We extend the construction of a G continuous curve based on a guiding polyline from the parametric form to the quadric and cubic algebraic spline form to avoid obstacles. First

a series of control polygons are obtained by adding the midpoints of guiding polylines except for the first and last line segments. Then

based on the control polygons and the corres- ponding obstacles

the shape parameter(s)of the whole algebraic spline curve

which avoids every obstacle

can be obtained. The new spline curve not only determines the position relation between the curve and the given point

but also shows its advantages directly

such as low degree

G continuity

simple calculation

shape-preserving

and adjustment by the control polygon. All shape parameters in the cubic algebraic spline were local

which enhances the flexibility of the geometric design.