Output details

BSP-fields: An exact representation of polygonal objects by differentiable scalar fields based on binary space partitioning

Originality - The paper presents a novel solution to an important problem in Computer-Aided design involving the interchange of geometric models from different representations. In geometric modelling and Computer-Aided Design, there are different ways to represent the models not from a storage point of view, but mathematically. This paper discusses the conversion of the objects from the popular representation of the geometry in form of a polygonal mesh and the representation of the solid object enclosed by the polygonal mesh in the implicit form.

Significance - The exactness of the method is an important aspect of the method that allows using it for the large variety of further geometric manipulations over the resulting object without losing any information from the source object. Another important aspect of the presented technique is the C1-continuity which is an important property for the geometric manipulations over the objects in computer-aided geometric design. The paper presents the wide range of the possible applications of the method for the purposes of geometric modelling with the objects represented in an implicit form.

Rigour - The paper presents the original rigorous formulation to solve the problem of the exact conversion from one representation to another. The theoretical basis for the method is a mathematically proven theorem. The formulation follows the related techniques without inheriting their disadvantages, such as extra zero level sets, therefore allowing to use the method for large variety of operation in implicit solid modelling systems.