Interactive display of generalized baseball and tennis-ball seam curves in 3D
Hypotrochoid offering perspectives on circle, lemniscate and related curves
Controls: Use cursor to rotate the configuration and to reconfgure curves (by shifting slider line in rectangle on right).
Use check buttons to render (in)visible portions of curve on reverse side of sphere.
If desired, wireframe checkbox shows sphere frame. NB: Avoid double-clicking on sphere since it shifts the centre of rotation unnecessarily. In that case reload.
Curve visibility:
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This model was kindly made by Sergey Bederov of Cortona 3D, who is not however responsible for the explanatory inferences. Also accessible are x3d and vrml versions. The display indicates changing parameters a, b and c, where c is defined by the slider, as moved by the user. The radius of the sphere is defined by a+b.
Commentary on the possible formulae relating them is given separately (Dean Allison, Ricardo Diaz, and Nathaniel Miller, Examples of generalized baseball curves, 2008). The formula used for this version is described by Robert Ferréol and Alain Esculier (Seam Line of a Tennis Ball, 2018; Hypotrochoid, 2017)
The seam curve of a baseball or tennis ball is evident when c is approximately 0.98. When c=1, four heart-like patterns are formed. When a or b=0, a circle is formed, splitting the sphere into two equal hemispheres.
Explanations: Enabling flying capacity with "headgear" -- cognitively comprehended? (2020).
Non-linear pathways curving between octants, and
Negligence of a " global wave" from a "wavelet" perspective?
Access to related displays: With general commentary and technical note
NB: Many alternative ring diameters, colours, rates and directions of movement can be envisaged.
Display currently developed in an experimental mode
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