BCAD: A Bayesian CAD System for Geometric Problems Specification and Resolution

Abstract

We present “BCAD”, a Bayesian CAD modeller for geometric problem definition and resolution. This modeller provides tools for (i) modelling geometric uncertainties and constraints, and (ii) solving inverse geometric problems while taking into account the propagation of these uncertainties. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements instead of as a simple equality or inequality. To solve geometric problems in this framework, we propose the Monte Carlo Simultaneous Estimation and Maximization (MCSEM) algorithm as a resolution technique able to adapt to problem complexity. Using three examples, we show how to apply our approach using the BCAD system.