Boolean Combinations of Implicit Functions for Model Clipping in Computer-Assisted Surgical Planning

Mesh Processing for Snapping Feature Points and Polylines in Orebody Modeling

The 3D refinement modeling of the orebody provides an important guarantee for the estimation of the resources and reserves of an ore deposit. Implicit modeling techniques can effectively improve the efficiency of orebody modeling and facilitate the dynamic updating of the model. However, due to the problems of ambiguity and missing features during implicit surface interpolation and implicit surface reconstruction, the mesh models of orebodies obtained by means of implicit modeling techniques do not easily snap to the geological feature points and feature polylines obtained based on geological sampling data. In essence, all models are inaccurate, but geological sampling data are very useful and valuable, which should be accurately and effectively involved in the orebody modeling process. This would help to improve the reliability of resource estimation and mining design. The main contribution of this paper is the proposal of a method for accurately snapping orebody features after implicit modeling. This method enables the orebody model to snap accurately to the geological feature points and feature polylines and realizes the accurate clipping of the model boundary. We tested the method with real geological datasets. The results showed that the method is applicable and effective when the geological feature points and feature polylines are close to those of the orebody mesh model and the shape trend changes little, and the model can thus meet the practical application requirements of mines.

Combination Constraints of Multiple Fields for Implicit Modeling of Ore Bodies

In this paper, we introduce combination constraints for modeling ore bodies based on multiple implicit fields interpolation. The basic idea of the method is to define a multi-labeled implicit function that combines different sub-implicit fields by the combination operations, including intersection, union and difference operators. The contribution of this paper resides in the application of combination of more general implicit fields with combination rules for the implicit modeling of ore bodies, such that the geologist can construct constraints honoring geological relationships more flexibly. To improve the efficiency of implicit surface reconstruction, a pruning strategy is used to avoid unnecessary calculations based on the hierarchical bounding box of the operation tree. Different RBF-based methods are utilized to study the implicit modeling cases of ore bodies. The experimental results of several datasets show that the combination constraints are useful to reconstruct implicit surfaces for ore bodies with mineralization rules involving multiple fields.