Research on structural surface feature refinement method based on fractal geometry in industrial design
Bibliographic record
Abstract
Fractal geometry is an emerging discipline that has developed rapidly in recent decades, and its study of irregular geometric shapes can be used to describe objects in nature that cannot be described by traditional geometry, and it has a broad space for development and application prospects.In this paper, the theory of fractal geometry is applied to industrial design to realize the refinement and analysis of surface features.The study includes an in-depth analysis of the theory of fractal geometry, the Koch curve as an example to illustrate the principle of fractal geometry.The study also investigates different dimension calculation methods, such as Hausdorff dimension, box dimension, correlation dimension, information dimension, generalized dimension, and self-similarity dimension of fractal geometry, and proposes a dimension calculation method for the refinement of structural surface features for industrial design.After the fractal geometry surface feature refinement simulation analysis, the porosity of the fractal map based on this paper's method ranges from 16% to 38%, and the comparison with the Serpinski method proves that the presently selected fractal model is more effective in the refinement of structural surface features for industrial design.As shown by the surface feature simulation results, there is indeed a certain degree of similarity between the roughness topography of the real structural surface of the two surface processing methods in industrial design and the roughness topography simulated by the fractal function.The above study proves that the method of refining the structural surface features of industrial design based on fractal geometry in this paper is scientific and feasible.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".