ba1212361f
Commit the previously-untracked standard directories and catalog them in the
root README alongside proof:
- aac/ — communication cargo class: portable boards + a ten-level
offline-first cascade (Apache-2.0 code / CC-BY-4.0 spec).
- map/ — geospatial cargo class: range-requestable signed tilesets +
an F0–F4 fidelity cascade (Apache-2.0 code / CC-BY-4.0 spec).
- sandbox/— isolated, metered, attested execution across the heterogeneous
compute fabric (Apache-2.0 code / CC-BY-4.0 spec).
- jouleclaw-otel-authz, jouleclaw-trust — new jouleclaw reference crates.
Root README now lists aac, map, sandbox, and proof in the catalog, the tree,
and the contribution guide.
Co-Authored-By: Claude Opus 4.8 <[email protected]>
118 lines
3 KiB
Rust
118 lines
3 KiB
Rust
// S2 cell metrics — area and edge length at each level.
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//
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// Earth radius: 6,371,000 m.
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// Total surface area: 4 * PI * R^2 = ~5.1e14 m^2.
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// At level 0, there are 6 face cells. Each covers ~8.5e13 m^2.
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// At each subsequent level, the area is divided by 4.
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use std::f64::consts::PI;
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/// Mean Earth radius in meters (IUGG definition).
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pub const EARTH_RADIUS_M: f64 = 6_371_000.0;
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/// Earth surface area in m^2.
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pub const EARTH_AREA_M2: f64 = 4.0 * PI * EARTH_RADIUS_M * EARTH_RADIUS_M;
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/// Average area of an S2 cell at the given level, in m^2.
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/// There are 6 * 4^level cells at level L.
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#[inline]
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pub fn avg_area_m2(level: u8) -> f64 {
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EARTH_AREA_M2 / (6.0 * 4.0_f64.powi(level as i32))
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}
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/// Average edge length of an S2 cell at the given level, in meters.
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/// Approximation: edge ~ sqrt(area).
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#[inline]
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pub fn avg_edge_m(level: u8) -> f64 {
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avg_area_m2(level).sqrt()
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}
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/// Maximum edge length of an S2 cell at the given level, in meters.
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/// The maximum edge is about 1.41x the average (diagonal factor for quad cells).
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#[inline]
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pub fn max_edge_m(level: u8) -> f64 {
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avg_edge_m(level) * 1.414
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}
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/// Minimum edge length of an S2 cell at the given level, in meters.
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/// The minimum is about 0.71x the average.
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#[inline]
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pub fn min_edge_m(level: u8) -> f64 {
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avg_edge_m(level) * 0.707
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}
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/// Average angular edge length in radians at the given level.
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#[inline]
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pub fn avg_edge_radians(level: u8) -> f64 {
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avg_edge_m(level) / EARTH_RADIUS_M
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}
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/// Number of cells at a given level.
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#[inline]
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pub fn num_cells(level: u8) -> u64 {
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6u64 * (1u64 << (2 * level as u32))
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn level_0_area() {
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let area = avg_area_m2(0);
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// ~85,011 km^2 per face
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let area_km2 = area / 1e6;
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assert!(
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(area_km2 - 85_011_012.0).abs() / 85_011_012.0 < 0.01,
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"level 0 area: {area_km2} km^2"
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);
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}
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#[test]
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fn area_halves_each_level() {
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for level in 0..29u8 {
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let a = avg_area_m2(level);
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let b = avg_area_m2(level + 1);
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let ratio = a / b;
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assert!(
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(ratio - 4.0).abs() < 1e-10,
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"area ratio at level {level}: {ratio}"
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);
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}
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}
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#[test]
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fn level_30_area() {
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let area = avg_area_m2(30);
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// At level 30, ~0.48 cm^2 per cell
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let area_cm2 = area * 1e4;
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assert!(area_cm2 > 0.0 && area_cm2 < 10.0, "level 30 area: {area_cm2} cm^2");
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}
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#[test]
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fn num_cells_level_0() {
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assert_eq!(num_cells(0), 6);
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}
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#[test]
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fn num_cells_level_1() {
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assert_eq!(num_cells(1), 24);
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}
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#[test]
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fn edge_length_reasonable() {
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// Level 12 should have edges around 2-3 km.
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let edge_km = avg_edge_m(12) / 1000.0;
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assert!(
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edge_km > 0.5 && edge_km < 10.0,
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"level 12 edge: {edge_km} km"
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);
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}
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#[test]
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fn max_edge_greater_than_avg() {
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for level in 0..30u8 {
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assert!(max_edge_m(level) > avg_edge_m(level));
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}
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}
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}
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