Contour School / method note

From heights
to lines.

One surface, three views

Grid coordinates use x east and y south, with elevation upward; every coordinate is in metres. Each valid rectangular cell is divided along its northwest–southeast diagonal into two linear triangles. The contour map, rendered surface and sampled profile use this same triangulation. Profile markers evaluate the exact selected position, rather than rounding to a chart vertex. Entire cells touching no-data nodes are omitted. Contour crossings use linear edge interpolation, and exact-level vertices use a consistent half-open rule. Constant-level plateaus have no unique contour boundary here; saddle critical levels may touch.

Original teaching shapes

Five deterministic surfaces cover x and y from −400 to 400 m. Their arbitrary teaching datum is not a place in Bryce. They use 65 × 65 nodes, 12.5 m spacing. Heights are computed from these equations:

Shape	Elevation z (m)
A rounded hill	1000 + 180 exp(−(x² + y²) / 60000)
An even slope	1100 + 0.2x + 0.1y
A valley	1080 − 0.18y + 0.0007x²
A ridge	1230 − 0.18y − 0.0007x²
A saddle	1160 + 0.0007x² − 0.0007y²

A hill maximum and saddle center are exactly 1180 m and 1160 m. The plane has slopes dz/dx = 0.2 and dz/dy = 0.1, giving a steepest grade of √0.05 ≈ 22.36% and a downhill aspect of about 296.565° from grid north.

The Bryce derivative

The crop uses exact sampled nodes from the existing assets/terrain/mesh-1537.webp. In its central square this is a 4 m grid derived from a recorded USGS 3DEP 1 m bare-earth DEM. Every second node is retained here: 97 × 97 nodes at 8 m spacing across 768 × 768 m. No new interpolation is applied during extraction. The source encoding is 1500 + (256R + G) × 0.1 metres; decimetre encoding is not decimetre accuracy.

Horizontal CRS: EPSG:26912, NAD83 / UTM zone 12N. Bounds west/south/east/north: 396748, 4164206, 397516, 4164974 m. Vertical datum: NAVD88, retained from the copied metadata. Grid row zero is north. The crop’s minimum and maximum are 2286.5 m and 2468.1 m. The original source-tile identity and acquisition date are not present in this copied regional record. No survey-grade or current-condition claim is made. Compared at all retained 4 m source-grid nodes, this 8 m triangular surface differs by 2.33 m RMS, 5.05 m at the 95th percentile of absolute differences, and up to 37.25 m at the sharpest sampled features. These are coarsening differences, not measured errors against real ground.

Grid and source hashes · Catalogue

Display and calculation choices

Contour levels are multiples of the selected 10, 20 or 40 m interval; every fifth line is heavier. Printed maps use 20 m. Contour labels are omitted where they would obscure another elevation or the section; unlabeled lines still follow the stated interval. A–B is a straight section sampled at 161 positions, not a route. Slope and aspect use central differences at one quarter of a grid spacing; edges and missing samples return no value. Symmetric critical points have no aspect. The aspect is referenced to grid north, not magnetic or geodetic north.

The oblique view is a software-projected orthographic 3D surface with illustrative lighting. Surface triangles are ordered by viewing depth. The teal section guide is deliberately always visible, even behind terrain. Height exaggeration multiplies the vertical display scale only; calculated elevations and slopes remain in the original units. Profile charts use the same declared vertical exaggeration; at 1×, one metre is drawn at equal scale on both axes. Responsive tick spacing changes labels, not geometry. The static library includes west–east and north–south central sections at 1×, each with a five-sample table. There is no continuous animation.

Rights and review

USGS National Map elevation data are public domain. Map services and data available from U.S. Geological Survey, National Geospatial Program. All vector artwork and analytic geometry in this kit are original BCC educational work. Reference-page photographs are not copied. This locally reviewed candidate has not received field, independent geological, physical-device or survey acceptance.