An algorithm to const ruct biarcs that not only match the interpolation requirement of the point positions and tangent vectors but also lie on one side of the const raint line is proposed1 For C2type biarc in2 terpolation with the line const raint , firstly twelve inequalities in total are provided according to different po2 sition relationships between the const raint line and the interpolation requirement1 These inequalities are used to check if biarcs lie on one side of the const raint line1 If there exist many biarcs satisfying both the interpo2 lation requirement and the line const raint , the optimal biarc can be obtained by solving a minimum problem1 Otherwise , one ext ra point is added to make it possible to obtain biarcs1 For S2type biarc interpolation with the line const raint , some result s are also listed1