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Per-stroke quality metrics (circle-fit residuals, closure gaps, template distances) were worked out in earlier prototyping, so this section covers only what sits above them: whole-diagram structure, calibration, and where models fail.
Structure-level accuracy lags symbol-level accuracy everywhere. Arrow R-CNN, which adds an arrow head-and-tail keypoint head to Faster R-CNN, raised whole-diagram recognition on a scanned flowchart dataset from 37.7% to 78.6% and recognised more than 68% of diagrams across four datasets combined, while symbol recall on FC_A reached 98.3%, in under 100 ms per diagram (Springer). Its weak point is arrows: overlapping arrow boxes confuse head attribution. A 2025 pipeline that feeds a fine-tuned detector's graph to GPT-4o reports arrow-related detection mAP of 0.235 against 0.653 for other classes (arXiv 2505.07864). In handwritten maths, a structural recogniser reaches 80.52, 83.63 and 74.14% expression rate on CROHME 2016, 2019 and 2023 with generated annotations, and 56.29, 54.63 and 52.82% without them (arXiv 2508.19773). DECIMER, trained only on up to 152 million synthetic renders, reads 73.25% of 5,088 real hand-drawn molecules exactly, where earlier tools score 0.57 to 26.98%, and quadrupling the synthetic set from 38 million added under 3 points (PMC11227129). A fixed grammar plus synthetic renders with jitter is the transferable recipe, and in a circle language the quality model doubles as the augmentation model.
LADDER is the closest precedent for a declarative circle grammar. Hammond and Davis describe shapes hierarchically from primitives (line, arc, ellipse, spiral and others) under a long predefined constraint list, about 44 named constraints across two lists with no stated total, plus draw order, rotation invariance and a beautifier that moves points as little as possible to satisfy constraints (LADDER). Its soft constraints were never implemented and it reports no accuracy figures. Turning each constraint into a normalised residual gives a quality score straight out of parsing, and the beautifier's total displacement is a second, calibratable precision signal.
Vision-language models fail exactly where circles need them. On FlowLearn's simulated flowcharts, 2024-era models counted nodes correctly 0.52 (Claude-3-Opus) and 0.58 (GPT-4V) of the time on a 100-sample subset, and in Mermaid generation Claude-3-Opus reached node F1 of about 0.94 but link F1 of only 0.30 (FlowLearn). On SketchJudge, which asks 16 multimodal models to diagnose errors in 1,015 hand-drawn student diagrams, the best (GPT-5) scored 78.42% accuracy against 83.33% for three non-expert human raters on a 160-answer subset, a gap of about five points, with error-type F1 of 61.13 against 66.42 (SketchJudge). The Visual Aesthetic Benchmark found the best of 20 frontier models identified both the best and worst image in only 26.5% of tasks against 68.9% for experts, and that scalar scores agree poorly with direct comparisons; its domain is fine art, photography and illustration, not drawings (arXiv 2605.12684). No study found for this report calibrates a VLM on drawing neatness. Counting, link topology and judging neatness are three things a magic circle needs and three things VLMs do worst, and their latency rules them out of a VR loop anyway.
Calibrate quality with pairwise human judgments, and grade rather than gate. The aesthetic benchmark's finding that ranking beats scoring, and the CHAED precedent of regressing hand-designed geometric features on 33 raters' handwriting scores (IJCAI 2015), both point to fitting existing geometric residuals to "which of these two is neater?" judgments. For converting a continuous error into tiers, osu! shrinks nested judgement windows linearly with difficulty (300 = 80 − 6·OD ms) and weights tiers non-uniformly at 100%, 33.33% and 16.67% (osu! wiki). Ido's kanji auto-scorer keeps stroke order, stroke count and shape deductions separate and stores penalty tables as data (JSiSE 2019). For VR, the evidence is thin: a Würzburg project call notes that arm ergonomics curve intended-straight mid-air strokes (Würzburg HCI), and no controller noise or latency-tolerance numbers were found, so per-device and per-player baselines must be measured. Accessibility is a design input, not an afterthought: a 2022 adaptation of the VR game Spellcasters let clinicians customise gestures per stroke-rehabilitation patient (eScholarship).
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