Bibliographic record
Abstract
In the late 1950s Terrell and Penrose produced a series of papers dealing with the appearance of the rapidly moving bodies while in rectilinear motion as photographed by a simple, pinhole camera. A few more articles on the same subject followed, for example, Penrose showed that a sphere is always seen having an exactly circular outline, at any velocity, at any distance and for any line of sight. In the present paper, we will deal with a more complex type of motion, the combination of translation and rotation that can be seen when observing the wheels of a vehicle passing by. Since Terrell and Penrose wrote their papers, great advances in the camera simulation via computer representation have been made. The field that deals with the simulation of realistic cameras via computers is called ray tracing. In the current paper, we will combine two different disciplines, relativistic physics and three-dimensional graphics to derive new results. Our paper is divided in two main parts, in the first half, we will derive the relativistic equations for rolling motion without slip and we will make some connections with the physical requirements of a relativistic ray-tracing algorithm. In the second half, we will review the foundations of classical ray-tracing algorithms and we will introduce the additional features for operation at relativistic speeds. We will demonstrate an interesting self-canceling effect of the relativistic Doppler shift on the colors wavelengths of the moving object.PACS No.: 03.30.+p
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".