14P-s-Qu1  14P-Quartic

A quartic is a curve of 4th degree and in general defined by 14 random points.

See Ref-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 Ref-71.

Examples of Quartics in EQF
QL-Qu1: Morley's Mono Cardioid
QL-Qu2: Kantor-Hervey Deltoid
QL-Qu3: Schmidt Quartic
QL-27Qu1: Morley's Multiple Cardioids