An Obstacle-Avoiding Rational Quadratic Bézier Spline Curve with G² Continuity

Given a set of obstacles in a plane, an algorithm for finding a G² continuous, obstacle-avoiding curve in the plane is presented in this paper.First, we partition the guiding polyline into control polygon sections by inserting several midpoints of polyline.Then, we find respectively shape parameter of each curve section to avoid the vertices of the convex hull of an obstacle.Finally, we choose the maximal shape parameter to avoid all the obstacles.Comparing with previous methods, the curves constructed by our approach have the following advantages: 1) it is G² continuous but with low degree;2) it is shape-preserving, and the number of inflection point is the same as the one of the guiding polyline path;3) it is obtained directly, and we need not to solve the fourth order equations;4) the control polygon is visual, and we can adjust the curve easily.Finally, two examples are presented to demonstrate the effectiveness and validity of the proposed algorithm.