#
# Curve - point/line/curve closest/"farest" location/intersection.
#
#					Gershon Elber, May 1993.
#

#
# Curve point distance.
#
crv1 = cbspline( 3,
		 list( ctlpt( E2,  0.5, -1.0 ),
		       ctlpt( E2, -1.5, -0.5 ),
		       ctlpt( E2,  1.5,  0.0 ),
		       ctlpt( E2, -0.5,  2.0 ),
		       ctlpt( E2, -0.5,  1.0 ) ),
		 list( KV_OPEN ) );
color( crv1, green );
attrib( crv1, "width", 0.02 );

pt_param = crvptdst( crv1, point( 0, 0, 0 ), false, -0.001 );
pt_extrem = nil();

for ( i = 1, 1, sizeof( pt_param ),
	pt = ceval( crv1, nth( pt_param, i ) ):
	snoc( coerce( pt, vector_type ) , pt_extrem )
    );
interact( list( axes, crv1, pt_extrem ) );
save( "crv1dist", list( axes, crv1, pt_extrem ) );

pt_min = ceval( crv1, crvptdst( crv1, point( 0, 0, 0 ), true, 0.001 ) );
interact( list( axes, crv1, coerce( pt_min, vector_type ) ) );

pt_max = ceval( crv1, crvptdst( crv1, point( 0, 0, 0 ), false, 0.001 ) );
interact( list( axes, crv1, coerce( pt_max, vector_type ) ) );
save( "crv2dist", list( axes, crv1, coerce( pt_max, vector_type ) ) );

crv2 = cbspline( 3,
		 list( ctlpt( E2, 0,  1 ),
		       ctlpt( E2, 1, -1 ),
		       ctlpt( E2, 0, -1 ),
		       ctlpt( E2, 1,  1 ) ),
		 list( KV_OPEN ) );
color( crv2, green );
attrib( crv2, "width", 0.02 );

pt_param = crvptdst( crv2, point( 0, 0, 0 ), false, -0.001 );
pt_extrem = nil();
for ( i = 1, 1, sizeof( pt_param ),
	pt = ceval( crv2, nth( pt_param, i ) ):
	snoc( coerce( pt, vector_type ) , pt_extrem )
    );
interact( list( axes, crv2, pt_extrem ) );
save( "crv3dist", list( axes, crv2, pt_extrem ) );

pt_min = ceval( crv2, crvptdst( crv2, point( 0, 0, 0 ), true, 0.001 ) );
interact( list( axes, crv2, coerce( pt_min, vector_type ) ) );
pt_max = ceval( crv2, crvptdst( crv2, point( 0, 0, 0 ), false, 0.001 ) );
interact( list( axes, crv2, coerce( pt_max, vector_type ) ) );
save( "crv4dist", list( axes, crv2, coerce( pt_max, vector_type ) ) );

crv3a = cbspline( 3,
		  list( ctlpt( E2, 0.0,  1.0 ),
		        ctlpt( E2, 0.1,  1.0 ),
		        ctlpt( E2, 0.1,  0.1 ),
		        ctlpt( E2, 0.5,  0.1 ),
		        ctlpt( E2, 0.5, -0.1 ),
		        ctlpt( E2, 0.1, -0.1 ),
		        ctlpt( E2, 0.1, -1.0 ),
		        ctlpt( E2, 0.0, -1.0 ) ),
		  list( KV_OPEN ) );
crv3b = crv3a * rotz( 180 );
crv3 = ( crv3a + crv3b ) * trans( vector( 0.1, 0.1, 0.0 ) );
color( crv3, green );
attrib( crv3, "width", 0.02 );

pt_param = crvptdst( crv3, point( 0, 0, 0 ), false, -0.001 );
pt_extrem = nil();
for ( i = 1, 1, sizeof( pt_param ),
	pt = ceval( crv3, nth( pt_param, i ) ):
	snoc( coerce( pt, vector_type ) , pt_extrem )
    );
interact( list( axes, crv3, pt_extrem ) );
save( "crv5dist", list( axes, crv3, pt_extrem ) );

pt_min = ceval( crv3, crvptdst( crv3, point( 0, 0, 0 ), true, 0.001 ) );
interact( list( axes, crv3, coerce( pt_min, vector_type ) ) );
pt_max = ceval( crv3, crvptdst( crv3, point( 0, 0, 0 ), false, 0.001 ) );
interact( list( axes, crv3, coerce( pt_max, vector_type ) ) );
save( "crv6dist", list( axes, crv3, coerce( pt_max, vector_type ) ) );

#
# Curve line distance.
#
line_pt = point( -1, 1.2, 0 );
line_vec = vector( 1, -1, 0 );
line_pt2 = line_pt + ( line_vec * 2 );
line = poly( list( line_pt, line_pt2 ), true );
crv1 = cbspline( 3,
		 list( ctlpt( E2,  1.5, -0.5 ),
		       ctlpt( E2,  0.5, -1.0 ),
		       ctlpt( E2, -1.5, -0.5 ),
		       ctlpt( E2,  2.5,  0.0 ),
		       ctlpt( E2, -1.5,  0.5 ) ),
		 list( KV_OPEN ) );
color( crv1, green );
attrib( crv1, "width", 0.02 );

pt_param = crvlndst( crv1, line_pt, line_vec, false, -0.001 );
pt_extrem = nil();
for ( i = 1, 1, sizeof( pt_param ),
	pt = ceval( crv1, nth( pt_param, i ) ):
	snoc( pt, pt_extrem )
    );

crv1A = cbspline( 4,
		  list( ctlpt( E2,  1.5, -0.5 ),
		        ctlpt( E2,  0.5, -1.0 ),
		        ctlpt( E2, -1.5, -0.5 ),
		        ctlpt( E2,  2.5,  0.0 ),
		        ctlpt( E2, -1.5,  0.5 ) ),
		  list( KV_OPEN ) );
color( crv1A, green );
attrib( crv1A, "width", 0.02 );

pt_paramA = crvlndst( crv1A, line_pt, line_vec, false, -0.001 );
pt_extremA = nil();
for ( i = 1, 1, sizeof( pt_paramA ),
	pt = ceval( crv1A, nth( pt_paramA, i ) ):
	snoc( pt, pt_extremA )
    );

crv1B = cbspline( 5,
		  list( ctlpt( E2,  1.5, -0.5 ),
		        ctlpt( E2,  0.5, -1.0 ),
		        ctlpt( E2, -1.5, -0.5 ),
		        ctlpt( E2,  2.5,  0.0 ),
		        ctlpt( E2, -1.5,  0.5 ) ),
		  list( KV_OPEN ) );
color( crv1B, green );
attrib( crv1B, "width", 0.02 );

pt_paramB = crvlndst( crv1B, line_pt, line_vec, false, -0.001 );
pt_extremB = nil();
for ( i = 1, 1, sizeof( pt_paramB ),
	pt = ceval( crv1B, nth( pt_paramB, i ) ):
	snoc( pt, pt_extremB )
    );

interact( list( axes, crv1, crv1A, crv1B, line,
		pt_extrem, pt_extremA, pt_extremB ) );

save( "crv1line", list( axes, crv1, crv1A, crv1B, line,
			pt_extrem, pt_extremA, pt_extremB ) );

free( pt_paramA );
free( pt_paramB );
free( pt_extremA );
free( pt_extremB );
free( crv1A );
free( crv1B );

pt_min = ceval( crv1, crvlndst( crv1, line_pt, line_vec, true, 0.001 ) );
interact( list( axes, crv1, line, pt_min ) );
pt_max = ceval( crv1, crvlndst( crv1, line_pt, line_vec, false, 0.001 ) );
interact( list( axes, crv1, line, pt_max ) );
save( "crv2line", list( axes, crv1, line, pt_max ) );

line_pt = point( -1, -1.5, 0 );
line_vec = vector( 1, 2, 0 );
line_pt2 = line_pt + ( line_vec * 2 );
line = poly( list( line_pt, line_pt2 ), true );
free( line_pt2 );

crv2 = cbspline( 3,
		 list( ctlpt( E2, 0,  1 ),
		       ctlpt( E2, 1, -1 ),
		       ctlpt( E2, 0, -1 ),
		       ctlpt( E2, 1,  1 ) ),
		 list( KV_OPEN ) );
color( crv2, green );
attrib( crv2, "width", 0.02 );

pt_param = crvlndst( crv2, line_pt, line_vec, false, -0.001 );
pt_extrem = nil();
for ( i = 1, 1, sizeof( pt_param ),
	pt = ceval( crv2, nth( pt_param, i ) ):
	snoc( pt, pt_extrem )
    );
interact( list( axes, crv2, line, pt_extrem ) );
save( "crv3line", list( axes, crv2, line, pt_extrem ) );

pt_min = ceval( crv2, crvlndst( crv2, line_pt, line_vec, true, 0.001 ) );
interact( list( axes, crv2, line, pt_min ) );
pt_max = ceval( crv2, crvlndst( crv2, line_pt, line_vec, false, 0.001 ) );
interact( list( axes, crv2, line, pt_max ) );
save( "crv4line", list( axes, crv2, line, pt_max ) );

crv3a = cbspline( 3,
		  list( ctlpt( E2, 0.0,  1.0 ),
		        ctlpt( E2, 0.1,  1.0 ),
		        ctlpt( E2, 0.1,  0.1 ),
		        ctlpt( E2, 0.5,  0.1 ),
		        ctlpt( E2, 0.5, -0.1 ),
		        ctlpt( E2, 0.1, -0.1 ),
		        ctlpt( E2, 0.1, -1.0 ),
		        ctlpt( E2, 0.0, -1.0 ) ),
		  list( KV_OPEN ) );
crv3b = crv3a * rotz( 180 );
crv3 = ( crv3a + crv3b ) * trans( vector( 0.1, 0.1, 0.0 ) );
free( crv3a );
free( crv3b );
color( crv3, green );
attrib( crv3, "width", 0.02 );

pt_param = crvlndst( crv3, line_pt, line_vec, false, -0.001 );
pt_extrem = nil();
for ( i = 1, 1, sizeof( pt_param ),
	pt = ceval( crv3, nth( pt_param, i ) ):
	snoc( pt, pt_extrem )
    );
free( pt_param );
interact( list( axes, crv3, line, pt_extrem ) );
save( "crv5line", list( axes, crv3, line, pt_extrem ) );

pt_min = ceval( crv3, crvlndst( crv3, line_pt, line_vec, true, 0.001 ) );
interact( list( axes, crv3, line, pt_min ) );
pt_max = ceval( crv3, crvlndst( crv3, line_pt, line_vec, false, 0.001 ) );
interact( list( axes, crv3, line, pt_max ) );
save( "crv6line", list( axes, crv3, line, pt_max ) );

free( line );
free( line_pt );
free( line_vec );
free( crv3 );
free( pt_extrem );
free( pt_min );
free( pt_max );

#
# Curve curve intersetion/distance square scalar field.
#
crv1 = cbspline( 3,
		 list( ctlpt( E2, 0, 0 ),
		       ctlpt( E2, 0.25, 0.5 ),
		       ctlpt( E2, 0.5, 0.7 ),
		       ctlpt( E2, 1, 1 ) ),
		  list( 0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0 ) );
crv2 = cbspline( 3,
		 list( ctlpt( E2, 1, 0 ),
		       ctlpt( E2, 0.7, 0.25 ),
		       ctlpt( E2, 0.3, 0.5 ),
		       ctlpt( E2, 0, 1 ) ),
		 list( 0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0 ) );
inter_pts = ccinter( crv1, crv2, 0.0001, false );
pt_inters = nil();
pt = nil();
for ( i = 1, 1, sizeof( inter_pts ),
	pt = ceval( crv1, coord( nth( inter_pts, i ), 0 ) ):
	snoc( pt, pt_inters ):
	pt = ceval( crv2, coord( nth( inter_pts, i ), 1 ) ):
	snoc( pt, pt_inters )
    );
interact( list( axes, crv1, crv2, pt_inters ) );
save( "crv1crv", list( axes, crv1, crv2, pt_inters ) );

dist_srf = ccinter( crv1, crv2, -1, true );
color( dist_srf, magenta );
interact( list( axes, dist_srf ) );
save( "crv2crv", list( axes, dist_srf ) );

crv1 = cbspline( 3,
		 list( ctlpt( E2, 0, 0 ),
		       ctlpt( E2, 0.25, 2 ),
		       ctlpt( E2, 0.5, -1 ),
		       ctlpt( E2, 1, 1 ) ),
		 list( 0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0 ) );
crv2 = cbspline( 3,
		 list( ctlpt( E2, 1, 0 ),
		       ctlpt( E2, -1, 0.25 ),
		       ctlpt( E2, 2, 0.5 ),
		       ctlpt( E2, 0, 1 ) ),
		 list( 0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0 ) );

inter_pts = ccinter( crv1, crv2, 0.001, false );
pt_inters = nil();
pt = nil();
for ( i = 1, 1, sizeof( inter_pts ),
	pt = ceval( crv1, coord( nth( inter_pts, i ), 0 ) ):
	snoc( pt, pt_inters ):
	pt = ceval( crv2, coord( nth( inter_pts, i ), 1 ) ):
	snoc( pt, pt_inters )
    );
interact( list( axes, crv1, crv2, pt_inters ) );
save( "crv3crv", list( axes, crv1, crv2, pt_inters ) );

dist_srf = ccinter( crv1, crv2, -1, true );
color( dist_srf, magenta );
interact( list( axes, dist_srf ) );
save( "crv4crv", list( axes, dist_srf ) );

crv1 = cbspline( 3,
		 list( ctlpt( E2, 0, 1 ),
		       ctlpt( E2, 1, 0 ),
		       ctlpt( E2, 0, 0 ),
		       ctlpt( E2, 1, 1 ) ),
		 list( 0.0, 0.0, 0.0, 0.5, 1.0, 1.0, 1.0 ) );
inter_pts = ccinter( crv1, crv1, 0.001, true );
pt_inters = nil();
pt = nil();
for ( i = 1, 1, sizeof( inter_pts ),
	pt = ceval( crv1, coord( nth( inter_pts, i ), 0 ) ):
	snoc( pt, pt_inters )
    );
free( i );
interact( list( axes, crv1, pt_inters ) );
save( "crv5crv", list( axes, crv1, pt_inters ) );

dist_srf = ccinter( crv1, crv1, -1, true );
color( dist_srf, magenta );
interact( list( axes, dist_srf ) );
save( "crv6crv", list( axes, dist_srf ) );

free( dist_srf );
free( inter_pts );
free( pt_inters );
free( crv1 );
free( crv2 );
free( pt );