Hello mill/cad

"Geometric Condition" in this sense refers to a condition in which an invalid solid would occur if the command executed as intended. The geometric condition can also occur after the fact, meaning that the command executed properly but the result is a geometric condition that left the geometry unstable.

To understand the fully, you need to unsetand the definition of a solid and how the topology of a solid is used to mathematically determine if the solid is in fact a solid and not "open" or invalid. An invalid solid could be one where one or more of the surfaces of the solid intersect one another or when there is a "sliver" surface whose angle is less than the geometry tolerance.

A B-Rep (Boundary Representation) solid (virtually all apps use B-Reps now), can be proven to be topologically correct if its elements are appropreately connected (e.g., all edges are connected to two vertices and bounded by two faces) and it adheres to an equation known as Euler's formula (derived by the 18th. century Swiss methematician Leonhard Euler).

Euler's formula:

V - E + F = 2

where

V = # of vertices (points)
E = # of edges
F = number of faces

For example, this formula can be easily verified with a simple solid cube.

V = 8
E = 12
S = 6

8 - 12 + 6 = 2

This simple formula must be true after every command is competed. If not, then a "geometric condition" has caused it to be not true. An example could be one vertice miss-matched over another (outside the geometry tolerance) where a corner now has two points instead of one. This is just one condition. There are many more.

Now, there can be a geometric condition even if the formula is true. For example if one face of the cube is stretched into the cude and it intersects the opposite face. All vertices, edges and faces are the correct # but an interferrance is calculated.

This topology relationship between vertices, edges and faces is the root cause of why solids require more CPU time than wireframe or surface modeling. Every time you intersect a solid with any other curve, face or solid, the CAD system must determine the resulting topology is correct and the the resulting solid is valid.

This is also why there are so many recommended best practices for working with solids, to minimize CPU time and more importantly to minimize the complexity of the topology of the solid so that error proned geometric condition do not occur.

Take a look at all of our "techBits" located in the following category:

TechBits > Solids (from the above menu tab)

I hope this helped. Let me know if you have any questions. Go to Google and search for Euler's Formula to find some examples.

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