The bezier Style Option

This option defines a single command, \bezier, that draws a curved line in a picture environment. Let P_i be the point with coordinates (x_i, y_i), for i = 1, 2, and 3. The command

\bezier{n}(x1,y1)(x2,y2)(x3,y3)

draws n points on the quadratic Bezier spline determined by the three points P₁, P₂, and P₃. The locus of points on this spline is a parabolic arc from P₁ to P₃ having the line P₁P₂ tangent to it at P₁ and the line P₂P₃ tangent to it at P₃. Note that P₂ is not on this arc unless P₁, P₂, and P₃ are colinear, in which case the arc is a straight line. Bezier splines are useful because it's easy to join two of them together smoothly by giving them the same tangent line where they meet.

It takes roughly 75 points per inch to form a solid line, depending upon the line thickness. See Section C.13.3 of the manual for commands to specify line thickness in a picture environment. This command is very slow, and TEX has enough memory to hold only about 1000 points plus a page of text. (Remember that TEX keeps the current page plus all as yet unprinted figures in memory.) So, the bezier command should be used for only a small number of small curves.