#
# Some examples of 3d alpha-sector computations of 3-space freeform curves.
#
#			Gershon Elber, October 1998.
#

#
# Set states.
#
save_mat = view_mat;
view_mat = view_mat * sc( 0.35 );
viewobj( view_mat );

IProd = iritstate( "InterpProd", off );

#############################################################################
#
# A point and a line in the XY plane
#
c1 = cbezier( list( ctlpt( E2, -0.3, -1.0 ),
		    ctlpt( E2, -0.3,  1.0 ) ) );
pt2 = point( 0.4, 0.2, 0.0 );
color( c1, red );
adwidth( c1, 3 );
color( pt2, red );
adwidth( pt2, 3 );

for ( t = 0.0, 0.03, 1.0,
    BisectCrv = calphasector( list( c1, pt2 ), t ):
    color( BisectCrv, green ):
    view( list( c1, pt2, BisectCrv ), true ));

save( "asect2d1", list( c1, pt2,
		        calphasector( list( c1, pt2 ), 0.1 ),
		        calphasector( list( c1, pt2 ), 0.5 ),
		        calphasector( list( c1, pt2 ), 1.0 ) ) );

pause();

#############################################################################
#
# A point and a cubic curve in the XY plane
#
c1 = cbezier( list( ctlpt( E2, -0.9, -0.1 ),
		    ctlpt( E2, -1.3, -1.3 ),
		    ctlpt( E2,  1.3,  0.3 ),
		    ctlpt( E2,  0.3,  1.0 ) ) );
pt2 = point( -0.5, 0.5, 0.0 );
color( c1, red );
adwidth( c1, 3 );
color( pt2, red );
adwidth( pt2, 3 );

for ( t = 0.0, 0.05, 1.0,
    BisectCrv = calphasector( list( c1, pt2 ), t ):
    color( BisectCrv, green ):
    view( list( axes, c1, pt2, BisectCrv ), true ));

save( "asect2d2", list( c1, pt2,
		        calphasector( list( c1, pt2 ), 0.1 ),
		        calphasector( list( c1, pt2 ), 0.5 ),
		        calphasector( list( c1, pt2 ), 1.0 ) ) );

pause();

#############################################################################
#
# A point and a circle in the XY plane
#
c1 = pcircle( vector( 0.3, 0.2, 0.0 ), 1.1 );
pt2 = point( -0.5, 0.5, 0.0 );

c1 = coerce( c1, E2);
color( c1, red );
adwidth( c1, 3 );
color( pt2, red );
adwidth( pt2, 3 );

for ( t = 0.0, 0.1, 1.05,
    BisectCrv = calphasector( list( c1, pt2 ), t ):
    color( BisectCrv, green ):
    view( list( axes, c1, pt2, BisectCrv ), true ));

save( "asect2d3", list( c1, pt2,
		        calphasector( list( c1, pt2 ), 0.1 ),
		        calphasector( list( c1, pt2 ), 0.5 ),
		        calphasector( list( c1, pt2 ), 1.0 ) ) );

pause();

#############################################################################
#
# Two linear curves
#
c1 = cbezier( list( ctlpt( E3,  0.0,  0.3, -1.0 ),
		    ctlpt( E3,  0.0,  0.3,  1.0 ) ) );
c2 = cbezier( list( ctlpt( E3, -1.0, -0.3,  0.0 ),
		    ctlpt( E3,  1.0, -0.3,  0.0 ) ) );
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.1, 1.0,
    BisectSrf = calphasector( list( c1, c2 ), t ):
    color( BisectSrf, green ):
    view( list( c1, c2, BisectSrf ), true ));

save( "asect3d1", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.3 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

#############################################################################
#
# Two quadratic curves
#
c1 = cbezier( list( ctlpt( E3,  0.0,  0.5, -1.0 ),
		    ctlpt( E3,  0.0,  0.1,  0.0 ),
		    ctlpt( E3,  0.0,  0.5,  1.0 ) ) );
c2 = cbezier( list( ctlpt( E3, -1.0,  1.0,  0.0 ),
		    ctlpt( E3,  0.0, -1.5,  0.0 ),
		    ctlpt( E3,  1.0,  1.0,  0.0 ) ) );
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.2, 1.0,
    BisectSrf = calphasector( list( c2, c1 ), t ):
    color( BisectSrf, green ):
    view( list( c1, c2, BisectSrf ), true ));

save( "asect3d2", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.7 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

#############################################################################
#
# A line and a (approximation of a) circle.
#
c1 = cbezier( list( ctlpt( E3,  0.0,  0.0, -1.0 ),
		    ctlpt( E3,  0.0,  0.0,  1.0 ) ) );
c2 = pcircle( vector( 0.0, 0.0, 0.0 ), 1 );

c2 = coerce( c2, E3);
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.2, 1.0,
    BisectSrf = calphasector( list( c1, c2 ), t ):
    color( BisectSrf, green ):
    view( list( c1, c2, BisectSrf ), true ));

save( "asect3d3", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.7 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

#############################################################################
#
# A line and a (approximation of a) circle.
#
c1 = pcircle( vector( 0.0, 0.0, 0.0 ), 1 );
c2 = cbezier( list( ctlpt( E3, -1.0, 0.0,  1.0 ),
		    ctlpt( E3,  1.0, 0.0, -1.0 ) ) );

c1 = coerce( c1, E3);
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.2, 1.0,
    BisectSrf = calphasector( list( c1, c2 ), t ):
    color( BisectSrf, green ):
    view( list( c1, c2, BisectSrf ), true ));

save( "asect3d4", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.7 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

#############################################################################
#
# A line and a (approximation of a) circle.
#
c1 = creparam( pcircle( vector( 0.0, 0.0, 0.0 ), 1 ), 0, 1 );
c2 = cbezier( list( ctlpt( E3, -2.0, 0.0,  1.0 ),
		    ctlpt( E3, -2.0, 0.0, -1.0 ) ) );

c1 = coerce(c1 , E3);
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.1, 1.05,
    BisectSrf = calphasector( list( c1, c2 ),  t ):
    BisectSrf1 = sregion( BisectSrf, col, 0.0, 0.3 ):
    BisectSrf2 = sregion( BisectSrf, col, 0.7, 1.0 ):
    BisectSrf3 = sregion( BisectSrf, col, 0.36, 0.64 ):
    color( BisectSrf1, green ):
    color( BisectSrf2, green ):
    color( BisectSrf3, green ):

    view( list( c1, c2, BisectSrf1, BisectSrf2, BisectSrf3 ), true ));

save( "asect3d5", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.7 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

#############################################################################
#
# A quadratic Bezier and a (exact rational) ellipse.
#

c1 = cbezier( list( ctlpt( E3, -2.0,  0.0, -1.0 ),
		    ctlpt( E3, -3.0,  0.0,  0.0 ),
		    ctlpt( E3, -2.0,  0.0,  1.0 ) ) );
c2 = circle( vector( 0.0, 0.0, 0.0 ), 1 ) * sy( 2 );

c2 = coerce(c2, E3);
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.2, 1.0,
    BisectSrf = calphasector( list( c1, c2 ), t ):
    color( BisectSrf, green ):
    view( list( c1, c2, BisectSrf ), true ));

save( "asect3d6", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.7 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

#############################################################################
#
# A tilted line and a (exact rational) circle.
#
c1 = cbezier( list( ctlpt( E3, -2.0,  0.0, -1.0 ),
		    ctlpt( E3, -2.5,  0.0,  1.0 ) ) );
c2 = circle( vector( 0.0, 0.0, 0.0 ), 1 );

c2 = coerce( c2, E3);
color( c1, red );
adwidth( c1, 3 );
color( c2, red );
adwidth( c2, 3 );

for ( t = 0.0, 0.2, 1.0,
    BisectSrf = calphasector( list( c1, c2 ), t ):
    BisectSrf1 = sregion( BisectSrf, row,  0.0,  1.3 ):
    BisectSrf2 = sregion( BisectSrf, row, 1.35, 2.65 ):
    BisectSrf3 = sregion( BisectSrf, row,  2.7,  4.0 ):
    color( BisectSrf1, green ):
    color( BisectSrf2, green ):
    color( BisectSrf3, green ):

    view( list( c1, c2, BisectSrf1, BisectSrf2, BisectSrf3 ), true ));

save( "asect3d7", list( c1, c2,
		        calphasector( list( c2, c1 ), 0.1 ),
		        calphasector( list( c2, c1 ), 0.7 ),
		        calphasector( list( c2, c1 ), 1.0 ) ) );

pause();

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

IProd = iritstate( "InterpProd", IProd );
free( IProd );

view_mat = save_mat;

free( c1 );
free( c2 );
free( pt2 );
free( t );
free( BisectCrv );
free( BisectSrf );
free( BisectSrf1 );
free( BisectSrf2 );
free( BisectSrf3 );