An algorithm to construct biarcs that not only match the interpolation requirement of the point positions and tangent vectors but also lie on one side of the constraint line is proposed. For C-type biarc interpolation with the line constraint , firstly twelve inequalities in total are provided according to different position relationships between the constraint line and the interpolation requirement. These inequalities are used to check if biarcs lie on one side of the constraint line. If there exist many biarcs satisfying both the interpolation requirement and the line constraint , the optimal biarc can be obtained by solving a minimum problem. Otherwise , one extra point is added to make it possible to obtain biarcs. For S-type biarc interpolation with the line constraint , some results are also listed.