Segmented structures such as targets or organs at risk are typically stored as 2D contours contained on evenly spaced cross sectional images (slices). Contour interpolation algorithms are implemented in radiation oncology treatment planning software to turn 2D contours into a 3D surface, however the results differ between algorithms, causing discrepancies in analysis. Our goal was to create an accurate and consistent contour interpolation algorithm that can handle issues such as keyhole contours, rapid changes, and branching. This was primarily motivated by radiation therapy research using the open source SlicerRT extension for the 3D Slicer platform. The implemented algorithm triangulates the mesh by minimizing the length of edges spanning the contours with dynamic programming. The first step in the algorithm is removing keyholes from contours. Correspondence is then found between contour layers and branching patterns are determined. The final step is triangulating the contours and sealing the external contours. The algorithm was tested on contours segmented on computed tomography (CT) images. Some cases such as inner contours, rapid changes in contour size, and branching were handled well by the algorithm when encountered individually. There were some special cases in which the simultaneous occurrence of several of these problems in the same location could cause the algorithm to produce suboptimal mesh. An open source contour interpolation algorithm was implemented in SlicerRT for reconstructing surfaces from planar contours. The implemented algorithm was able to generate qualitatively good 3D mesh from the set of 2D contours for most tested structures.