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Cubic Bezier Curve Construction

This activity shows how to construct a cubic Bezier curve geometrically. Points E, F and P are the midpoints of segments e, f and l1, respectively. Lines s, l, k, t, g, h, p, q and b1 are parallel to segments h, c, a, i1, f, e, m, n and a1, respectively. Lines j and i are both parallel to segment b. Move points A, B, C and D to change the shape of the quadrilateral. Move point G to trace the locus of point Q.