Glossary
This glossary fixes the vocabulary used by the forward and separator-inverse documentation. The theory pages give the mathematical details.
Power weight
The scalar \(w_i\) in the power function
Power weights have squared-coordinate units. Only differences between weights affect pairwise separators, and adding one common constant to all weights leaves the complete power diagram unchanged.
Backend radius
The non-negative length-unit value passed to Voro++ for power/Laguerre computation. pyvoro2 converts weights to radii through a common additive shift before taking square roots. Backend radii are a representation of weights, not unique physical radii.
Representation shift
The one common constant added to every mathematical weight so that the shifted values can be represented as non-negative squared backend radii. It chooses one backend representation within the global gauge and does not add scientific information.
Global gauge
The freedom to add the same constant to every power weight without changing the complete diagram. A reported weight vector therefore needs a documented gauge or representation convention.
Disconnected-component offset
An independent additive offset between components of a disconnected informative separator-observation graph. Separator observations inside each component do not determine these relative offsets. Unlike one global gauge shift, changing component offsets can change the complete realized diagram by changing competition between components.
Separator observation
One measured or hypothesized position of the power separator for an ordered site pair and, in a periodic problem, one requested image of the second site. The observation may be represented as a fraction along the connector or as a position. It implies one desired weight difference.
Informative observation
A separator observation with positive confidence. Informative rows contribute to data identification and the observation Laplacian. Zero-confidence rows may remain in records and may carry hard restrictions or penalties, but they do not identify weight differences from observed data.
Observation graph
The row-indexed multigraph whose vertices are sites and whose edges are separator observations. Repeated rows and different periodic images remain separate edges. Connectivity controls which weight differences are identified.
Realized face
A positive-measure boundary that actually exists between two cells in the computed power diagram. In 2D this boundary is an edge. In a periodic problem, realization includes the specific neighbor image shift.
A fitted separator equation can have a small residual even when the requested pair is not a realized face.
Realization diagnostics
Post-fit geometric information that compares requested pairs and image shifts with the boundaries of a forward-computed diagram. It is separate from the fixed-observation algebraic fit.
Active set
The subset of candidate separator observations currently used by the realization-aware outer algorithm. The active-set workflow alternates fitting and geometric checks, then adds or removes rows according to hysteretic rules. It is experimental and is not part of the exact fixed-observation theory.
Cell measure
The dimension-neutral term for cell area in 2D or cell volume in 3D.
TessellationResult.cell_measures is an input-aligned forward result. Fitting
weights from prescribed cell measures is planned for v0.9 and is not implemented
in v0.7.
Static sparse observation graph
A fixed separator-observation graph whose number of rows is sparse relative to all possible site pairs. v0.7 provides an optional explicit SciPy-backed quadratic solve for this regime. The term does not imply trajectory processing, all-pairs scalability, automatic backend selection, or parallel execution.