Interval arithmetic has been considered as a step forward to counter numerical robustness problem in geometric and solid modeling. The interval arithmetic boundary representation (B-rep) scheme was developed to tackle this problem. In constructing an interval B-rep solid, robust and efficient computation of intersections between the bounding surfaces of the solid is a critical issue. To address this problem, a marching method based on a validated interval ordinary differential equation (ODE) solver was proposed, motivated by its potential for the interval B-rep model construction. In this paper, we concentrate on the issue of error control in model space using the validated ODE solver, and further explain that the validated ODE solver can be used in the construction of an interval B-rep solid model using such an error control.

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