Description
Return internal diagonal and triangle counts for a polygon triangulation.
Graph and lattice counts depend on the allowed moves, edges and geometric or incidence assumptions. A necessary count identity or local conflict test may hold even when no valid complete object with the requested structure has been supplied.
Return internal diagonal and triangle counts for a polygon triangulation.
When to use this tool
Use Catalan Triangulation Diagonal Budget when checking one supplied path, tree, matching or rook-placement condition.
How to use the tool and how it works
- Enter vertices. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read diagonals, triangles. Use the output convention below.
Return internal diagonal and triangle counts for a polygon triangulation. Require whole vertices >= 3; diagonals = vertices-3, triangles = vertices-2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertices | Vertices | Required. Safe integer; minimum 3. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| diagonals | Diagonals | Required. Safe integer. |
| triangles | Triangles | Required. Safe integer. |
{
"input": {
"vertices": 6
},
"output": {
"diagonals": 3,
"triangles": 4
}
}Limitations and assumptions
- This assumes a simple polygon triangulated without additional vertices; it does not count triangulations or validate polygon geometry.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Inspect or construct the complete graph/path and apply all relevant structural constraints for a full validity or counting result.
References
Similar or alternative tools
- Plane Tree Edge Vertex Balance
Check the edge-count identity of a tree.
- Matching Unpaired Vertex Budget Tool
Calculate matching unpaired vertex budget from explicit caller-supplied inputs.