Scaling and Modeling Tolerances

Scaling can sometimes be confusing. This is because everything in a model is scaled simultaneously, something that can produce poor results from a numerical standpoint.

For instance, when a model is scaled up, the sizes of the faces and edges and gaps (mathematically) are enlarged. For instance, consider a model that numerically contains a gap of 1e-8 between a vertex and the edge on which it lies. This is not a problem with respect to the default coincident distance i.e. 1.0 e-06 (File > Properties > Units). However, if the model is scaled by 1000, this gap numerically becomes 1.0e-05. This constitutes an actual gap in the model with respect to the coincident distance and becomes an error. This is not a bug, but the natural result of applying the scaling matrix to the model.

The opposite problem occurs when the model has some very small faces and edges. Say the length of one such edge is 1.0e-04. Although the edge is incredibly small, it is still acceptable before scaling because it is larger than the coincident distance (1.0 e-06). When the model is scaled (say by 0.001), these edge lengths become 1.0 e-07, which naturally makes their vertices coincident with respect to the coincident distance. Similarly, some control points on minute spline faces become coincident with respect to the coincident distance after scaling.