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LEDAS Geometry Comparison

Background

The LEDAS team has many man-years of experience in the research and development of Boolean operations through its work on the Russian Geometric Kernel (RGK) project. They know in detail the drawbacks and bottlenecks to the Boolean approach. In particular, Boolean operations are not that reliable in complicated cases due to the construction of the so-called Intersection Graph. (It defines how parts of the original body are merged to produce the resulting body with only valid topology – no self-intersections, unbounded faces, hanging edges, and so on.)

LEDAS determined that it was not essential to compute an Intersection Graph, and they found how to compute which parts of one model lay within a tolerance of the other model (and which do not) without Intersection Graph.

From this, the LEDAS team created its innovative technology that compares 3D geometry without using unstable Boolean operations. Instead, they use a mixture of powerful methods, including bounding volume hierarchies, identification and mapping of similar entities, and local search routines.

Experts in 3D geometry know that there are two levels of geometry representation: topology (made of faces, edges, vertices), and underlying geometry (surfaces and curves that define the form of faces and edges). It is relatively easy to map topology of one 3D model to the topology of another model: each entity gets its counterpart, and if mapping for some entities does not exist, then the difference is found at the topological level. It is more complicated to find difference (or to check that there are no differences) when taking into account actual underlying geometry and specified tolerances. The solution developed by LEDAS makes it possible to detect differences at both the topological and geometric levels.

Also important is the information provided by the software to the user. Some competitors illustrate differences as set of points on one model that do not lay on the second one. Another software marks faces that do not match faces on the second model. The approach LEDAS takes is more informative: they output all the faces and parts of faces that lie beyond the tolerance of the second model; for the remaining faces and parts of faces, they provide identifiers of faces that match.

This level of information is useful to both the user and the software that processes the output through APIs.

LEDAS decided to use mature geometric kernel for performing base level geometric operations, that, unlike Boolean operations, are very stable and efficient. In early 2014, C3D kernel from ASCON was chosen thanks to its quality, well-tested by several generations of KOMPAS users, and ability to deal with different formats of input CAD data. As a part of deal of LEDAS with ASCON, some part of C3D was especially tuned in order to deliver best performance to LGC technology.
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