| In the CAGD/CAD system, Archimedes helix is an important and basic geometry object. The effective method of curve designing is to adopt control polygon. And now, almost all polynomial curves use this method, it's the leading method in the CAGD/CAD system. At the same time, Archimedes helix is not polynomial curve, butthe curve which belongs to .spaw{l,sint,cost,t sint,tcost}, so it hasn't been appliedin the CAGD/CAD system. Consequently, we need to create new method which can represent Archimedes helix with control polygon.In order to represent Archimedes helix with control polygon, we construct Bernstein-like basis. This Bernstein-like basis has many similar properties, for example: port property;linearly independent;symmetry;unitary property;plus property etc.This paper discusses the necessary and sufficient condition to represent the Archimedes helix with Bernstein-like basis of order four and five. Under this condition, we can obtain the control points of the Bezier-represented Archimedes helix. Then we can express the Archimedes helix expediently, and obtain the representation of Archimedes helix with control polygon. Otherwise, we study the geometrically constructing of control points, which has obvious geometric meaning.Finally, with the Archimedes helix and circular arc, we can construct a cam, so the control of the cam with a polygon comes true. This is useful to construct and control cam. |
