Abstract: Based on envelope idea,the smallest error interpolation principle on computer generated curve is presented.If the curve is monotone and smooth,a strip region can be constructed and in the strip region marching path has the smallest error.Based on strip region,the smallest error interpolation algorithm on computer generated curve is also proposed and the recurrence formula for computing the marching step number is introduced.This approach is better than old ones where the decision function is calculated for each marching step.