0,  1.0 ) ) );

r2 = ruledSrf( c1, c2 ) * rx( 90 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          20, false ), 1 );
color( c, red );
adwidth( c, 3 );

interact( list( r1, r2, c ) );

c = nth( rrinter( cMesh( r1, row, 0 ),
	     cMesh( r1, row, 1 ),
	     cMesh( r2, row, 0 ),
	     cMesh( r2, row, 1 ),
	     -20, false ), 1 );
color( c, red );
adwidth( c, 3 );

interact( list( r1, r2, c ) );


zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      10, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 0.1 );
zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 0.00001 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );

interact( list( axes, zeroSetSrfE3, zeroSet ) );

#############################################################################
#
# Case 5
#

c1 = cbezier( list( ctlpt( E3, -1.0,  -1.0, -1.0 ),
	            ctlpt( E3, -0.5,   8.0, -1.0 ),
		    ctlpt( E3,  0.0, -15.0, -1.0 ),
		    ctlpt( E3,  0.5,   8.0, -1.0 ),
		    ctlpt( E3,  1.0,  -1.0, -1.0 ) ) );

c2 = c1 * sc( 0.7 ) * tz( 1.7 );

r1 = ruledSrf( c1, c2 );
awidth( r1, 0.007 );

c1 = pcircle( vector( 0, 0, 0 ), 0.3 ) * tz( 2 );

c2 = c1 * sc( 0.5 ) * tz ( -3 );

r2 = ruledSrf( c1, c2 ) * ry( 90 );
awidth( r2, 0.007 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          50, false ), 1 );
color( c, red );
adwidth( c, 3 );
awidth( c, 0.02 );
attrib( c, "gray", 0.5 );

interact( list( r1, r2, c ) );

save( "rrint5a", list( r1, r2, c ) );

zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      25, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 0.02 );
awidth( zeroSetSrfE3, 0.007 );

zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 0.00001 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );
awidth( zeroSet, 0.02 );

interact( list( GenAxes, zeroSetSrfE3, zeroSet ) );

save( "rrint5b", list( GenAxes, zeroSetSrfE3, zeroSet ) );

#############################################################################
#
# Case 6
#

c1 = pcircle( vector( 0, 0, 0 ), 0.3 ) * tz( 1 );

c2 = c1 * tz ( -2 );

r1 = ruledSrf( c1, c2 );
awidth( r1, 0.007 );

r2 = r1 * rx( 10 ) ;
awidth( r2, 0.007 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1 );
color( c, red );
adwidth( c, 3 );
awidth( c, 0.02 );
attrib( c, "gray", 0.5 );

interact( list( r1, r2, c ) );

save( "rrint6a", list( r1, r2, c ) );


r2 = r1 * rx( 1 ) ;
awidth( r2, 0.007 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	 	  cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1 );
color( c, red );
adwidth( c, 3 );
awidth( c, 0.02 );
attrib( c, "gray", 0.5 );

interact( list( r1, r2, c ) );

save( "rrint6b", list( r1, r2, c ) );


r2 = r1 * rx( 0.1 ) ;
awidth( r2, 0.007 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1 );
color( c, red );
adwidth( c, 3 );
awidth( c, 0.02 );
attrib( c, "gray", 0.5 );

interact( list( r1, r2, c ) );

save( "rrint6c", list( r1, r2, c ) );


r2 = r1 * rx( 0.01 ) ;
awidth( r2, 0.007 );

c = nth( rrinter( cMesh( r1, row, 0 ),
	          cMesh( r1, row, 1 ),
	          cMesh( r2, row, 0 ),
	          cMesh( r2, row, 1 ),
	          10, false ), 1 );
color( c, red );
adwidth( c, 3 );
awidth( c, 0.02 );
attrib( c, "gray", 0.5 );

interact( list( r1, r2, c ) );

save( "rrint6d", list( r1, r2, c ) );


r2 = r1 * rx( 10 ) ;
awidth( r2, 0.007 );

zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      10, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 0.3 );
awidth( zeroSetSrfE3, 0.007 );

zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 0.00001 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );
awidth( zeroSet, 0.02 );

interact( list( GenAxes, zeroSetSrfE3, zeroSet ) );

save( "rrint6u", list( GenAxes, zeroSetSrfE3, zeroSet ) );


r2 = r1 * rx( 0.01 ) ;
awidth( r2, 0.007 );

zeroSetSrf = rrinter( cMesh( r1, row, 0 ),
		      cMesh( r1, row, 1 ),
		      cMesh( r2, row, 0 ),
		      cMesh( r2, row, 1 ),
		      10, true );
zeroSetSrfE3 = coerce( zeroSetSrf, e3 )
				* rotx( -90 ) * roty( -90 ) * sz( 1 );
awidth( zeroSetSrfE3, 0.007 );

zeroSet = contour( zeroSetSrfE3, plane( 0, 0, 1, 1e-8 ) );
color( zeroSet, red );
adwidth( zeroSet, 3 );
awidth( zeroSet, 0.02 );

UExtreme = EvalUVtoE3( zeroSetSrfE3, 
		       ciextreme( zeroSetSrf, col, 0.01, -1e-9 ),
		       yellow );
adwidth( UExtreme, 2 );

interact( list( GenAxes, zeroSetSrfE3, zeroSet, UExtreme ) );

save( "rrint6v", list( GenAxes, zeroSetSrfE3, zeroSet, UExtreme ) );

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

free( UExtreme );
free( GenAxes );
free( c );
free( c1 );
free( c2 );
free( r1 );
free( r2 );
free( zeroSet );
free( zeroSetSrf );
free( zeroSetSrfE3 );