Module rd_knee 

Fixed-frame R-D curve parameterization with corner-based angles.

Every encode lives in a triangle: the worst corner (max bpp, zero quality) is the origin, and the angle from that corner describes position on the rate-distortion tradeoff. This is comparable across codecs, corpora, and resolutions because the frame is fixed by the metric scales and a practical bpp ceiling.

Fixed frame (web targeting)

Axis	Min	Max	Notes
bpp	0	4.0	Practical web ceiling
s2	0	100	SSIMULACRA2 scale
ba	0	15	Butteraugli practical floor (inverted)

Corner angle

θ = atan2(quality_norm * aspect, 1.0 - bpp_norm)

The aspect ratio is calibrated from the reference codec knee (mozjpeg 4:2:0 on CID22) so that the knee lands at exactly 45°.

• θ < 0° → worse than the worst corner (negative quality)
• θ = 0° → worst corner (max bpp, zero quality)
• θ < 45° → compression-efficient (below the knee)
• θ = 45° → reference knee (balanced tradeoff)
• θ ≈ 52° → ideal diagonal (zero bpp, perfect quality)
• θ > 52° → quality-dominated (spending bits for diminishing returns)
• θ = 90° → no compression (max bpp, max quality)
• θ > 90° → over-budget (bpp exceeds frame ceiling)

The knee (45° tangent on the corpus-aggregate curve) is a landmark within this system, not the origin. Its angle tells you where the “balanced tradeoff” falls for a given codec.

Dual-metric angles

SSIMULACRA2 and Butteraugli produce different angles for the same encode. Comparing theta_s2 and theta_ba reveals what kind of artifacts the codec configuration produces at that operating point.

Modules

defaults

Measured defaults from corpus calibration runs (2026-02-03).

Structs

AngleBin

A single angular bin.

AxisRange

Range for normalizing an axis to [0, 1].

BinScheme

Defines how the [0°, 90°] range is divided into bins.

CodecConfig

The full set of tuning knobs that produced a particular encode.

ConfiguredParetoFront

Pareto frontier with angular binning.

ConfiguredRDPoint

A point on the configuration-aware Pareto frontier.

CorpusAggregate

Aggregated R-D data from a corpus.

DualAngleBin

Dual-metric bin.

EncodeResult

A single encode result from one image at one quality level.

FixedFrame

Fixed normalization frame for web-targeted R-D analysis.

NormalizationContext

Normalization context for knee detection (uses per-curve observed ranges).

RDCalibration

Dual-metric calibration with knee landmarks in the fixed frame.

RDKnee

The 45° tangent point on a corpus-aggregate R-D curve.

RDPosition

An encode’s position in the fixed-frame corner coordinate system.

Enums

ParamValue

A single tuning parameter value.

QualityDirection

Direction of a quality metric.

Functions

plot_rd_svg

Generate an SVG plot of the R-D curve with corner angle grid and knee markers.