Dynamically orienting solution, giving the points of tangency, and merging the formulas for 2nd order Bezier curve, Archimedes triangle, Vector Parabola:
Parabola from Four Tangents, Geometric construction: [url]http://www.geogebratube.org/material/show/id/38334[/url]
General Vector Parabola: [url]http://www.geogebratube.org/material/show/id/32226[/url]
2nd order Bezier curve: [url]http://www.geogebratube.org/material/show/id/37814[/url]
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This is part of a larger project:
1) Create a system for working with splines in three dimensions. In particular, allowing the curves to retain algebraic and geometric definitions and operations when desired.
2) Integrate this system with general formulas for conic sections, and parametric cycloids.
3) Use the integrated system to build simple, flexible, closed spherical harmonic surfaces/volumes to represent sound propagation patterns.
