| Setting | Value |
|---|---|
| Training points | |
| Noise σ | |
| Random seed |
The random seed is included in the HTML version so the training example is reproducible.
| FEATURE | LEARNED WEIGHT |
|---|
Learned weights need not equal generating coefficients because the representation omits x⁴ and y⁴. High confidence in the estimated parameters does not necessarily imply an accurate representation of the environment.
| ID | Split | x | y | True z | Noise | Observed z | Prediction error | Trace of covariance P | w(1) | w(x) | w(y) | w(x²) | w(x·y) | w(y²) | w(x³) | w(x²·y) | w(x·y²) |
|---|
| LINE-OF-SIGHT PROMPT | VALUE |
|---|---|
| X GRID POINTS | |
| Y GRID POINTS | |
| TOTAL GRID POINTS | 20 × 20 (400 points) |
| DOMAIN RESOLUTION |
Unchecked = weights generated by the Training section. Checked = frozen example/book weights.
| Weight source |
| FEATURE | ACTIVE WEIGHT | GENERATED | BOOK WEIGHTS |
|---|
| Observer locations evaluated | — |
| Maximum visible grid points | — |
| Percentage visible | — |
| Best observer X | — |
| Best observer Y | — |
| Best observer Z | — |
| Observer | Grid i | Grid j | X | Y | Z | Visible Points | Visibility % | Best So Far |
|---|
| Chosen Mode | — |
| Weight Source | — |
| Grid | 20 × 20 |
| Observer | — |
| Chosen-Mode Visible Points | — |
| Chosen-Mode Visibility | — |
| HIGH-RES Visible Points | — |
| HIGH-RES Visibility | — |
Visualization is a display utility only. It does not participate in training, candidate evaluation, observer selection, or the generation loop.
Clicking changes only the visualization observer; it does not change the best observer selected by the generation loop.
For convenience, RE-GEN NOISE is also available here when LOW RESOLUTION uses GENERATED WEIGHTS. It retrains TIM with a fresh noise realization and regenerates the visibility result.
The Training page is unchanged from TIM. Recursive Least Squares estimates the same nine-weight learned domain characterization from noisy observations of the Himmelblau surface.
The x⁴ and y⁴ terms present in the true Himmelblau surface are deliberately omitted. The learned surface is therefore a compressed approximation rather than an exact representation of the environment.
The Inference page uses the same domain characterization and the same generic generation-loop structure as TIM, but with a different prompt: find the grid location that provides maximum line-of-sight coverage.
Use a user-specified X × Y uniformly spaced grid over −5 ≤ x ≤ 5 and −5 ≤ y ≤ 5. Candidate observer locations and observed locations are restricted to those grid points. For each observer-target pair, the active domain characterization is evaluated along the straight line joining the two locations to determine whether terrain blocks the line of sight. If several observer locations have the same maximum visibility, choose the one with the lowest terrain elevation.
For each observer-target pair, parameterize the straight line between them and compare the terrain height supplied by the selected domain characterization with the height of the straight line of sight. LOW RESOLUTION uses the nine-parameter polynomial; HIGH RESOLUTION uses the exact Himmelblau function. The grid determines observer and target locations, not the terrain between them.
The LLM Prompt Generator expresses the same line-of-sight inference problem as a complete natural-language specification that can be submitted to a general-purpose LLM with numerical code execution.
The generator inherits the X × Y grid specification, Domain Resolution, Weight Source, and Domain Characterization.
Select COPY PROMPT and submit the copied text to an LLM. The resulting observer table and selected maximum-visibility location can be compared directly with TIM's deterministic result.