Analysis of Speed in Traditional Animation
Bibliographic record
Abstract
Frame-to-frame movement (speed) in animation is commonly de-scribed as easing in, easing out, and moving evenly between key-frames. We examined the 2D movement of the salient parts of characters in freehand animation and identified a pattern in speed resembling these descriptions. To identify this pattern we first de-veloped a manual annotation procedure to identify trajectories, their speed related key-frames and their intermediate subsequences in a variety of animations. We found that the speed of a subsequence is related to its average acceleration. Our analysis indicates that a cubic polynomial best approximates the subsequence speed over time and each of the polynomial coefficients are related to average acceleration by four additional polynomials of degree 2, 3, 2 and 3. We develop a polynomial model for speed with least squares polynomial regression and validate our results and annotations with several statistical tests that use 10-fold cross-validation. Our experi-mental animation interface demonstrates that this relationship has the potential to ease the burden of controlling speed by replacing the control points that otherwise must be specified with a single parameter for average acceleration.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".