14P-s-Qu1  14P-Quartic

A quartic is a fourth-degree curve and is, in general, defined by 14 arbitrary points.

Construction

See [63], pages 299-309.

Roger Cuppens gives here useful construction methods for these types of quartics:

1. Quartic with 3 double points (amongst others the Deltoid).
2. Quartic with a triple point
3. Quartic with 2 double points
4. Quartic with 1 double point

About the general case where the quartic is constructed from 14 points, he tells about a perfect theoretical method (from Chasles), however the memory and the computation time will exceed limits on our present day used computers.

Another interesting page about drawing special Quartics and a special tangent to a Quartic can be found at [71].

Examples of Quartics in EPG

• QL-Qu1: Morley’s Mono Cardioid
• QL-Qu2: Kantor-Hervey Deltoid
• QL-Qu3: Schmidt Quartic
• QL-27Qu1: Morley’s Multiple Cardioids

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