No-Fit Polygon

Geometric primitive describing all overlap-free relative placements of two pieces.

Also called: No-Fit Polygon · NFP · 무적합 폴리곤

A geometry primitive (held under method in v1) central to irregular nesting: the NFP encodes every relative position where two pieces touch without overlapping, turning overlap resolution into a point-location problem. See Bennell & Oliveira (2008) for the canonical tutorial treatment.

Claims & evidence

Every relationship is a claim with an evidence grade; applicable problem-to-problem relationships also carry an equivalence level. See the evidence policy.

A–X describes evidence reliability; E0–E4 describes mathematical similarity between problems. The two axes are independent.

Relationships to this entry 4

uses method
2D Irregular Nesting to No-Fit Polygon
The No-Fit Polygon is the canonical geometric primitive for testing and resolving overlap between two irregular pieces in nesting.
EvidenceA · Peer-reviewed / official
Sources
- Source grade: A — Peer-reviewed / officialThe geometry of nesting problems: A tutorial
  Citation details
  Bennell, J.A., Oliveira, J.F. (2008). The geometry of nesting problems: A tutorial. EJOR 184(2):397-415.
shares method with
Inner-Fit Polygon to No-Fit Polygon
The Inner-Fit Polygon (IFP) gives the region where a piece fits inside the sheet boundary while the No-Fit Polygon (NFP) handles piece-to-piece overlap — complementary geometric primitives that reduce irregular-nesting placement to point-location queries.
EvidenceA · Peer-reviewed / official
Equiv.E2 · shared methodology
Sources
- Source grade: A — Peer-reviewed / officialThe geometry of nesting problems: A tutorial
  Citation details
  Bennell, J.A., Oliveira, J.F. (2008). The geometry of nesting problems: A tutorial. EJOR 184(2):397-415.
shares method with
Minkowski Sum to No-Fit Polygon
The No-Fit Polygon of A and B equals the Minkowski sum of A and the reflection (−B); computing the NFP is computing a Minkowski sum.
EvidenceA · Peer-reviewed / official
Equiv.E0 · near-identical formulation
Sources
- Source grade: A — Peer-reviewed / officialThe geometry of nesting problems: A tutorial
  Citation details
  Bennell, J.A., Oliveira, J.F. (2008). The geometry of nesting problems: A tutorial. EJOR 184(2):397-415.
shares method with
Phi-functions to No-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.
EvidenceA · Peer-reviewed / official
Equiv.E3 · structural analogy
Sources
- Source grade: A — Peer-reviewed / officialPhi-Functions for 2D Objects Formed by Line Segments and Circular Arcs
  Citation details
  Chernov, N., Stoyan, Yu., Romanova, T., Pankratov, A. (2012). Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs. Advances in Operations Research, vol. 2012. Phi-functions encode pairwise interaction analytically (positive = apart, zero = touching, negative = overlapping), enabling nonlinear-programming packing models with continuous rotation.

Relationships to this entry
Relationship	Claim	Evidence	Equiv.	Sources
uses method 2D Irregular Nesting to No-Fit Polygon	The No-Fit Polygon is the canonical geometric primitive for testing and resolving overlap between two irregular pieces in nesting.	A · Peer-reviewed / official	—	Source grade: A — Peer-reviewed / officialThe geometry of nesting problems: A tutorial Citation details Bennell, J.A., Oliveira, J.F. (2008). The geometry of nesting problems: A tutorial. EJOR 184(2):397-415.
shares method with Inner-Fit Polygon to No-Fit Polygon	The Inner-Fit Polygon (IFP) gives the region where a piece fits inside the sheet boundary while the No-Fit Polygon (NFP) handles piece-to-piece overlap — complementary geometric primitives that reduce irregular-nesting placement to point-location queries.	A · Peer-reviewed / official	E2 · shared methodology	Source grade: A — Peer-reviewed / officialThe geometry of nesting problems: A tutorial Citation details Bennell, J.A., Oliveira, J.F. (2008). The geometry of nesting problems: A tutorial. EJOR 184(2):397-415.
shares method with Minkowski Sum to No-Fit Polygon	The No-Fit Polygon of A and B equals the Minkowski sum of A and the reflection (−B); computing the NFP is computing a Minkowski sum.	A · Peer-reviewed / official	E0 · near-identical formulation	Source grade: A — Peer-reviewed / officialThe geometry of nesting problems: A tutorial Citation details Bennell, J.A., Oliveira, J.F. (2008). The geometry of nesting problems: A tutorial. EJOR 184(2):397-415.
shares method with Phi-functions to No-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.	A · Peer-reviewed / official	E3 · structural analogy	Source grade: A — Peer-reviewed / officialPhi-Functions for 2D Objects Formed by Line Segments and Circular Arcs Citation details Chernov, N., Stoyan, Yu., Romanova, T., Pankratov, A. (2012). Phi-Functions for 2D Objects Formed by Line Segments and Circular Arcs. Advances in Operations Research, vol. 2012. Phi-functions encode pairwise interaction analytically (positive = apart, zero = touching, negative = overlapping), enabling nonlinear-programming packing models with continuous rotation.