#
# Computing the kernel and diameter of a freeform simple closed curve.
#

save_res = resolution;
resolution = 70;

bg = poly( list( point( -3, -3, -1 ),
		 point( -3,  3, -1 ),
		 point(  3,  3, -1 ),
		 point(  3, -3, -1 ) ), false );
color( bg, yellow );
view_mat1 = tx( 0 );
view( list( view_mat1 ), 1 );
view_mat2 = view_mat * sc( 0.5 ) * ty( 0.5 );

viewstate( "DepthCue", 0 );
viewstate( "DrawSolid", 1 );
viewstate( "PolyAprx", 1 );

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

C4 = cbspline( 4,
    list( ctlpt( E3, -0.6, -0.3, 0 ),
          ctlpt( E2,  0.6, -0.3 ),
          ctlpt( E2,  0.6,  0.3 ),
          ctlpt( E2, -0.6,  0.3 ) ),
    list( kv_periodic ) );

k = CrvKernel( C4, 0, 0, list( 3, 3, 3 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C4, bg, k * sz( 0 ), view_mat1 ) );

attrib( k, "rgb", "0,255,255" );
interact( list( C4, k * sz( -3 ), view_mat2 ) );

k1 = CrvKernel( C4, 20, 0, list( 3, 3, 3 ), 0 );
attrib( k1, "rgb", "100,1,1" );
k2 = CrvKernel( C4, -20, 0, list( 3, 3, 3 ), 0 );
attrib( k2, "rgb", "1,100,1" );
interact( list( C4, bg, k1 * sz( 0 ), k2 * sz( 0 ), view_mat1 ) );

s = CrvKernel( C4, 0, 0, list( 0.25, -0.01 ), 1 );
attrib( s, "rgb", "255,0,255" );

interact( list( C4, k * sz( -3 ), s, view_mat2 ) );

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

C4 = cbspline( 4,
    list( ctlpt( E3, 0.616, -0.0552, 0 ),
          ctlpt( E2, -0.744, -0.444 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, -0.179, 0.872 ) ),
    list( kv_periodic ) );

k = CrvKernel( C4, 0, 0, list( 2, 3, 2 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C4, bg, k * sz( 0 ), view_mat1 ) );

save( "crv1krnl", list( C4, bg, k * sz( 0 ), view_mat1 ) );

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

C3 = cbspline( 3,
    list( ctlpt( E3, -0.668, 0.333, 0 ),
          ctlpt( E2, 0.253, 0.00684 ),
          ctlpt( E2, -0.252, -0.417 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, 0.325, 0.502 ),
          ctlpt( E2, 0.0699, 0.656 ),
          ctlpt( E2, 0.227, 0.171 ) ),
    list( kv_periodic ) );

C4 = cbspline( 4,
    list( ctlpt( E3, -0.668, 0.333, 0 ),
          ctlpt( E2, 0.253, 0.00684 ),
          ctlpt( E2, -0.252, -0.417 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, 0.325, 0.502 ),
          ctlpt( E2, 0.0699, 0.656 ),
          ctlpt( E2, 0.227, 0.171 ) ),
    list( kv_periodic ) );

d = CrvDiamtr( C3, 0.1, -1e-6, 2 );
Lns = nil();
for ( i = 1, 1, sizeof( d ),
    pt = nth( d, i ):
    snoc( ceval( C3, coord( pt, 0 ) ) + ceval( C3, coord( pt, 1 ) ),
	  Lns ) );

MaxD = CrvDiamtr( C3, 0.1, -1e-6, 1 );
MaxD = ceval( C3, coord( MaxD, 0 ) ) + ceval( C3, coord( MaxD, 1 ) );
color( MaxD, green );
adwidth( MaxD, 3 );

MinD = CrvDiamtr( C3, 0.1, -1e-6, 0 );
MinD = ceval( C3, coord( MinD, 0 ) ) + ceval( C3, coord( MinD, 1 ) );
color( MinD, yellow );
adwidth( MinD, 3 );

interact( list( C3, Lns, MaxD, MinD, view_mat1 ) );


k = CrvKernel( C3, 0, 0, list( 2, 2, 2 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C3, bg, k * sz( 0 ), view_mat1 ) );

save( "crv2krnl", list( C3, bg, k * sz( 0 ), view_mat1 ) );

k = CrvKernel( C4, 0, 0, list( 2, 3, 1 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C4, bg, k * sz( 0 ), view_mat1 ) );

attrib( k, "rgb", "0,255,255" );
interact( list( C4, k * sz( -3 ), view_mat2 ) );

s = CrvKernel( C4, 0, 0, list( 0.25, -0.01 ), 1 );
attrib( s, "rgb", "255,0,255" );
interact( list( C4, k * sz( -3 ), s, view_mat2 ) );

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

C3 = cbspline( 3,
    list( ctlpt( E3, -0.02, 0.289, 0 ),
          ctlpt( E2, -0.668, 0.333 ),
          ctlpt( E2, -0.192, 0.156 ),
          ctlpt( E2, -0.252, -0.417 ),
          ctlpt( E2, 0.0858, 0.0777 ),
          ctlpt( E2, 0.194, -0.00113 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, 0.362, 0.228 ),
          ctlpt( E2, 0.171, 0.265 ),
          ctlpt( E2, 0.325, 0.502 ),
          ctlpt( E2, 0.0699, 0.656 ),
          ctlpt( E2, -0.137, 0.5 ) ),
    list( kv_periodic ) );
C4 = cbspline( 4,
    list( ctlpt( E3, -0.02, 0.289, 0 ),
          ctlpt( E2, -0.668, 0.333 ),
          ctlpt( E2, -0.192, 0.156 ),
          ctlpt( E2, -0.252, -0.417 ),
          ctlpt( E2, 0.0858, 0.0777 ),
          ctlpt( E2, 0.194, -0.00113 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, 0.362, 0.228 ),
          ctlpt( E2, 0.171, 0.265 ),
          ctlpt( E2, 0.325, 0.502 ),
          ctlpt( E2, 0.0699, 0.656 ),
          ctlpt( E2, -0.137, 0.5 ) ),
    list( kv_periodic ) );

d = CrvDiamtr( C3, 0.1, -1e-6, 2 );
Lns = nil();
for ( i = 1, 1, sizeof( d ),
    pt = nth( d, i ):
    snoc( ceval( C3, coord( pt, 0 ) ) + ceval( C3, coord( pt, 1 ) ),
	  Lns ) );

MaxD = CrvDiamtr( C3, 0.1, -1e-6, 1 );
MaxD = ceval( C3, coord( MaxD, 0 ) ) + ceval( C3, coord( MaxD, 1 ) );
color( MaxD, green );
adwidth( MaxD, 3 );

MinD = CrvDiamtr( C3, 0.1, -1e-6, 0 );
MinD = ceval( C3, coord( MinD, 0 ) ) + ceval( C3, coord( MinD, 1 ) );
color( MinD, yellow );
adwidth( MinD, 3 );

interact( list( C3, Lns, MaxD, MinD, view_mat1 ) );


k = CrvKernel( C3, 0, 0, list( 2, 2, 2 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C3, bg, k * sz( 0 ), view_mat1 ) );

k = CrvKernel( C4, 0, 0, 2, 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C4, bg, k * sz( 0 ), view_mat1 ) );

k1 = CrvKernel( C4, 5, 0, 2, 0 );
attrib( k1, "rgb", "100,1,1" );
k2 = CrvKernel( C4, -5, 0, 2, 0 );
attrib( k2, "rgb", "1,100,1" );
interact( list( C4, bg, k1 * sz( 0 ), k2 * sz( 0 ), view_mat1 ) );

attrib( k, "rgb", "0,255,255" );
interact( list( C4, k * sz( -3 ), view_mat2 ) );

s = CrvKernel( C4, 0, 0, list( 0.25, -0.01 ), 1 );
attrib( s, "rgb", "255,0,255" );
interact( list( C4, k * sz( -3 ), s, view_mat2 ) );

save( "crv3krnl", list( C4, k * sz( -3 ), s, view_mat2 ) );

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

C3 = cbspline( 3,
    list( ctlpt( E3, -0.0398, 0.263, 0 ),
          ctlpt( E2, -0.668, 0.333 ),
          ctlpt( E2, -0.0634, 0.161 ),
          ctlpt( E2, -0.299, -0.378 ),
          ctlpt( E2, 0.0664, 0.0859 ),
          ctlpt( E2, 0.444, -0.359 ),
          ctlpt( E2, 0.161, 0.149 ),
          ctlpt( E2, 0.723, 0.2 ),
          ctlpt( E2, 0.362, 0.228 ),
          ctlpt( E2, 0.171, 0.265 ),
          ctlpt( E2, 0.424, 0.813 ),
          ctlpt( E2, 0.0703, 0.283 ),
          ctlpt( E2, -0.244, 0.88 ) ),
    list( kv_periodic ) );

C4 = cbspline( 4,
    list( ctlpt( E3, -0.0398, 0.263, 0 ),
          ctlpt( E2, -0.668, 0.333 ),
          ctlpt( E2, -0.0634, 0.161 ),
          ctlpt( E2, -0.299, -0.378 ),
          ctlpt( E2, 0.0664, 0.0859 ),
          ctlpt( E2, 0.444, -0.359 ),
          ctlpt( E2, 0.161, 0.149 ),
          ctlpt( E2, 0.723, 0.2 ),
          ctlpt( E2, 0.362, 0.228 ),
          ctlpt( E2, 0.171, 0.265 ),
          ctlpt( E2, 0.424, 0.813 ),
          ctlpt( E2, 0.0703, 0.283 ),
          ctlpt( E2, -0.244, 0.88 ) ),
    list( kv_periodic ) );

d = CrvDiamtr( C4, 0.03, -1e-6, 2 );
Lns = nil();
for ( i = 1, 1, sizeof( d ),
    pt = nth( d, i ):
    snoc( ceval( C4, coord( pt, 0 ) ) + ceval( C4, coord( pt, 1 ) ),
	  Lns ) );

MaxD = CrvDiamtr( C4, 0.03, -1e-6, 1 );
MaxD = ceval( C4, coord( MaxD, 0 ) ) + ceval( C4, coord( MaxD, 1 ) );
color( MaxD, green );
adwidth( MaxD, 3 );

MinD = CrvDiamtr( C4, 0.03, -1e-6, 0 );
MinD = ceval( C4, coord( MinD, 0 ) ) + ceval( C4, coord( MinD, 1 ) );
color( MinD, yellow );
adwidth( MinD, 3 );

interact( list( C4, Lns, MaxD, MinD, view_mat1 ) );


k = CrvKernel( C3, 0, 0, 2, 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C3, bg, k * sz( 0 ), view_mat1 ) );

k = CrvKernel( C4, 0, 0, 2, 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C4, bg, k * sz( 0 ), view_mat1 ) );

save( "crv4krnl", list( C4, bg, k * sz( 0 ), Lns, MaxD, MinD, view_mat1 ) );

#############################################################################
#
# Possible extensions to open curves.
#
C3 = cbspline( 3,
    list( ctlpt( E3, -0.668, 0.333, 0 ),
          ctlpt( E2, 0.253, 0.00684 ),
          ctlpt( E2, -0.252, -0.417 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, 0.325, 0.502 ),
          ctlpt( E2, 0.0699, 0.656 ),
          ctlpt( E2, 0.227, 0.171 ) ),
    list( kv_open ) );

d = CrvDiamtr( C3, 0.1, -1e-6, 2 );
Lns = nil();
for ( i = 1, 1, sizeof( d ),
    pt = nth( d, i ):
    snoc( ceval( C3, coord( pt, 0 ) ) + ceval( C3, coord( pt, 1 ) ),
	  Lns ) );

MaxD = CrvDiamtr( C3, 0.1, -1e-6, 1 );
MaxD = ceval( C3, coord( MaxD, 0 ) ) + ceval( C3, coord( MaxD, 1 ) );
color( MaxD, green );
adwidth( MaxD, 3 );

MinD = CrvDiamtr( C3, 0.1, -1e-6, 0 );
MinD = ceval( C3, coord( MinD, 0 ) ) + ceval( C3, coord( MinD, 1 ) );
color( MinD, yellow );
adwidth( MinD, 3 );

interact( list( C3, Lns, MaxD, MinD, view_mat1 ) );


k = CrvKernel( C3, 0, 0, list( 2, 2, 2 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C3, bg, k * sz( 0 ), view_mat1 ) );

C3c = cbspline( 3,
    list( ctlpt( E3, -0.668, 0.333, 0 ),
          ctlpt( E2, 0.253, 0.00684 ),
          ctlpt( E2, -0.252, -0.417 ),
          ctlpt( E2, 0.416, -0.298 ),
          ctlpt( E2, 0.691, 0.175 ),
          ctlpt( E2, 0.325, 0.502 ),
          ctlpt( E2, 0.0699, 0.656 ),
          ctlpt( E2, 0.227, 0.171 ),
          ctlpt( E2, 0.226, 0.171 ),
	  ctlpt( E3, -0.668, 0.333, 0 ) ),
    list( kv_open ) );

k = CrvKernel( C3c, 0, 0, list( 2, 2, 2 ), 0 );
attrib( k, "rgb", "1,1,1" );
interact( list( C3c, bg, k * sz( 0 ), view_mat1 ) );
free( c3c );

interact( list( C3, bg, k * sz( 0 ), view_mat1 ) );

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

viewstate( "DepthCue", 1 );
viewstate( "DrawSolid", 0 );
viewstate( "PolyAprx", 0 );

resolution = save_res;

free( C4 );
free( C3 );
free( Lns );
free( MaxD );
free( MinD );
free( Pt );
free( s );
free( i );
free( d );
free( bg );
free( view_mat1 );
free( view_mat2 );
free( k );
free( k1 );
free( k2 );