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## Regular Closed Plane Curve Reference

Class Reg_Cl_Plane_Curve is defined in curves.web. It is derived from Path using public derivation.

Reg_Cl_Plane_Curve is not called "Regular_Closed_Plane_Curve" because the longer name causes too many "Overfull boxes"1 in the CWEAVE output of the program code. See CWEB Documentation.

Reg_Cl_Plane_Curve is meant to be used as a base class; no objects should be declared of type Reg_Cl_Plane_Curve. Currently, class Ellipses is derived from Reg_Cl_Plane_Curve and class Circle is derived from Ellipse.

At present, I have no fixed definition of what constitutes "regularity" as far as Reg_Cl_Plane_Curves are concerned. Ellipses and circles are "regular" in the sense that they have axes of symmetry. There must be an equation for a Reg_Cl_Plane_Curve, such as x^2 + y^2 = r^2 for a circle. A derived class should have a solve() function that uses this equation. Reg_Cl_Plane_Curve::intersection_points() in turn uses solve() to find the intersection points of a line with the Reg_Cl_Plane_Curve. This way, the derived classes don't need their own functions for finding their intersections with a line. However, such functions can be added, if desired.

It is assumed that classes derived from Reg_Cl_Plane_Curve are fillable, which implies that they must be closed Paths. Reg_Cl_Plane_Curves inherit their drawing and filling functions from Path.

The constructors and setting functions of classes derived from Reg_Cl_Plane_Curve must ensure that the resulting geometric figures are planar, convex, and that the number of Points they contain is a multiple of 4. The latter assumption is of importance in intersection_points(), segment(), half(), and quarter(). See Regular Closed Plane Curve Reference; Intersections, and Regular Closed Plane Curve Reference; Segments.

#### Footnotes

1. If you don't know what ``overfull boxes'' are, don't worry about it. It has to do with TeX's line and page breaking algorithms. If you want to know more, see Knuth, Donald E., The TeXbook.