Curved Spirolaterals

A spirolateral consists of lines drawn between two vertices.  Instead of using the actual lines, one idea was to use only the vertices.  Using CAD-based software, procedures were written to interpret the vertices as control points for curves.  Figure 12 displays this concept.  The simple 190 spirolateral, a square, consists of four vertices.  These vertices can be fitted with arcs at the start and end of adjacent vertices.  The vertices can also be control points to generate a spline curve.

                         Original                           Vertices                                          Curve Fit                                   Spline
                                                                              Figure 12: Curved spirolateral 190

Many of the spirolaterals reviewed as curves were found to be interesting but not visually exciting nor did they generate any unexpected images.  The first set reviewed were ones that consisted on ten or less turns.  Figure 13 displays one of these. 

Figure 13: Curved spirolateral 190

Only when the number of turns increased to a range of 11 to 15, with reversed turns included, did the number of control points increase to the point where they begin to generate images of unexpected detail and complexity.  Figure 14 displays two such examples.

Figure 14: Curved spirolaterals of 1490


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