This study aims to design a simple and effective transition curve. First

three quasi-cubic Bézier curves with monotone decreasing curvature are constructed after studying the base functions. Three other quasi-cubic Bézier curves with monotone increasing curvature are then obtained by parameter symmetry. These new curves have similar properties with the cubic Bézier curves

including endpoint

convex hull

and geometry invariability properties. However

unlike the cubic Bézier curves

the quasi-cubic Bézier curves only have three control points. We then provide strict mathematical proofs in relation to the sufficient conditions of the monotone curvature of these curves. Two of the quasi-cubic Bézier curves covered a broader scope than the cubic Bézier curves with monotone curvature. The specific positional relationship between the quasi-cubic Bézier spiral curves and the cubic Bézier spiral curves were determined. Four of the six quasi-cubic Bézier curves had zero curvature at one endpoint and can therefore be combined into four pairs of S-shaped or C-shaped transition curves for separated circles; the ratio of two radii had no restriction. The remaining two quasi-cubic Bézier curves can be used to form a single transition curve with no curvature extreme for separated circles when the difference of two radii is large. Finally

examples were given to show the effectiveness of these curves. In transition curve design

the quasi-cubic Bézier spiral curve with three control points is more simple and effective than the cubic Bézier spiral curve.