1416 lines
63 KiB
TeX
1416 lines
63 KiB
TeX
% !TEX program = xelatex
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% Epiphany --- Quality Metric Catalog (companion specification)
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% Companion to the Core Specification. Compile with XeLaTeX.
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%
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% This document is versioned independently of the Core Specification
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% (independent semver; see the Versioning note in the front matter). Its preamble
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% is intentionally a self-contained copy of the core specification's preamble so
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% the two documents build independently; factoring a shared preamble file is a
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% ---------------------------------------------------------------------------
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% Document
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% ---------------------------------------------------------------------------
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\begin{document}
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\begin{titlepage}
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\thispagestyle{empty}
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\centering
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\vspace*{2.2in}
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{\color{epiphanygold}\rule{3in}{0.8pt}}\\[18pt]
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{\titlefont\fontsize{34pt}{38pt}\selectfont\color{epiphanyteal}\bfseries Epiphany}\\[10pt]
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{\Large\scshape\color{epiphanyslate}Quality Metric Catalog}\\[6pt]
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{\large\itshape\color{epiphanyslate}A companion to the Core Specification}\\[14pt]
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{\color{epiphanygold}\rule{3in}{0.8pt}}\\[24pt]
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{\normalsize\color{epiphanyink}Version 0.3.0 --- Phase 3 (the normative metric set: formal definitions, normalization, weights, tier thresholds, profile registry; \texttt{spacing\_distortion} scoped to rhythmic columns; \texttt{vertical\_density\_penalty} counted per realization)}\\[4pt]
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{\small\color{epiphanyslate}Normative for the metrics and thresholds it defines}
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\vfill
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\end{titlepage}
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\tableofcontents
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% ===========================================================================
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\chapter{About This Companion}
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\label{ch:about}
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The \emph{Quality Metric Catalog} is a companion to the Epiphany Core
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Specification. It fulfils the delegation of the core specification's
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\sectionsc{Companion Specifications} appendix --- the section labeled
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\texttt{sec:deferred:companions} --- which charters this document to
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deliver ``per-metric normalization functions mapping raw measurements to
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\texttt{NormalizedMetric} values, default tie-breaking weights, per-tier
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metric thresholds, and the formal definition of each quality metric in the
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normative metric set.''
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This companion (v0.3.0) delivers all four chartered items, plus two small
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registries the core specification names but defers here:
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\begin{itemize}
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\item the formal definition of each of the \textbf{nine normative metric
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axes} --- the measured phenomenon, the raw measurement over resolved
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layout geometry, and the normalization function with its pinned anchor
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constant (Chapter~\ref{ch:metrics});
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\item the \textbf{default tie-breaking weights}
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(Chapter~\ref{ch:weights});
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\item the \textbf{per-tier metric thresholds} for the Minimal and
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Standard conformance tiers, the Advanced-tier extension rule, and the
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\texttt{QualityFloorApproached} warning trigger
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(Chapter~\ref{ch:thresholds});
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\item the \texttt{QualityMetricKind} enumeration, which the core
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specification references (as the payload of the
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\texttt{QualityFloorApproached} solver warning) but never lists
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(Section~\ref{sec:model:kind});
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\item the \textbf{registered \texttt{SolverProfile} catalog}, which the
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core specification's vocabulary appendix explicitly defers to this
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companion (Chapter~\ref{ch:profiles});
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\item the \textbf{Standard-tier constraint family} declaration, which the
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core specification's Standard-tier requirement points at this companion
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(Section~\ref{sec:thresholds:families}).
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\end{itemize}
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This document does \emph{not} cover:
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\begin{itemize}
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\item the reference suite's test scores, per-tier entry inclusion, and any
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per-entry threshold overrides --- those are the \emph{Reference Suite}
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companion's;
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\item performance conformance (edit traces, frame budgets) --- the
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\emph{Performance Reference Suite} companion's;
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\item the reference solving algorithm --- the non-normative
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\emph{Reference Algorithm} companion's.
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\end{itemize}
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\section{Relationship to the Core Specification}
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\label{sec:about:relationship}
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This companion does not restate the metric framework; it \emph{references}
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it. The framework --- the \texttt{NormalizedMetric} validity rules (finite,
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in $[0.0, 1.0]$, lower is better), the \texttt{QualityMetricVector} field
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set, extension metrics, the \texttt{TieBreakingWeights} structure, the
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Pareto-frontier design target, the conformance-tier ladder, and the
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suite-based conformance model --- is the core specification's Chapter~9
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(\sectionsc{The Constraint Solver Interface}, the \texttt{ch:solver}
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chapter), in particular its \sectionsc{Quality Metrics},
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\sectionsc{Conformance Tiers}, and \sectionsc{Conformance: The Reference
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Suite} sections (\texttt{sec:solver:quality},
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\texttt{sec:solver:tiers}, \texttt{sec:solver:conformance}).
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Two core requirements bind this document into the conformance story:
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\begin{itemize}
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\item The core \sectionsc{Quality Metrics} normalization requirement:
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``Per-metric normalization functions (mapping raw measurements to
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$[0.0,1.0]$) are specified in the Quality Metric Catalog companion
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document. Implementations \MUST{} use the catalog's normalization;
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arbitrary normalization is non-conforming.'' Chapter~\ref{ch:metrics}
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is that normalization.
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\item The core tie-breaking requirement: ``Tie-breaking weights \MUST{}
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have normative defaults specified in the Quality Metric Catalog.''
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Chapter~\ref{ch:weights} is those defaults.
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\end{itemize}
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Where this document and a ratified core requirement disagree, \textbf{the
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core requirement governs} and the discrepancy is a defect in this document.
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Graph types, the layout IR pipeline
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(\texttt{LogicalLayoutIR} $\rightarrow$ \texttt{ConstrainedLayoutIR}
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$\rightarrow$ \texttt{ResolvedLayoutIR}),
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the spring-slot and vertical-band models, and the built-in
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\texttt{LayoutConstraint} kinds are the core specification's Chapter~7
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(\texttt{ch:layout-ir}); this document's formulas range over those
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structures without redefining them.
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\begin{rationale}
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\textbf{Versioning.} This companion is versioned independently of the core
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specification (independent semver), like the Operation Catalog and the
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Binary Format companions. Metric definitions and thresholds are expected to
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be tuned on a faster cadence than the solver framework: threshold revisions
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informed by reference-suite experience are \textsc{minor} revisions here and
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require no core-spec change, while a change to the metric \emph{field set}
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(a new normative axis) is a core-spec change first, mirrored here.
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\end{rationale}
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\section{Conformance}
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\label{sec:about:conformance}
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The metric definitions, normalization functions, default weights, threshold
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tables, and profile registry in this document are \textbf{normative}. A
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solver that reports a \texttt{QualityMetricVector} computed by any function
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other than the ones defined here is non-conforming, per the core
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\sectionsc{Quality Metrics} requirement quoted above.
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Conformance \emph{claims} are evaluated on the Reference Suite companion's
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entry set: a solver claiming tier $T$ must keep every normative metric
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within tier $T$'s threshold (Chapter~\ref{ch:thresholds}) on every suite
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entry required at tier $T$. This document defines \emph{what is measured
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and how much is tolerable}; the Reference Suite companion defines
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\emph{on which scores}.
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Two boundaries of that claim, developed in Chapter~\ref{ch:model}:
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\begin{itemize}
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\item Metric values are \emph{diagnostic}, never canonical state
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(Section~\ref{sec:model:diagnostic}). No byte of canonical document
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state depends on them.
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\item Numeric agreement across implementations is \emph{not} required
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(Section~\ref{sec:model:determinism}). The cross-implementation
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contract is threshold conformance, not value equality.
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\end{itemize}
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% ===========================================================================
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\chapter{The Metric Model}
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\label{ch:model}
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\section{Diagnostic Status}
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\label{sec:model:diagnostic}
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The quality metric vector rides on the \texttt{SolveReport} (core
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specification Chapter~9, \sectionsc{The Solver Report}:
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\texttt{SolveReport.metric\_vector}). It describes the layout; it is not
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part of the layout. The solver's canonical output ---
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\texttt{ResolvedLayoutIR} --- carries no metric field, and the core
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specification's observational-equivalence rule is stated over
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\texttt{ResolvedLayoutIR} bytes alone.
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\begin{requirement}
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\label{req:qmc:diagnostic}
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Quality metrics are \textbf{diagnostic output}, never canonical state.
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\begin{itemize}
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\item A \texttt{QualityMetricVector} appears only on the
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\texttt{SolveReport}. The canonical serialized form of
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\texttt{ResolvedLayoutIR} \MUSTNOT{} contain quality-metric values,
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and a \texttt{NormalizedMetric} value \MUSTNOT{} enter canonical
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document bytes by any other path.
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\item Two solves whose \texttt{ResolvedLayoutIR} values are
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byte-identical under canonical serialization are observationally
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equivalent regardless of their metric vectors. A metric value
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\MUSTNOT{} be an input to any canonical-state decision.
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\end{itemize}
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\end{requirement}
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\begin{rationale}
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Keeping metrics off the canonical path is what makes them safely
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improvable. A solver revision that measures more honestly (or a catalog
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revision that tunes a formula) changes reports, warnings, and conformance
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verdicts --- but not one byte of any document. The reference implementation
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already has this shape: \texttt{ResolvedLayoutIR} has no metric field, the
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\texttt{SolveReport} is never serialized, and no consumer reads the vector
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to make a state decision.
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\end{rationale}
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\section{Determinism and Numeric Agreement}
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\label{sec:model:determinism}
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\begin{requirement}
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\label{req:qmc:determinism}
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Within one implementation version, metric computation \MUST{} be
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deterministic: identical solve inputs (the same
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\texttt{ConstrainedLayoutIR}, configuration, and declared page geometry)
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\MUST{} yield bitwise-identical \texttt{QualityMetricVector} values.
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Across implementations (and across versions of one implementation),
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numeric agreement is \textbf{not} required. Two conforming solvers \MAY{}
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report different metric values for the same score; the
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cross-implementation contract is the core specification's four
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suite-conformance conditions --- in particular, that every metric is within
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the claimed tier's threshold on every required suite entry --- not value
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equality.
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Metric values are ordinary IEEE~754 \texttt{f64} values subject to the
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core \texttt{NormalizedMetric} validity rules (finite, in $[0.0, 1.0]$).
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This document imposes no additional quantization, rounding, or evaluation-
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order discipline on their computation.
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\end{requirement}
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\begin{rationale}
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Different conforming solvers legitimately produce different layouts, so
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their metric values differ even under identical formulas; demanding numeric
|
|
agreement would smuggle cross-implementation layout equality in through the
|
|
diagnostics. Within-implementation determinism, by contrast, is load-
|
|
bearing: reproducible reports are what make threshold conformance testable
|
|
and regressions attributable.
|
|
\end{rationale}
|
|
|
|
\section{The Normative Metric Set and \texttt{QualityMetricKind}}
|
|
\label{sec:model:kind}
|
|
|
|
The nine normative metric axes are the nine non-extension fields of the
|
|
core specification's \texttt{QualityMetricVector}. The core references a
|
|
\texttt{QualityMetricKind} enumeration (the payload of
|
|
\texttt{SolverWarningKind::QualityFloorApproached}) without listing it;
|
|
this catalog pins it.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:kind}
|
|
The \texttt{QualityMetricKind} enumeration is exactly:
|
|
|
|
\begin{lstlisting}[language=Rust]
|
|
pub enum QualityMetricKind {
|
|
Collision,
|
|
Spacing,
|
|
SlurShape,
|
|
BeamSlope,
|
|
VerticalDensity,
|
|
SystemBreak,
|
|
PageFill,
|
|
CastingOff,
|
|
SymbolDensity,
|
|
}
|
|
\end{lstlisting}
|
|
|
|
Each kind names exactly one \texttt{QualityMetricVector} field and exactly
|
|
one \texttt{TieBreakingWeights} field, per
|
|
Table~\ref{tab:kind-mapping}. Extension metrics are not
|
|
\texttt{QualityMetricKind} values; they are identified by
|
|
\texttt{ExtensionMetricId}.
|
|
\end{requirement}
|
|
|
|
\begin{table}[h]
|
|
\centering
|
|
\small
|
|
\begin{tabular}{lll}
|
|
\toprule
|
|
\textbf{Kind} & \textbf{Vector field} & \textbf{Weight field} \\
|
|
\midrule
|
|
\texttt{Collision} & \texttt{collision\_penalty} & \texttt{collision} \\
|
|
\texttt{Spacing} & \texttt{spacing\_distortion} & \texttt{spacing} \\
|
|
\texttt{SlurShape} & \texttt{slur\_shape\_penalty} & \texttt{slur\_shape} \\
|
|
\texttt{BeamSlope} & \texttt{beam\_slope\_penalty} & \texttt{beam\_slope} \\
|
|
\texttt{VerticalDensity} & \texttt{vertical\_density\_penalty} & \texttt{vertical\_density} \\
|
|
\texttt{SystemBreak} & \texttt{system\_break\_penalty} & \texttt{system\_break} \\
|
|
\texttt{PageFill} & \texttt{page\_fill\_efficiency} & \texttt{page\_fill} \\
|
|
\texttt{CastingOff} & \texttt{casting\_off\_quality} & \texttt{casting\_off} \\
|
|
\texttt{SymbolDensity} & \texttt{symbol\_density\_uniformity} & \texttt{symbol\_density} \\
|
|
\bottomrule
|
|
\end{tabular}
|
|
\caption{The nine normative axes: kind, vector field, tie-breaking weight.}
|
|
\label{tab:kind-mapping}
|
|
\end{table}
|
|
|
|
A naming caution: three field names read as higher-is-better words ---
|
|
\begin{center}
|
|
\texttt{page\_fill\_efficiency},\ \texttt{casting\_off\_quality},\ \texttt{symbol\_density\_uniformity}
|
|
\end{center}
|
|
--- but they are not. The core specification fixes the orientation of
|
|
\emph{every} normative metric ($0.0$ best, $1.0$ worst tolerable), and
|
|
the definitions in Chapter~\ref{ch:metrics} follow it: each of the three
|
|
measures a \emph{deficiency} (unfilled page area, uneven casting-off,
|
|
uneven density).
|
|
|
|
\section{The Measurement Domain}
|
|
\label{sec:model:domain}
|
|
|
|
Every raw measurement in Chapter~\ref{ch:metrics} is a deterministic
|
|
function of three inputs, all of which exist at the moment the solver
|
|
assembles its \texttt{SolveReport}:
|
|
|
|
\begin{enumerate}
|
|
\item the solve's resolved output $L$ (a \texttt{ResolvedLayoutIR}:
|
|
positioned glyphs with bounding boxes, strokes, and the page/system
|
|
tree);
|
|
\item the solve's constrained input $C$ (a \texttt{ConstrainedLayoutIR}:
|
|
horizontal spring slots, vertical bands, declared constraints);
|
|
\item the declared page geometry the solve was configured with: the
|
|
content width $W$ and content height $H$, in staff spaces. (Schema
|
|
major~1 defines \texttt{Canvas.layout\_defaults} and its type
|
|
\texttt{CanvasLayoutDefaults}, P12-I7; the reference implementation's
|
|
code graph home lands in a later phase, so until then the geometry is a
|
|
solver parameter, and the Reference Suite companion requires each suite
|
|
entry to declare it.)
|
|
\end{enumerate}
|
|
|
|
Notation used throughout Chapter~\ref{ch:metrics}:
|
|
|
|
\begin{itemize}
|
|
\item $G$ is the set of resolved glyphs of $L$. For $g \in G$, the
|
|
\emph{ink box} $B(g) = [l_g, r_g] \times [b_g, t_g]$ is the glyph's
|
|
bounding box translated to its resolved position. Strokes (staff
|
|
lines, ledger lines, stems, barline strokes) are not members of $G$.
|
|
\item $\mathit{sys}(g)$ is the system that positioned $g$ under the
|
|
solve's casting-off; every system belongs to exactly one region, and
|
|
every page carries an ordered list of systems. A glyph positioned by
|
|
no system belongs to no collision pair and to no per-system
|
|
aggregate.
|
|
\item $\mathit{slot}(g)$ is the horizontal spring slot of $g$'s source
|
|
glyph in $C$ --- the musical time column that groups a chord's
|
|
noteheads with their accidentals, dots, and same-column symbols.
|
|
\item For a system $s$: its \emph{columns} are the ascending sequence of
|
|
distinct resolved baseline $x$-coordinates
|
|
$x^s_1 < \dots < x^s_{m_s}$ of the glyph-bearing slots realized in
|
|
$s$; its \emph{advances} are $a^s_i = x^s_{i+1} - x^s_i$ for
|
|
$i = 1, \dots, m_s - 1$ (equivalently, the spacing pass's per-slot
|
|
advances); $w_s$ is the width of $s$'s content extent (the horizontal
|
|
span of the ink boxes assigned to $s$); $n_s$ is the number of glyphs
|
|
assigned to $s$.
|
|
\item $\mathrm{CV}(v_1, \dots, v_k)$, defined for $k \ge 2$ with
|
|
$\operatorname{mean} > 0$, is the population standard deviation
|
|
divided by the arithmetic mean.
|
|
\item The arithmetic mean over an \emph{empty} index set is defined as
|
|
$0$ (this is the vacuous-geometry rule of
|
|
Section~\ref{sec:model:vacuous} in aggregate form).
|
|
\end{itemize}
|
|
|
|
Because numeric agreement across implementations is not required
|
|
(Requirement~\ref{req:qmc:determinism}), a formula may reference the
|
|
solve's \emph{own} internal assignments --- which glyph landed in which
|
|
system, which columns a system realizes --- without threatening
|
|
conformance: the assignments are deterministic within an implementation
|
|
version, which is all the metric contract needs. No formula in this
|
|
catalog requires an optical-spacing model, font metrics beyond glyph
|
|
bounding boxes, or any geometry class the layout pipeline does not
|
|
produce.
|
|
|
|
\section{The Vacuous-Geometry Rule}
|
|
\label{sec:model:vacuous}
|
|
|
|
Each axis in Chapter~\ref{ch:metrics} names its \emph{contributing units}:
|
|
the glyph pairs, systems, pages, gaps, slurs, or beams the raw measurement
|
|
ranges over. A layout may simply not contain a metric's geometry class ---
|
|
no drawn slurs, no beams, a single system, a single page.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:vacuous}
|
|
When a normative metric's contributing-unit set is empty for a given
|
|
layout, the metric \MUST{} evaluate to exactly $0.0$: where there is
|
|
nothing to penalize, the penalty is zero. In particular:
|
|
|
|
\begin{itemize}
|
|
\item a layout containing no drawn slur geometry has
|
|
$\texttt{slur\_shape\_penalty} = 0.0$;
|
|
\item a layout containing no drawn beam geometry has
|
|
$\texttt{beam\_slope\_penalty} = 0.0$;
|
|
\item a region cast onto a single system contributes no units to
|
|
\texttt{system\_break\_penalty}, \texttt{casting\_off\_quality}, or
|
|
\texttt{symbol\_density\_uniformity}, and a single-page layout
|
|
contributes no units to \texttt{page\_fill\_efficiency} --- each axis
|
|
degenerates exactly as its per-axis definition states;
|
|
\item a solve configured without positive finite content bounds ($W$ or
|
|
$H$) has an empty contributing set for every axis defined over that
|
|
bound.
|
|
\end{itemize}
|
|
|
|
An implementation \MUSTNOT{} report a sentinel (such as $1.0$) for a
|
|
metric whose contributing-unit set is empty. The all-worst placeholder
|
|
vector remains correct only for a solver that \emph{computes no metrics at
|
|
all} and claims no conformance tier (the core's \texttt{Stub} tier).
|
|
\end{requirement}
|
|
|
|
\begin{openquestion}
|
|
\textbf{The notated-but-unrendered honesty edge.} A score whose
|
|
\emph{source} notates geometry a solver does not draw scores
|
|
vacuous-$0.0$ on that axis under this rule --- the axis sees nothing
|
|
drawn and finds nothing to penalize, even though the output is arguably
|
|
\emph{worse} than a badly-drawn one. The metric axes evaluate the geometry
|
|
the solver produced, and \emph{rendering completeness} --- whether notated
|
|
content is realized at all --- is governed by constraint families and
|
|
visual acceptance testing, not by the quality metrics. Should a future
|
|
revision instead score notated-but-unrendered geometry classes at the
|
|
worst value, so that the metric vector cannot flatter an incomplete
|
|
renderer? Resolving this requires a normative definition of ``notated
|
|
content that demands drawn geometry,'' which does not exist yet.
|
|
\emph{Slurs no longer instance this edge} (they render and are measured,
|
|
schema-major-2); it persists for still-logical-only classes such as beams.
|
|
\end{openquestion}
|
|
|
|
\section{Normalization Form}
|
|
\label{sec:model:normalization}
|
|
|
|
Every normative axis uses the same one-parameter normalization shape, so
|
|
that anchors --- not curve families --- are the entire tuning surface.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:normalization-form}
|
|
Each normative metric defines a raw measurement
|
|
$\mathit{raw} \ge 0$ (dimensionless, per its axis definition) and a pinned
|
|
anchor constant $R_{\mathrm{worst}} > 0$. The normalized value is the
|
|
clamped-linear map
|
|
\[
|
|
n \;=\; \min\!\left(1,\; \frac{\mathit{raw}}{R_{\mathrm{worst}}}\right),
|
|
\]
|
|
so that $\mathit{raw} = 0$ (the ideal) normalizes to $0.0$ and
|
|
$\mathit{raw} \ge R_{\mathrm{worst}}$ (the worst-tolerable anchor and
|
|
beyond) normalizes to $1.0$. Implementations \MUST{} use the per-axis raw
|
|
measurements and anchors of Chapter~\ref{ch:metrics} exactly; per the core
|
|
specification, arbitrary normalization is non-conforming. Extension
|
|
metrics \MAY{} use other normalization shapes but \MUSTNOT{} change
|
|
orientation or range.
|
|
\end{requirement}
|
|
|
|
% ===========================================================================
|
|
\chapter{The Nine Normative Metrics}
|
|
\label{ch:metrics}
|
|
|
|
Each section below defines one axis under a fixed template: the
|
|
\emph{phenomenon} (what an engraver would point at), the \emph{contributing
|
|
units} (what the raw measurement ranges over --- the set whose emptiness
|
|
triggers Requirement~\ref{req:qmc:vacuous}), the \emph{raw measurement},
|
|
and the \emph{normalization anchor} with a brief justification. All
|
|
lengths are in staff spaces; all raw measurements are dimensionless
|
|
ratios.
|
|
|
|
Four axes measure horizontal-distribution phenomena at different
|
|
granularities, and the boundaries are deliberate:
|
|
|
|
\begin{itemize}
|
|
\item \texttt{spacing\_distortion} is \emph{within-system} advance
|
|
regularity;
|
|
\item \texttt{system\_break\_penalty} is the \emph{per-break} absolute
|
|
cost of each chosen system break (looseness or overflow of
|
|
non-final systems);
|
|
\item \texttt{casting\_off\_quality} is \emph{across-system} width
|
|
evenness, including the final system (the stub-last-line failure);
|
|
\item \texttt{symbol\_density\_uniformity} is \emph{across-system}
|
|
crowding evenness (equal widths can hide very different symbol
|
|
densities).
|
|
\end{itemize}
|
|
|
|
\section{\texttt{collision\_penalty}}
|
|
\label{sec:metrics:collision}
|
|
|
|
\textbf{Phenomenon.} Overlapping ink between symbols that belong to
|
|
different musical time columns: a notehead striking the previous column's
|
|
accidental, a chord symbol over a barline, any cross-column ink contact.
|
|
Professional engraving contains none.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:collision}
|
|
\textbf{Contributing units:} unordered glyph pairs $\{g, h\} \subseteq G$
|
|
with $\mathit{sys}(g) = \mathit{sys}(h)$ and
|
|
$\mathit{slot}(g) \ne \mathit{slot}(h)$.
|
|
|
|
A pair \emph{collides} when its ink boxes intersect with positive area in
|
|
both axes:
|
|
\[
|
|
\begin{gathered}
|
|
\min(r_g, r_h) - \max(l_g, l_h) > 0
|
|
\quad\text{and}\\
|
|
\min(t_g, t_h) - \max(b_g, b_h) > 0 .
|
|
\end{gathered}
|
|
\]
|
|
Edge-touching boxes do not collide. Pairs sharing a horizontal spring slot
|
|
are \textbf{excluded}: a column's internal cluster --- a chord's noteheads,
|
|
their accidentals, dots, and other same-slot symbols --- is arranged by the
|
|
constrained stage, and its legitimate internal ink contact is not a
|
|
spacing failure of the solver. Strokes are not glyphs and join no pair:
|
|
staff lines legitimately cross every notehead.
|
|
|
|
\textbf{Raw measurement:} with $P$ the set of colliding pairs,
|
|
\[
|
|
\mathit{raw} \;=\; \frac{|P|}{|G|}
|
|
\qquad (\mathit{raw} = 0 \text{ when } G = \emptyset).
|
|
\]
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.05$;
|
|
$n = \min(1, \mathit{raw} / 0.05)$.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
The anchor says: one cross-column collision per twenty glyphs is
|
|
unmistakably broken layout --- the worst a report should be able to
|
|
distinguish. The count is divided by the glyph population, not by the pair
|
|
population, so that the measure does not vanish quadratically on large
|
|
scores: a score with one collision per page stays visible. The reference
|
|
pipeline evaluates overlap today only for \emph{declared}
|
|
\texttt{NoCollision} constraints; this axis is the full pairwise
|
|
same-system sweep over ink boxes, which is new but cheap work over data
|
|
the resolved layout already carries.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{spacing\_distortion}}
|
|
\label{sec:metrics:spacing}
|
|
|
|
\textbf{Phenomenon.} Uneven horizontal distribution within a system: the
|
|
\emph{rhythmic} columns --- those carrying notes and rests --- bunched
|
|
together here and stretched apart there, where the underlying spring model
|
|
asked for near-uniform advances.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:spacing}
|
|
\textbf{Rhythmic columns.} A \emph{rhythmic column} of a system is a
|
|
horizontal spring slot at least one of whose glyphs is a notehead or a
|
|
rest. The clef, key-signature, and time-signature lead and the barlines are
|
|
\textbf{not} rhythmic columns: their horizontal extent is notational
|
|
furniture, fixed by their content rather than by rhythm.
|
|
|
|
\textbf{Contributing units:} systems $s$ with at least three rhythmic
|
|
columns (so at least two rhythmic advances).
|
|
|
|
\textbf{Raw measurement:} let $x^s_1 < \dots < x^s_{k_s}$ be the reference
|
|
x-positions of the system's $k_s$ rhythmic columns in order, and
|
|
$a^s_i = x^s_{i+1} - x^s_i$ the advance between consecutive rhythmic columns
|
|
(a note-to-note advance spans any barline or furniture that falls between
|
|
the two, so barlines are transparent, not breaks in the sequence). Then
|
|
$\mathit{raw}_s = \mathrm{CV}(a^s_1, \dots, a^s_{k_s - 1})$, and the axis
|
|
raw value is the arithmetic mean of $\mathit{raw}_s$ over contributing
|
|
units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 1.0$;
|
|
$n = \min(1, \mathit{raw})$.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
A coefficient of variation of $1.0$ means the typical advance deviates from
|
|
the mean by the whole mean --- spacing with no discernible regularity. v0.2
|
|
defines \emph{geometric} regularity over the \emph{rhythmic} columns
|
|
deliberately: the reference spring model's preferred widths are uniform, so
|
|
regular note/rest advances are exactly what its ideal output looks like,
|
|
and the collision minima (accidental overhangs, wide columns) that
|
|
legitimately perturb those advances are modest on realistic scores. The
|
|
axis is scoped to rhythmic columns because a leading clef, key signature,
|
|
or time signature is furniture whose width the spring model does not govern:
|
|
folding the wide clef-to-first-note gap into the CV would flag a
|
|
perfectly-spaced short line as distorted purely for carrying a clef ---
|
|
measuring furniture, not spacing.
|
|
\end{rationale}
|
|
|
|
\begin{openquestion}
|
|
\textbf{Optical spacing at the Standard tier.} Mature engraving spaces
|
|
rhythmic columns proportionally to musical duration (with an optical
|
|
correction), not uniformly; under a duration-proportional model, this
|
|
axis's ideal would be ``advances proportional to the column's duration
|
|
share,'' and a perfectly optically-spaced line would score \emph{worse}
|
|
than a uniform one under the v0.2 definition. When the layout pipeline
|
|
gains duration-aware preferred widths, should the Standard tier redefine
|
|
$\mathit{raw}_s$ as deviation from the duration-proportional ideal while
|
|
Minimal keeps geometric regularity? v0.2 scopes the geometric definition to
|
|
rhythmic columns (removing the leading-furniture false positive on short
|
|
scores) but still measures geometric, not duration-proportional, regularity.
|
|
\end{openquestion}
|
|
|
|
\section{\texttt{slur\_shape\_penalty}}
|
|
\label{sec:metrics:slur}
|
|
|
|
\textbf{Phenomenon.} Badly-shaped slur arcs: flat, tape-like slurs or
|
|
bulging semicircles, measured against the shallow-arc norm of engraving
|
|
practice.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:slur}
|
|
\textbf{Contributing units:} drawn slurs in $L$ with chord length
|
|
$c > 0$, where the \emph{chord} is the segment between the \emph{whole}
|
|
slur's endpoints and the \emph{apex height} $h \ge 0$ is the maximum
|
|
perpendicular distance from the curve to its chord. The unit is the whole
|
|
slur, not a per-system fragment: a slur that a casting-off pass splits
|
|
across a system break is measured once, as the arc it was shaped to be, so
|
|
a well-shaped slur that happens to break is not spuriously penalized (its
|
|
fragments' diagonal chords each read flatter than the whole).
|
|
|
|
\textbf{Raw measurement:} per unit, with arc ratio $\rho = h / c$,
|
|
\[
|
|
\mathit{raw}_u \;=\; \max\bigl(0,\;\; 0.08 - \rho,\;\; \rho - 0.25\bigr),
|
|
\]
|
|
i.e.\ the shortfall below the ideal band $[0.08, 0.25]$ or the excess
|
|
above it; the axis raw value is the arithmetic mean over contributing
|
|
units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.25$;
|
|
$n = \min(1, \mathit{raw} / 0.25)$.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
The band $[0.08, 0.25]$ brackets the shallow arcs engraving practice
|
|
prefers: an arc rising less than about $1/12$ of its span reads as a
|
|
straight line; one rising more than a quarter of its span begins to bulge.
|
|
The anchor makes a semicircular slur ($\rho = 0.5$, $\mathit{raw}_u =
|
|
0.25$) exactly worst-tolerable, and a completely flat slur ($\rho = 0$,
|
|
$\mathit{raw}_u = 0.08$) roughly a third of the way to failing.
|
|
|
|
The implementation now \emph{draws} slurs as cubic-B\'ezier curves and
|
|
measures this axis directly (schema-major-2 rendering; the first
|
|
slur-drawing release, as the pinned definition anticipated). A layout with
|
|
no drawn slur curve still evaluates to $0.0$ under the vacuous-geometry
|
|
rule. A tier that draws the ideal shallow arc for every slur measures $0$
|
|
on this axis; a fixed-height engraver scores non-zero on slurs whose span
|
|
pushes the arc ratio outside the $[0.08, 0.25]$ band (a very short or very
|
|
long slur), which a duration-aware height corrects.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{beam\_slope\_penalty}}
|
|
\label{sec:metrics:beam}
|
|
|
|
\textbf{Phenomenon.} Over-steep beams. Engraving practice keeps beam
|
|
slants gentle regardless of the melodic interval they span.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:beam}
|
|
\textbf{Contributing units:} drawn beam segments in $L$ with horizontal
|
|
run $\Delta x > 0$ (endpoint-to-endpoint).
|
|
|
|
\textbf{Raw measurement:} per unit, with absolute slope
|
|
$\sigma = |\Delta y| / \Delta x$,
|
|
\[
|
|
\mathit{raw}_u \;=\; \max\bigl(0,\; \sigma - 0.25\bigr);
|
|
\]
|
|
the axis raw value is the arithmetic mean over contributing units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.25$;
|
|
$n = \min(1, \mathit{raw} / 0.25)$.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
Slopes up to $0.25$ (about $14^\circ$) are penalty-free --- within the
|
|
range engraving manuals tolerate for short, wide-interval beams --- and the
|
|
anchor places $\sigma = 0.5$ (about $27^\circ$, roughly double any
|
|
published maximum) at worst-tolerable. Like the slur axis, this is pinned
|
|
ahead of implementation: the v0.1 reference pipeline draws no beam
|
|
geometry, so the axis evaluates to $0.0$ under the vacuous-geometry rule.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{vertical\_density\_penalty}}
|
|
\label{sec:metrics:vertical}
|
|
|
|
\textbf{Phenomenon.} Vertical crowding or sprawl: inter-staff and
|
|
inter-system gaps realized far from the spacing the band model asked for.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:vertical}
|
|
\textbf{Contributing units:} each \emph{realization} in $L$ of a vertical
|
|
band of $C$ of kind \texttt{InterStaffGap} or \texttt{InterSystemGap} with
|
|
preferred height $p > 0$ (a band is realized wherever the adjacent content
|
|
it separates was laid out). A band realized in several systems contributes
|
|
\textbf{one unit per system}, not one per band: a vertical solve sizes each
|
|
system's gaps from that system's own content, so one band's realized height
|
|
genuinely differs from system to system. This matches how the realized
|
|
inter-system gaps are already counted --- one unit per adjacent system pair
|
|
on a page.
|
|
|
|
\textbf{Raw measurement:} per unit, with $r \ge 0$ the realized vertical
|
|
separation between the adjacent content extents the band separates
|
|
(measured in resolved coordinates),
|
|
\[
|
|
\mathit{raw}_u \;=\; \frac{|r - p|}{p};
|
|
\]
|
|
the axis raw value is the arithmetic mean over contributing units.
|
|
|
|
\textbf{Content extent} means \emph{every} primitive the adjacent band
|
|
owns --- glyphs, strokes, and curves alike, each attributed by its declared
|
|
\texttt{vertical\_band} (core spec
|
|
\sectionsc{ConstrainedLayoutIR}, primitive band ownership) --- and not the
|
|
band's glyph \texttt{members} alone. A staff's outermost ink is usually not
|
|
a glyph: ledger lines, stems, and slurs reach past every notehead. A solver
|
|
separates staves until their content clears the gap, so scoring it against
|
|
its noteheads alone would charge it for the very ink it made room for.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 1.0$;
|
|
$n = \min(1, \mathit{raw})$.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
A gap off by its own preferred size --- staves twice as far apart as asked,
|
|
or fully collapsed --- is unambiguous vertical failure; proportional
|
|
deviation makes one anchor serve both tight inter-staff gaps and wide
|
|
inter-system gaps.
|
|
|
|
The v0.1 reference pipeline preserved constrained $y$ verbatim, so realized
|
|
gaps equalled preferred gaps wherever bands were realized and the axis
|
|
reported its honest near-zero. The vertical spring solve has since landed
|
|
(inter-staff gap renegotiation and inter-system vertical justification), and
|
|
the axis now measures what it was defined to measure. The
|
|
\textbf{content extent} clarification above is the lesson from that landing:
|
|
the reference implementation read ``content extents'' as the band's glyph
|
|
\texttt{members}, because until primitive band ownership was ratified a band
|
|
listed no strokes or curves to own. A correctly separated two-staff system
|
|
then scored a saturated $1.0$ and tripped the \textsc{Standard} floor
|
|
warning --- the metric charging the solver for the ledger and slur ink it had
|
|
correctly cleared. The formula, units, anchor, and normalization are
|
|
unchanged; only a non-conforming measurement was.
|
|
|
|
The inter-system half of the axis is a genuine trade-off, not a defect: the
|
|
vertical justification pass deliberately stretches inter-system gaps past
|
|
preferred to fill a non-final page, trading this axis against
|
|
\texttt{page\_fill\_efficiency}. Both axes are reported; neither is wrong.
|
|
|
|
\textbf{Per-realization units} (0.3.0) followed from the same landing. While
|
|
the reference pipeline preserved constrained $y$ verbatim, a band had exactly
|
|
one realized height and the distinction was moot. Once the inter-staff solve
|
|
began sizing each system's gaps from that system's own content, a band's
|
|
realized height became per-system, and counting one unit per band would let a
|
|
well-solved system average away a badly spaced one. The axis is deliberately
|
|
symmetric: a gap wider than preferred is sprawl exactly as a narrower one is
|
|
crowding. A solver that only ever \emph{expands} a fixed stacking --- never
|
|
compressing an over-wide gap back toward preferred --- will therefore report
|
|
honest sprawl on its slack systems. That is the axis working, not
|
|
mis-measuring, and it is how the reference implementation's expand-only solve
|
|
was found: it now renegotiates in both directions.
|
|
|
|
Where a solver realizes each band's declared height exactly, the inter-staff
|
|
half of this axis reads its honest zero and serves as a \emph{self-check} on the
|
|
solve rather than a judgement on the score. A conforming implementation should
|
|
therefore measure the realized separation back from the geometry it produced,
|
|
not from the target it aimed at: the two agree only if the solve and the bake
|
|
both did what they claimed. The reference implementation reads it back from the
|
|
baked output, and that is how a defect in its multi-staff cascade --- one that
|
|
over-separated every pair below the first --- was caught.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{system\_break\_penalty}}
|
|
\label{sec:metrics:system-break}
|
|
|
|
\textbf{Phenomenon.} Bad break choices, one system at a time: a non-final
|
|
system left loose (broken far short of the available width) or overfull
|
|
(content past the content width).
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:system-break}
|
|
\textbf{Contributing units:} non-final systems --- for each region, every
|
|
system the casting-off produced except the region's last --- defined only
|
|
when the declared content width $W$ is finite and positive.
|
|
|
|
\textbf{Raw measurement:} per unit,
|
|
\[
|
|
\mathit{raw}_s \;=\; \frac{|W - w_s|}{W},
|
|
\]
|
|
penalizing looseness ($w_s < W$) and overflow ($w_s > W$) alike; the axis
|
|
raw value is the arithmetic mean over contributing units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.5$;
|
|
$n = \min(1, \mathit{raw} / 0.5)$.
|
|
|
|
A region cast onto a single system contributes no units (the break axis
|
|
degenerates to nothing-to-penalize, per
|
|
Requirement~\ref{req:qmc:vacuous}); the final system of each region is
|
|
never a unit, because a short last line is not a break failure.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
Non-final systems half-empty on average --- or overflowing by half the
|
|
content width --- mark casting-off that has effectively failed, hence the
|
|
$0.5$ anchor. The raw quantities are exactly what the reference
|
|
casting-off pass already computes: per-system content extents against the
|
|
declared content width, with breaks chosen among barline candidates.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{page\_fill\_efficiency}}
|
|
\label{sec:metrics:page-fill}
|
|
|
|
\textbf{Phenomenon.} Underfilled non-final pages: vertical white space a
|
|
better page-break policy would have used. Despite the field's name, the
|
|
metric follows the fixed orientation --- it measures \emph{unfilled}
|
|
fraction, so $0.0$ is best.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:page-fill}
|
|
\textbf{Contributing units:} non-final pages of $L$, defined only when
|
|
the declared content height $H$ is finite and positive.
|
|
|
|
\textbf{Raw measurement:} per unit, with $\mathit{span}_p$ the vertical
|
|
extent of page $p$'s content (from the top of its first system's content
|
|
extent to the bottom of its last system's content extent) and fill
|
|
fraction $f_p = \min(1, \mathit{span}_p / H)$,
|
|
\[
|
|
\mathit{raw}_p \;=\; 1 - f_p;
|
|
\]
|
|
the axis raw value is the arithmetic mean over contributing units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.75$;
|
|
$n = \min(1, \mathit{raw} / 0.75)$.
|
|
|
|
A single-page layout contributes no units; the final page is never a
|
|
unit, because a short last page is not a fill failure.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
A non-final page three-quarters empty is a page break with no plausible
|
|
justification --- worst-tolerable. The span-based fill fraction is
|
|
computable directly from the casting-off pass's vertical cursor walk and
|
|
per-system extents, and clamping $f_p$ at $1$ keeps slight margin
|
|
overshoot from producing a negative raw value.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{casting\_off\_quality}}
|
|
\label{sec:metrics:casting-off}
|
|
|
|
\textbf{Phenomenon.} Uneven casting-off across a region's systems taken as
|
|
a whole: some lines full, others sparse --- including the classic failure
|
|
this axis exists to catch, a stub final system carrying one straggling
|
|
measure. Despite the field's name, $0.0$ is best.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:casting-off}
|
|
\textbf{Contributing units:} regions whose casting-off produced at least
|
|
two systems, each with content-extent width $w_s > 0$.
|
|
|
|
\textbf{Raw measurement:} per unit region $R$,
|
|
\[
|
|
\mathit{raw}_R \;=\; \mathrm{CV}\bigl(\, w_s : s \in \mathrm{systems}(R) \,\bigr),
|
|
\]
|
|
over \emph{all} of the region's systems, the final system included; the
|
|
axis raw value is the arithmetic mean over contributing units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.5$;
|
|
$n = \min(1, \mathit{raw} / 0.5)$.
|
|
|
|
A single-system region contributes no units.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
Including the final system is the deliberate difference from
|
|
\texttt{system\_break\_penalty} (which exempts it): a lone stub last line
|
|
drags the width spread up and is penalized \emph{here}, as a global
|
|
casting-off failure rather than a per-break one. The anchor: per-system
|
|
widths whose standard deviation is half their mean describe a page where
|
|
line lengths visibly disagree.
|
|
\end{rationale}
|
|
|
|
\section{\texttt{symbol\_density\_uniformity}}
|
|
\label{sec:metrics:symbol-density}
|
|
|
|
\textbf{Phenomenon.} Uneven crowding across systems: one line crammed with
|
|
symbols, the next sparse --- even when the lines' widths agree. Despite the
|
|
field's name, $0.0$ is best.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:symbol-density}
|
|
\textbf{Contributing units:} regions whose casting-off produced at least
|
|
two systems with $w_s > 0$.
|
|
|
|
\textbf{Raw measurement:} per unit region $R$, with per-system symbol
|
|
density $\rho_s = n_s / w_s$ (glyphs per staff space of content width),
|
|
\[
|
|
\mathit{raw}_R \;=\; \mathrm{CV}\bigl(\, \rho_s : s \in \mathrm{systems}(R),\ w_s > 0 \,\bigr);
|
|
\]
|
|
the axis raw value is the arithmetic mean over contributing units.
|
|
|
|
\textbf{Normalization:} $R_{\mathrm{worst}} = 0.5$;
|
|
$n = \min(1, \mathit{raw} / 0.5)$.
|
|
|
|
A single-system region contributes no units.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
Width evenness (\texttt{casting\_off\_quality}) and density evenness are
|
|
independent failures: equal-width systems can still alternate between
|
|
sixteenth-note walls and whole-note deserts when break choices ignore
|
|
content weight. Density varying by half its mean across systems reads as
|
|
visibly uneven engraving, hence the shared $0.5$ anchor.
|
|
\end{rationale}
|
|
|
|
% ===========================================================================
|
|
\chapter{Default Tie-Breaking Weights}
|
|
\label{ch:weights}
|
|
|
|
The core specification requires normative default
|
|
\texttt{TieBreakingWeights}: they select among Pareto-equivalent layouts,
|
|
deterministically, and are ``the basis for reference-suite conformance.''
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:weights}
|
|
The normative default tie-breaking weights are $1.0$ for every one of the
|
|
nine fields of \texttt{TieBreakingWeights}:
|
|
|
|
\begin{center}
|
|
\small
|
|
\begin{tabular}{lc@{\hspace{2.5em}}lc}
|
|
\toprule
|
|
\textbf{Weight} & \textbf{Default} & \textbf{Weight} & \textbf{Default} \\
|
|
\midrule
|
|
\texttt{collision} & \tablenums{1.0} & \texttt{system\_break} & \tablenums{1.0} \\
|
|
\texttt{spacing} & \tablenums{1.0} & \texttt{page\_fill} & \tablenums{1.0} \\
|
|
\texttt{slur\_shape} & \tablenums{1.0} & \texttt{casting\_off} & \tablenums{1.0} \\
|
|
\texttt{beam\_slope} & \tablenums{1.0} & \texttt{symbol\_density} & \tablenums{1.0} \\
|
|
\texttt{vertical\_density} & \tablenums{1.0} & & \\
|
|
\bottomrule
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
Implementations \MAY{} let users customize weights, per the core
|
|
specification; conformance evaluation on the reference suite uses these
|
|
defaults.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
No aesthetic priority ordering among the nine axes has been ratified, and
|
|
inventing one ahead of measurement experience would encode a preference no
|
|
evidence supports. Uniform weights are the honest neutral default --- they
|
|
make tie-breaking deterministic (the core's actual requirement) without
|
|
pretending to a house style. They also bless the reference
|
|
implementation's existing \texttt{Default} for \texttt{TieBreakingWeights}
|
|
(every field $1.0$). Revisions of this catalog are expected to tune the
|
|
defaults once reference-suite experience shows which axes dominate
|
|
perceived quality.
|
|
\end{rationale}
|
|
|
|
% ===========================================================================
|
|
\chapter{Per-Tier Metric Thresholds}
|
|
\label{ch:thresholds}
|
|
|
|
\section{The Default Threshold Table}
|
|
\label{sec:thresholds:table}
|
|
|
|
A tier's threshold for an axis is the maximum permitted
|
|
\texttt{NormalizedMetric} value on a reference-suite entry evaluated at
|
|
that tier. The core specification fixes the relationship: Minimal-tier
|
|
thresholds are relaxed relative to Standard; the Standard tier corresponds
|
|
to professional engraving quality.
|
|
|
|
\begin{table}[h]
|
|
\centering
|
|
\small
|
|
\begin{tabular}{lcc}
|
|
\toprule
|
|
\textbf{Axis} & \textbf{Minimal (max)} & \textbf{Standard (max)} \\
|
|
\midrule
|
|
\texttt{collision\_penalty} & \tablenums{0.90} & \tablenums{0.25} \\
|
|
\texttt{spacing\_distortion} & \tablenums{0.90} & \tablenums{0.40} \\
|
|
\texttt{slur\_shape\_penalty} & \tablenums{0.90} & \tablenums{0.30} \\
|
|
\texttt{beam\_slope\_penalty} & \tablenums{0.90} & \tablenums{0.30} \\
|
|
\texttt{vertical\_density\_penalty} & \tablenums{0.90} & \tablenums{0.40} \\
|
|
\texttt{system\_break\_penalty} & \tablenums{0.90} & \tablenums{0.35} \\
|
|
\texttt{page\_fill\_efficiency} & \tablenums{0.90} & \tablenums{0.40} \\
|
|
\texttt{casting\_off\_quality} & \tablenums{0.90} & \tablenums{0.35} \\
|
|
\texttt{symbol\_density\_uniformity} & \tablenums{0.90} & \tablenums{0.40} \\
|
|
\bottomrule
|
|
\end{tabular}
|
|
\caption{Default per-tier maximum \texttt{NormalizedMetric} values.
|
|
Minimal is uniformly more permissive than Standard on every axis.}
|
|
\label{tab:tier-thresholds}
|
|
\end{table}
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:thresholds}
|
|
The default per-tier thresholds are given by
|
|
Table~\ref{tab:tier-thresholds}. A solver claiming a tier \MUST{} keep
|
|
every normative metric at or below the tier's threshold on every
|
|
reference-suite entry required at that tier, per the core specification's
|
|
suite-conformance conditions. The Reference Suite companion \MAY{}
|
|
override these defaults for individual entries; absent an override, the
|
|
values of Table~\ref{tab:tier-thresholds} govern.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
\textbf{Minimal = 0.90 everywhere: relaxed but non-vacuous.} A Minimal
|
|
solver may be aesthetically mediocre --- the core says so --- but it must
|
|
not be \emph{pathological}, and its metric vectors must be accurate. A
|
|
uniform $0.90$ admits every honestly-mediocre layout while excluding two
|
|
things: layouts at an axis's worst-tolerable anchor, and the all-worst
|
|
placeholder vector of a solver that computes nothing. That second
|
|
exclusion is deliberate --- a solver reporting the unmeasured $1.0$
|
|
placeholder cannot pass the Minimal suite, which is exactly the
|
|
honest-tier discipline: measuring is part of the Minimal claim.
|
|
|
|
\textbf{Standard = 0.25--0.40 per axis: professional quality.} Collisions
|
|
get the tightest bound ($0.25$: at most one cross-column collision per
|
|
eighty glyphs) because they are the most jarring single defect. The
|
|
break-family axes ($0.35$) sit slightly tighter than the distribution and
|
|
vertical axes ($0.40$), whose v0.1 definitions are coarser proxies
|
|
(geometric spacing regularity; a not-yet-solved vertical dimension). Slurs
|
|
and beams ($0.30$) allow modest shape deviation across a piece. All values
|
|
are round v0.1 defaults chosen to be defensible, not optimal; the tuning
|
|
open question below owns their evolution.
|
|
\end{rationale}
|
|
|
|
\section{The Advanced Tier}
|
|
\label{sec:thresholds:advanced}
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:advanced}
|
|
The Advanced tier imposes the Standard-tier thresholds of
|
|
Table~\ref{tab:tier-thresholds} on the nine normative axes, \emph{plus}
|
|
per-extension thresholds on extension metrics: a registered extension
|
|
whose layout requirements are part of the Advanced reference suite
|
|
\MUST{} declare, in its extension declaration, a maximum
|
|
\texttt{NormalizedMetric} value for each extension metric it contributes,
|
|
and an Advanced-tier solver \MUST{} meet each declared threshold on every
|
|
Advanced suite entry that exercises that extension. An extension metric
|
|
with no declared threshold imposes no Advanced-tier obligation.
|
|
\end{requirement}
|
|
|
|
\section{The \texttt{QualityFloorApproached} Warning}
|
|
\label{sec:thresholds:floor}
|
|
|
|
The core specification gives \texttt{SolverWarningKind} a
|
|
\texttt{QualityFloorApproached} variant carrying a
|
|
\texttt{QualityMetricKind} payload, without defining its trigger. This
|
|
catalog pins it.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:floor-warning}
|
|
A solver \SHOULD{} emit a \texttt{QualityFloorApproached} warning for
|
|
metric kind $k$ when the computed value of $k$'s axis exceeds
|
|
$\mathbf{0.8}$ times the applicable threshold for that axis. The
|
|
applicable threshold is the one selected by the solve's
|
|
\texttt{SolverProfile} (Chapter~\ref{ch:profiles});
|
|
the warning fraction is pinned at $0.8$ exactly. The warning is
|
|
diagnostic: emitting it does not change the solve's status, and a value
|
|
\emph{over} the threshold still warns (it exceeds $0.8$ of it a
|
|
fortiori) --- threshold \emph{enforcement} exists only in reference-suite
|
|
evaluation, not in ordinary solves.
|
|
\end{requirement}
|
|
|
|
\section{Standard-Tier Constraint Families}
|
|
\label{sec:thresholds:families}
|
|
|
|
The core specification's Standard-tier requirement obliges a Standard
|
|
solver to ``support every Standard-tier constraint family declared in the
|
|
Quality Metric Catalog.'' This section is that declaration.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:standard-families}
|
|
The Standard-tier constraint families are the core specification's
|
|
built-in layout-constraint surface (Chapter~7,
|
|
\sectionsc{ConstrainedLayoutIR}):
|
|
|
|
\begin{itemize}
|
|
\item the \textbf{spring families}: horizontal spring slots and vertical
|
|
bands, with their min/preferred/max and stretch/compress parameters;
|
|
\item the five built-in \texttt{LayoutConstraint} kinds:
|
|
\texttt{NoCollision}, \texttt{Align}, \texttt{PositionWithin},
|
|
\texttt{SystemBreakAt}, and \texttt{PageBreakAt} (both
|
|
\texttt{Hard} and \texttt{Soft} break kinds).
|
|
\end{itemize}
|
|
|
|
These same families constitute ``the standard constraint families'' of
|
|
the core's Minimal-tier requirement: Minimal and Standard support the
|
|
same family set and differ in metric thresholds and incremental-solving
|
|
obligations, not in constraint vocabulary.
|
|
\texttt{LayoutConstraint::Registered} (extension-contributed) families
|
|
are per-extension obligations of the Advanced tier only.
|
|
\end{requirement}
|
|
|
|
\begin{openquestion}
|
|
\textbf{Threshold tuning.} Every number in
|
|
Table~\ref{tab:tier-thresholds} and every anchor constant in
|
|
Chapter~\ref{ch:metrics} is a v0.1 default pinned ahead of measurement
|
|
experience: no implementation has yet reported real vectors across the
|
|
reference suite. Once the reference implementation computes real metrics
|
|
on the v0.1 entry set, are the Standard columns achievable-but-meaningful
|
|
(neither trivially passed nor unreachable), and do any anchors need
|
|
rescaling? Threshold and anchor revisions are \textsc{minor} versions of
|
|
this catalog and are expected.
|
|
\end{openquestion}
|
|
|
|
% ===========================================================================
|
|
\chapter{The Registered Profile Catalog}
|
|
\label{ch:profiles}
|
|
|
|
The core specification's vocabulary appendix defines
|
|
\texttt{SolverProfile} as a registered profile identifier that ``selects
|
|
the solver's hard-constraint set, normalized-metric thresholds,
|
|
tie-breaking weights, and active extension catalog,'' and defers the
|
|
registry to this companion.
|
|
|
|
\begin{requirement}
|
|
\label{req:qmc:profiles}
|
|
The registered \texttt{SolverProfile} catalog is exactly three profiles:
|
|
\texttt{Draft}, \texttt{Standard}, and \texttt{Publication}. Their
|
|
selections:
|
|
|
|
\begin{center}
|
|
\small
|
|
\begin{tabular}{lllll}
|
|
\toprule
|
|
\textbf{Profile} & \textbf{Constraint families} & \textbf{Threshold column} &
|
|
\textbf{Weights} & \textbf{Extensions} \\
|
|
\midrule
|
|
\texttt{Draft} & Standard-tier set & Minimal
|
|
& defaults & none required \\
|
|
\texttt{Standard} & Standard-tier set & Standard
|
|
& defaults & none required \\
|
|
\texttt{Publication} & Standard-tier set & Standard
|
|
& defaults & none required \\
|
|
\bottomrule
|
|
\end{tabular}
|
|
\end{center}
|
|
|
|
\begin{itemize}
|
|
\item \emph{Constraint families}: all three profiles activate the
|
|
Standard-tier constraint families of
|
|
Requirement~\ref{req:qmc:standard-families}; hard constraints are
|
|
never traded away by any profile (the core's
|
|
hard-constraints-are-inviolable rule).
|
|
\item \emph{Threshold column}: the column of
|
|
Table~\ref{tab:tier-thresholds} the profile selects --- the thresholds
|
|
against which Requirement~\ref{req:qmc:floor-warning}'s warning
|
|
fraction is evaluated during ordinary solves. \texttt{Draft} selects
|
|
the Minimal column (few warnings, fast iteration);
|
|
\texttt{Standard} and \texttt{Publication} select the Standard
|
|
column. As of v0.2 no column tighter than Standard is ratified;
|
|
\texttt{Publication} is registered now so that documents and
|
|
configurations can name it, and a future revision \MAY{} give it a
|
|
tighter column without a schema change.
|
|
\item \emph{Weights}: all three profiles use the default tie-breaking
|
|
weights of Requirement~\ref{req:qmc:weights}.
|
|
\item \emph{Extensions}: no profile requires an active extension
|
|
catalog; extensions activate by document declaration, not by
|
|
profile.
|
|
\end{itemize}
|
|
|
|
\texttt{Standard} is the default profile.
|
|
\end{requirement}
|
|
|
|
\begin{rationale}
|
|
\textbf{Profiles are configuration; tiers are claims.} A
|
|
\texttt{SolverProfile} is a runtime input (\texttt{SolverConfig.profile})
|
|
that any solver may be asked to run under; a conformance tier is a claim
|
|
about the solver evaluated on the reference suite. The two meet in
|
|
exactly one place: the profile's threshold column determines which
|
|
thresholds the solver's own \texttt{QualityFloorApproached} diagnostics
|
|
reference during ordinary solves. Suite evaluation at a claimed tier
|
|
always uses that \emph{tier's} column, whatever profile the solver runs
|
|
under day to day. The three-profile registry matches the reference
|
|
implementation's existing \texttt{SolverProfile} enum
|
|
(\texttt{Draft} / \texttt{Standard} / \texttt{Publication}, default
|
|
\texttt{Standard}) so that registration blesses shipped reality rather
|
|
than inventing a parallel one.
|
|
\end{rationale}
|
|
|
|
% ===========================================================================
|
|
\chapter{Revision History}
|
|
\label{ch:history}
|
|
|
|
\begin{longtable}{p{2cm} p{2.5cm} p{9cm}}
|
|
\toprule
|
|
\textbf{Date} & \textbf{Section} & \textbf{Change} \\
|
|
\midrule
|
|
\endhead
|
|
\today & All & 0.1.0 --- Initial companion: pins the diagnostic-only
|
|
status of quality metrics, within-implementation determinism without
|
|
cross-implementation numeric agreement, the \texttt{QualityMetricKind}
|
|
enumeration, the measurement domain, and the vacuous-geometry rule;
|
|
defines all nine normative axes (phenomenon, raw measurement over
|
|
resolved geometry, clamped-linear normalization with pinned anchors);
|
|
sets the default tie-breaking weights (all $1.0$); establishes the
|
|
Minimal/Standard threshold table, the Advanced extension rule, the
|
|
\texttt{QualityFloorApproached} trigger ($0.8\times$ threshold), and
|
|
the Standard-tier constraint family declaration; registers the
|
|
\texttt{Draft}/\texttt{Standard}/\texttt{Publication} profile catalog.
|
|
Open questions: the notated-but-unrendered honesty edge, optical
|
|
spacing at the Standard tier, threshold tuning pending reference-suite
|
|
experience. \\
|
|
\today & \hyperref[sec:metrics:spacing]{\texttt{spacing\_distortion}}
|
|
& 0.2.0 --- Scope the \texttt{spacing\_distortion} raw measurement to the
|
|
system's \emph{rhythmic} columns (slots bearing a notehead or rest),
|
|
excluding the clef / key-signature / time-signature lead and treating
|
|
barlines transparently (a note-to-note advance spans them). Resolves the
|
|
reference-suite false positive in which a short healthy line's wide
|
|
clef-to-first-note gap inflated the CV above the Standard warning floor
|
|
(measured 0.36--0.41 on the three- to eight-column entries $\to$
|
|
0.08--0.22, below the floor) without weakening the axis on real spacing
|
|
irregularity. Normalization anchor, orientation, range, thresholds, and
|
|
the eight other axes are unchanged; the optical-spacing open question
|
|
(duration-proportional spacing) stays open. Batch item P12-I12. \\
|
|
\midrule
|
|
\today & \hyperref[sec:metrics:vertical]{\texttt{vertical\_density\_penalty}}
|
|
& 0.3.0 --- Count \textbf{one contributing unit per realization} of an
|
|
\texttt{InterStaffGap} band rather than one per band, matching how realized
|
|
inter-system gaps were already counted. The inter-staff vertical solve sizes
|
|
each system's gaps from that system's own content, so a band's realized
|
|
height is per-system; one unit per band let a well-solved system average away
|
|
a badly spaced one. Also \emph{clarifies} (no semantic change) that the
|
|
``content extents'' the raw measurement compares are every primitive the
|
|
adjacent band owns --- glyphs, strokes, and curves, each attributed by its
|
|
declared \texttt{vertical\_band} --- and not the band's glyph
|
|
\texttt{members}, a reading that was arguably unimplementable before
|
|
primitive band ownership was ratified. Raw formula, normalization anchor,
|
|
orientation, range, thresholds, and the eight other axes are unchanged. The
|
|
reference implementation's non-conforming glyph-only measurement is fixed
|
|
alongside. \\
|
|
\bottomrule
|
|
\end{longtable}
|
|
|
|
\end{document}
|