1. A computerized system for modeling a pontic to facilitate orthodontic treatment of teeth of a patient through a sequence of treatment stages, the computerized system comprising a processor configured for: calculating space measurements of a digital representation of a space located between a digital representation of a first tooth having a first geometry and a second tooth having a second geometry by getting a first tooth transformation of the first tooth at a given treatment stage i and a second tooth transformation of the second tooth at the treatment stage i, wherein the first tooth defines a first coordinate system having a first Y-axis and the second tooth defines a second coordinate system having a second Y-axis; applying the first tooth transformation to the first geometry and applying the second tooth transformation to the second geometry to get first and second positions of the first and second teeth, respectively, at the stage i; calculating a direction vector of the space measurements at the stage i, wherein the direction vector is derived from an interpolated Y-axis between the first Y-axis and the second Y-axis; calculating a reference plane for the space measurements by using the direction vector as a normal; 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; generating an original pontic geometry to provide a digital representation of an initial pontic object for use in a first stage of the sequence of treatment stages; and generating stage-dependent pontic geometries at each treatment stage during successive treatment stages of the sequence of treatment stages, by calculating deformation parameters based on the original pontic geometry, size characteristics of the space, and size characteristics of the first and second teeth at each of the treatment stages, to provide digital representations of stage-dependent pontic objects.