1. Given three arbitrary points in space, A, B, C, the second order Bézier curve has equation: [math]A + 2(B-A)t + (C-2B +A)t^2, \;\;\; 0 ≤ t ≤1[/math] 2. Let ΔABC be an Archimedes triangle with base (chord) AC, and tangents AB, BC. ΔABC encloses a parabola section. [i]The two curves are the same.[/i]
__________________ Archimedes Triangle: [url]http://www.geogebratube.org/material/show/id/35781[/url] Vector Equation of a Parabola: [url]http://www.geogebratube.org/material/show/id/32226[/url] Tool: Parabola from Archimedes Triangle (two points and the intersection of their tangents): [url]http://www.geogebratube.org/material/show/id/38279[/url]