Interactive application
Interactive
What counts as a good circle?

Circle · Roundness Lab

What should closeness to a circle mean? Draw a loop, inspect radial error, curvature and harmonics, then compare scoring rules against counterexamples. Scale-normalized measurements expose defects that a single convenient score can hide.

Fourier analysisComputational geometryJavaScriptAlgorithm visualizationSignal processing
Explore connections
A familiar shape; competing definitions
DrawMeasureCompare
Open Roundness Lab Draw a loop, compare the declared scoring policies and inspect the measurements behind the result.
Recorded contour with fitted circle, residual extrema and the five-component geometric score.
Recorded contour with fitted circle, residual extrema and the five-component geometric score.
Quick start · live feature guide

From a gesture to a defensible measurement

Make the geometric choices visible before reducing a drawing to one number.

  1. 01

    Capture the contour

    Keep the original stroke and show any accepted closure seam.

  2. 02

    Normalize and sample

    Resample by arc length and separate drawing size from dimensionless shape error.

  3. 03

    Inspect the signals

    Compare radius, minimum-zone width, compactness, curvature and harmonics.

  4. 04

    Challenge the score

    Change aggregation and inspect defects, scale changes and smoothing sensitivity.

Question

A simple game becomes a geometric problem

Several plausible definitions of roundness react differently to dents, lobes and local roughness.

Method

Every component stays inspectable

Circle fits, a numerical minimum-zone annulus, curvature and radial spectra expose complementary errors.

Validation

Counterexamples are part of the interface

Compare aggregate policies and an explicit absolute-error baseline; distinguish shape quality from capture eligibility.

When a high score describes the wrong shape

Draw-a-perfect-circle games turn a contour into a number, but a score can conceal large defects or reward an outline merely because it is small. Roundness Lab asks what the measurement should preserve: invariance to scale, sensitivity to visible departures, and a clear treatment of incomplete or unreliable input.

The baseline uses a stated scoring rule, without attempting to reproduce a particular online game. Counterexamples show which defects each measurement notices and which it misses.

Five measurements, several aggregation policies

The lab computes least-squares radial error, an approximate minimum-zone annulus, isoperimetric compactness, normalized curvature and radial Fourier harmonics. A fixed resampling and smoothing procedure makes the declared score reproducible, while separate diagnostic plots expose sensitivity to scale.

Weighted geometric, arithmetic and weakest-component policies show how a strong component can—or cannot—compensate for a weak one. Weights and thresholds are explicit design choices, not a perceptual ground truth or a calibrated metrology standard.

The drawing process remains part of the evidence

A near-complete stroke can be closed with a visible straight segment or a bounded tangent-matched bridge. Large gaps and ambiguous returns are rejected rather than silently completed. The exported report separates the original stroke, the analyzed points and any segment added to close the loop.

Uniformly shrinking a resolved contour preserves its dimensionless shape score. A separate size/coverage eligibility rule addresses tiny drawing submissions without changing mathematical roundness. This separates the quality of the shape from the evidence supplied by its capture.

Recorded examples · 1Interface and technical resultThe recorded view keeps the result beside the controls and intermediate explanation.
Image Recorded contour with fitted circle, residual extrema and the five-component geometric score.
More recorded views · 2
Image The same dented contour at radii 100 and 8. The illustrative absolute-error score rises when the shape shrinks, while the normalized geometric score stays at 31.2. This baseline is a teaching model, not a measured score from another game.
Mathematical schematic: a threefold radial defect appears both in a contour and its radius signal. This is an illustration, not an application screenshot or measured score.
Diagram Mathematical schematic: a threefold radial defect appears both in a contour and its radius signal. This is an illustration, not an application screenshot or measured score.
Explore this fieldCurve Atlas Drawing with harmonics
Page reviewed September 6, 2026. Demonstrations and technical notes reflect the showcased version.
Project overview