Intersect Faces… generates new Edges where Faces from one set intersect Faces from a second set. This operation is available only when you have something pre-selected (or implicitly select something by right-click) and that something includes Faces. These Faces from the Selection form one set to be intersected.
The options “With Model”, “With Context”, and “With Selection” tell SketchUp what to use for the second set of Faces.
- “With Model” means to use all Faces from anywhere else in the entire Model, including nested inside Groups or Components. This option is available whenever you select anything containing Faces.
- “With Context” means to use only other Faces found in the currently active edit context (a Group or Component that is open for edit), including ones from Groups or Components nested in the context. It is only available when you have opened a Group or Component for Edit.
- “With Selection” means to use the same Selection as provides the first set. It is only available when you have pre-selected more than one Face, since a single Face can’t intersect with itself.
The Edges created by the operation are always placed in the currently active edit context: the model or a Group or Component that has been opened for edit. This behavior likely causes more confusion than anything else for newbies. For example, they will create a Group and want to slice it with a cutting Face they draw in the model (to avoid “sticking” to contents in the Group while drawing). Doing Intersect With on these two items will place the new Edges in the model, not the Group, no matter which option you choose. Since Edges loose in the model cannot cut Faces within a Group, the slice won’t have happened! To cut Faces in the Group, you must either draw or copy the cutting Face into the Group before the intersection operation. Or do the considerably less efficient method of exploding the Group, doing Intersect With, and then regenerating the Group from the results.
Intersect With quite often leaves behind extra Edges and Faces that you don’t need, especially when you are using a set of Faces to cut an object into parts. After the Intersect With, you will need to clean up by deleting the extra parts. Good selection techniques are essential during the cleanup, since there could be a lot of little bits to erase. The right-to-left “crossing selection” box technique is your friend! Avoiding this sometimes tedious cleanup is one of the biggest advantages of the Pro version’s Solids Tools. They do it automatically and in fast compiled code.
Intersect With will also fairly often create tiny Edges that may be deleted by SketchUp’s cleanup operation because they are below the minimum length threshold. To avoid this, you must scale the relevant parts of the model up by some factor - typically 10 or 100 though sometimes more - before doing the Intersect With, and scale it back down afterward. Scaling does not trigger a cleanup, so the Edges will survive when they are scaled back down to their correct size.
There are two closely-related reasons to choose one of the options “With Context” and “With Selection”. One is obviously to avoid getting intersections with undesired Faces from other parts of the model. If they aren’t in the Context or the Selection, the Faces aren’t examined for intersections. The other is to reduce the run time of the intersection operation. Intersect With must test every Face from the first set against every Face from the second set, even when there is no intersection. So the amount of effort grows as the product of the numbers of Faces in the two sets. Intersecting two sets of many Faces can take a long time. Anything you can do to reduce the number of candidates will reduce this run time.
LIke @DaveR I tend to prefer “With Selection” because it provides the tightest control over what is tested. However, sometimes it is tedious or awkward to select just some Faces. The temptation is to do a “select all” and then run “With Selection”. However, because that requires testing every Face in the selection against every other Face in the selection, it might actually take longer than carefully selecting a few Faces and doing “With Context”.
Most of the time when you draw a new Face or perform an operation such as pushpull that implicitly creates a new Face, SketchUp will automatically generate the intersections between the new Face and any pre-existing ones that it overlaps. It is not necessary to manually invoke Intersect With in this situation. But in a few known special cases and sometimes when there are tiny errors in the model’s data about a Face, SketchUp may fail to realize that the new Face should cut the prior one. Often, though not always, manually running Intersect With may fix the situation.