Phi-functions
Analytic non-overlap modeling that encodes the interaction of two pieces.
Also called: Phi-functions · Φ-functions · phi-function · quasi-phi-functions
Last verified: 2026-05-27
Another primitive for the overlap side of irregular placement (classified as a
method in v1). Where the No-Fit Polygon describes the
locus of overlap-free relative positions combinatorially, a phi-function gives a
single signed analytic value for the relationship between two pieces (positive =
apart, zero = touching, negative = overlapping). Its smoothness lets placement be
cast as nonlinear programming (NLP), including continuous rotation. See Chernov,
Stoyan, Romanova & Pankratov (2012) for the standard definition.
Claims & evidence
Every relationship is a claim with an equivalence level and an evidence grade. See the evidence policy.
| Relationship | Claim | Equiv. | Evidence | Sources |
|---|---|---|---|---|
| shares method withNo-Fit Polygon | Phi-functions and the No-Fit Polygon both encode piece-to-piece overlap — the NFP as a combinatorial locus, phi-functions as a continuous analytic expression suited to nonlinear optimization and continuous rotation. | E3 | A |
|
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