Pick's Theorem
Area = I + B/2 − 1 | click the grid to add vertices, drag to move them
Shoelace O(n)
Boundary Σ gcd
Interior via Pick
Integer-exact
Vertex
Boundary point (B)
Interior point (I)
Outside
Controls
Click empty grid = add vertex. Drag a vertex = move it. Vertices snap to the integer lattice.
Preset:
Right triangle (0,0)(8,0)(0,6)
Square 8×8
L-shape
Thin staircase
Diamond
Load
Clear
Undo vertex
Live Pick Relation
Add at least 3 vertices.
Interior I
–
Boundary B
–
Area A
–
Per-edge gcd boundary count
–
Complexity
Step
Time
Notes
Shoelace 2A
O(n)
exact integer
Boundary B
O(n log C)
gcd per edge
Interior I
O(1)
Pick rearranged
Grid scan
O(W·H)
brute force only
Operation Log