Shape preserving interpolation by space curves

Shape preserving interpolation for planar data has been well studied while little has been done for shape preserving curve interpolation in space. We consider some criteria for shape preserving interpolation by space curves: convexity and inflections of the projections of the curve onto certain planes, the sign of the torsion, coplanarity and collinearity. Based upon these criteria we then derive an algorithm for interpolating given points in space with a shape preserving piecewise rational cubic curve. The scheme is local and produces curves which are unit tangent continuous and also continuous in curvature magnitude apart from some exceptional cases where the curve contains linear segments. We illustrate the scheme with some graphical examples.