Dual Bézier curves and convexity preserving interpolation (Q1195751)

Convexity preserving interpolation has been considered by several points of view. The problem reduces to the problem of finding a strictly convex function on an interval with prescribed function values and derivatives at the end points \(f(x_ 0) = y_ 0\), \(f(x_ 1) = y_ 1\), \(f'(x_ 0) = m_ 0\), \(f'(x_ 1) = m_ 1\). In the present paper the author studies this approach by a geometrical point of view. He considers the equivalent problem of finding an arc of a curve \(\Gamma\) passing through the points \(P_{00}(x_ 0,y_ 0)\), \(P_{11}(x_ 1,y_ 1)\) with non-vertical tangents \(y = t_{00}(x)\), \(y = t_{11}(x)\) at these two points.