A proposal for a coordinate system for handling deformations of models is the subject of the paper. Deformations of models require transformations from the original model to the deformed model. The scheme proposed by the authors eliminates some drawbacks of earlier such systems. The proposed system is named celestial coordinates. The earlier cage-based systems have connectivity among cage points, whereas celestial coordinates do not. The paper observes that this difference is particularly useful for interactive simulations of deformations on models. It shows application in simulations of biological tissues and organs. It derives the formulas for computing coordinates transformation.

The paper is organized in eight sections. Sections 3 through 5 describe the basics of celestial coordinates and proposed T-celestial and S-celestial coordinates. Celestial coordinates are a family of positive generalized barycentric coordinate schemes. The transformation functions, proofs of existence, and implementation details are part of the basics of S-celestial and T-celestial coordinates. Section 6, on analysis, compares the computation times of both celestial coordinates. The comparison with existing schemes in Sections 2 and 7 is with respect to properties including computation cost, “cage-freeness,” detail preservation, and the need for discretization. The limitation of both schemes is shown to be that they do not ensure the preservation of the local details on the deformed models.

A background in geometry is required, apart from modeling, simulation, and graphics, to understand the paper. Algorithms from numerical analysis are used to implement the celestial coordinates. The paper attaches the celestial sphere with the celestial coordinates. It is not clear from the paper visually how a celestial sphere would look in deformed and nondeformed states. Will the end user of the visually interactive simulator be able to get an idea of a specific deformation by looking at control points? Graphical interactive simulations of deformations can be useful in medical fields and civil engineering applications.