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Hammer provides a built-in error checker that will find most invalid brushes. Press
Alt+P or navigate to Check for problems under the Map menu to launch it.
Invalid brushes will often appear to change between saving and reloading maps due to Hammer's automatic fixing process (which also causes a shape to appear to change when clipped).
There are three categories of problems that cause invalid brushes:
See concave for a description of concave shapes. To fix a concave shape, either adjust the vertices until it is no longer concave, or use the clip tool to split the brush into two or more brushes.
Floating vertices are basically any vertices with fewer than three adjacent faces. Without those three adjacent faces, it is impossible for a brush to enclose an area. If the brush shape is not continuous and has holes then it cannot be defined by the algorithms used in Hammer. Fixing it requires merging vertices to cover the holes.
Improperly defined faces
An improperly defined face refers to any face that is not flat or has no surface area. All points on a face should exist in the same two dimensional plane. The plane can be at any rotation, but they need to exist on the same plane. It determines what planes are possible by sampling three sequential points from the face. If one or more vertices don’t line up with the rest it will cause errors. The face ends up unable to determine which two dimensional plane it exists in as sampling different points finds different planes. Fixing it requires the definition of new edges to give each face its own plane, or manipulation of the vertices to line up.