Geometry

3DLDF currently provides a set of basic plane and solid geometrical figures. However, some important ones are still missing. There are many useful geometrical data types and functions whose implementation would require no more than elementary geometry.

• Add constructors with a normal vector argument rather than angles of rotation about the main axes.
• I have started defining class Triangle, which can be used for calculating triangle solutions.
• Add a class Conic_Section and derive Ellipse from it. This will be the first case of multiple inheritance¹ in 3DLDF, since Ellipse is already derived from Path. See Ellipse Reference. Add the classes Parabola and Hyperbola.
• Add more functions for finding the intersections of objects of various types, starting with the plane figures. In particular, I believe I've found an algebraic solution for the intersection of an Ellipse and a Circle in a plane, but I haven't had a chance to try implementing it yet.

  If this works, I think it will make it possible to find the intersection of two coplanar ellipses algebraically, because it will be possible to transform them both such that one of them becomes circular.

• Class Octahedron will complete the set of regular Platonic polyhedra.
• Add classes for the Kepler-Poinsot polyhedra, the semi-regular Archimedean polyhedra, the dual solids, the stellated Archimedean polyhedra, and the regular compounds.²
• Add class Ellipsoid and a derived class Sphere.
• Improve the specification of Solid and Solid_Faced. In particular, it would help to store the vertices of Polyhedra as individual Points, rather than using Reg_Polygons. I'd also like to find a better way of generating Solids, without using rotations, if possible.