1. Introduction

Next version of OCCT will feature new mode of Boolean Operation Algorithm (BOA), called "Fuzzy". Fuzzy Boolean operations are the type of Boolean operations in which additional user-specified tolerance is used. This mode allows Boolean operations to handle robustly cases of touching and near-coincident entities of the argument shapes.

2. Use of Fuzzy Boolean operations

The Fuzzy Boolean Operations are useful on the shapes with gaps or embeddings between the entities of these shapes which are not covered by the tolerance values of these entities. Such shapes can be the result of modeling mistakes, or translating process, or import from other systems with loss of precision, or errors in some algorithms. Most likely, the standard Boolean operations will give unsatisfactory results on such models. The result may contain unexpected and unwanted small entities, faulty entities (in terms of BRepCheck_Analyzer), or there can be no result at all. With the Fuzzy Boolean operations it is possible to get the expected result - it is just necessary to define the appropriate fuzzy tolerance for the operation. To define that value it is necessary to measure the value of the gap (or the value of embedding depth) between the entities of the models, slightly increase it (to make the shifted entities coincident in terms of their tolerance plus the additional one) and pass it to the algorithm.

3. Implementation

Fuzzy Boolean operations are integrated in the current development version of OCCT (6.8.1.dev). The class BRepAlgoAPI_BooleanOperation contains the corresponding API for its usage: new method SetFuzzyValue(const Standard_Real theFuzz) allows to set the fuzzy tolerance value. Default is zero, that is, no fuzzy treatment.

4. Examples

The following examples demonstrate the advantages of Fuzzy Boolean operations over the standard ones in typical situations.

4.1. Example 1

In this example the cylinder (shown in yellow and transparent) is subtracted from the box (shown in red). The cylinder is shifted on the 5.e-5 value relatively to the box along its axis (the distance between rear faces of the box and cylinder is 5.e-5).

The results obtained using standard Boolean operations and the Fuzzy ones with the fuzzy value 5.e-5 are:

Result of CUT operation obtained with standard BO	Result of CUT operation obtained with Fuzzy BO

Here Fuzzy option allowed eliminating very thin part of the result shape produced by standard algorithm due to misalignment of rear faces of the box and the cylinder.

4.2. Example 2

In this example two boxes are fused. One of them has dimensions 10*10*10, and the other is 10*10.000001*10.000001 and adjacent to the first one. There is no gap in this case as the surfaces of the neighboring faces coincide, but one box is slightly grater than the other.

The results obtained using standard Boolean operations and the Fuzzy ones with the fuzzy value 1.e-6 are:

Result of CUT operation obtained with standard BO	Result of CUT operation obtained with Fuzzy BO

Here Fuzzy option allowed to get rid of extremely narrow face in the result produced by standard operation.

4.3. Example 3

In this example the small planar face (shown in orange) is subtracted from the big one (shown in yellow). There is a gap 1.e-5 between the edges of these faces.

The results obtained using standard Boolean operations and the Fuzzy ones with the fuzzy value 1.e-5 are:

Result of CUT operation obtained with standard BO	Result of CUT operation obtained with Fuzzy BO

Here Fuzzy options eliminated pin-like protrusion resulting from the gap between edges of the argument faces.

4.4. Example 4

In this example the small edge is subtracted from the big one. The edges are overlapping not precisely, with max deviation between them equal to 5.28004e-05. We will use 6.e-5 value for Fuzzy Boolean operations.

The results obtained using standard Boolean operations and the Fuzzy ones with the fuzzy value 6.e-5 are:

Result of CUT operation obtained with standard BO	Result of CUT operation obtained with Fuzzy BO

This example stresses not only the validity, but also the performance issue. The fuzzy Boolean operations with the appropriate value work much faster than the standard ones. To measure the performance of Boolean operations on this case the following environment is used:

The following results have been obtained:

5.Conclusion

Fuzzy Boolean operations provide a way to perform operations on the shapes with near-coincidence between their entities robustly, filling gaps and eliminating small entities resulting from misalignment of input shapes. Fuzzy Boolean operations are able to produce the correct result while the standard ones are not.