Efficient geometrically exact continuous collision detection
Bibliographic record
Abstract
Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| 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".