Modeling pontics at successive treatment stages includes: (1) calculating space measurements between first and second teeth by getting first and second tooth transformations at a treatment stage i； (2) applying the first and second tooth transformations to get positions of the first and second teeth at the stage i； (3) calculating a direction vector of the space measurements at the stage i； (4) calculating a reference plane using the direction vector as a normal； (5) determining whether the space is available for a pontic by measuring the distance from the closest point on each of the first and second teeth to the reference plane； (6) generating an original pontic geometry for a first treatment stage； and (7) generating pontic geometries at each successive stage by calculating deformation parameters based on the original pontic geometry and size characteristics of the space and of the first and second teeth at each stage.
