Plane picking

As explained in Geometry for Programmers

Plane picking is the selection of connected mesh triangles that lie in a specified geometric plane.

Plane picking selects connected mesh triangles lying in the same geometric plane. Starting from a chosen triangle, it follows neighboring triangles and keeps only those sharing its plane. section 2.2.2

A practical plane-picking traversal follows this pattern:

• Pick a starting triangle, such as CBD. section 2.2.2
• Traverse its neighbors, then the neighbors of matching triangles. section 2.2.2
• Stop expanding when neighboring triangles no longer share the plane. section 2.2.2
• Treat degenerate triangles as outside the test because they belong to no specific plane. section 2.2.2

CAD face selection

A CAD operation can select the connected triangles forming one planar face. A degenerate proxy triangle between two apparent neighbors is not accepted as part of that plane, so traversal does not continue through it. section 2.2.2

Figure 2.13 A degenerate triangle ABC in an otherwise manifold mesh

Use the mesh illustration to see how a degenerate triangle can sit between otherwise planar-looking neighbors. section 2.2.2

How Geometry for Programmers covers it

How deep it goes

Explains width-first neighbor traversal and its stopping condition, but defers explicit handling of degenerate triangles.

Examples

Uses triangle CBD, proxy triangle ABC, and the apparent BCD–ABE neighbor relationship to illustrate selection boundaries.

What it assumes

Assumes triangle-neighbor relationships and recognizes that degenerate triangles have no specific plane.

What you can do after

Apply it by traversing neighboring triangles and collecting the connected members that share the starting triangle’s plane.

How it connects

Connects plane picking with triangle meshes, neighbor traversal, CAD, degenerate triangles, and near-degenerate triangles.

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This explainer was generated by Manning's knowledge graph from the text of Geometry for Programmers. The section links point to the parts of the book it draws on.