Figure 12.19 Bézier Curve
Map1(target, u1, u2, stride, order, matrix)
The target argument defines what the control points represent. Values of the target argument are shown in Table 12.6. Note that you must use the Enable command to enable the argument.
Table 12.6 Map1 Target Arguments and Default Values 
target Argument
MAP1_VERTEX_3
(x, y, z) vertex coordinates
MAP1_VERTEX_4
(x, y, z, w) vertex coordinates
MAP1_INDEX
MAP1_COLOR_4
MAP1_NORMAL
MAP1_TEXTURE_COORD_1
s texture coordinates
MAP1_TEXTURE_COORD_2
s, t texture coordinates
MAP1_TEXTURE_COORD_3
s, t, r texture coordinates
MAP1_TEXTURE_COORD_4
s, t, r, q texture coordinates
The second two arguments (u1 and u2) define the range for the map. The stride value is the number of values in each block of storage (in other words, the offset between the beginning of one control point and the beginning of the next control point). The order should equal the degree of the curve plus one. The matrix holds the control points.
For example, Map1(MAP1_VERTEX_3, 0, 1, 3, 4, <4x3 matrix>) is typical for setting the two end points and two control points to define a Bézier line.
You use the MapGrid1 and EvalMesh1 commands to define and apply an evenly spaced mesh.
MapGrid1(un, u1, u2)
sets up the mesh with un divisions spanning the range u1 to u2. Code is simplified by using the range 0 to 1.
EvalMesh1(mode, i1, i2)
actually generates the mesh from i1 to i2. The mode can be either POINT or LINE. The EvalMesh1 command makes its own Begin and End clause.
boxwide = 500;
boxhigh = 400;
 
gridsize = 100; // bigger for finer divisions
 
NPOINTS = 4;
	/* We suggest you use only values between 2 and 8 (inclusively). Numbers beyond these might be interpreted differently, depending on implementation. This value is the degree+1 of the fitted curve */
 
point = J( NPOINTS, 3, 0 );
	// create an array of x,y,z triples
For( x = 1, x <= NPOINTS, x++,
	point[x, 1] = (x - 1) / (NPOINTS - 1) - .5;
		// x from -.5 to +.5
	point[x, 2] = Random Uniform() - .5;
		// y is random in same range
	point[x, 3] = 0;
		// z is always zero, which causes the curve to stay in a plane
);
 
spline = Scene Box( boxwide, boxhigh );
 
spline << Ortho( -.6, .6, -.6, .6, -2, 2 );
	// data from -.5 to .5 in x and y; this is a little larger
 
spline << Enable( MAP1_VERTEX_3 );
spline << MapGrid1( gridsize, 0, 1 );
spline << Color( .2, .2, 1 ); // blue curve
 
spline << Map1( MAP1_VERTEX_3, 0, 1, 3, NPOINTS, point );
spline << Line Width( 2 ); // not-so-skinny curve
spline << EvalMesh1( LINE, 0, gridsize ); // also try LINE, POINT
 
spline << Color( .2, 1, .2 );
spline << Point Size( 4 ); // big fat green points
 
// show the points and label them
For( i = 1, i <= NPOINTS, i++,
	spline << Begin( "POINTS" );
	spline << Vertex( point[i, 1], point[i, 2], point[i, 3] );
	spline << End;
	spline << Push Matrix;
	spline << Translate( point[i, 1], point[i, 2], point[i, 3] );
	spline << Text( center, bottom, .05, Char( i ) );
	spline << Pop Matrix;
);
 
New Window( "Spline", spline );
https://www.tinaja.com/glib/bezconn.pdf offers an explanation of connecting cubic segments so that both the slope and the rate of change match at the connection point. This example does not illustrate doing so; there is only one segment here.

Help created on 7/12/2018