| //! QLG Sphere: Canonical six-point integer geometry | |
| //! | |
| //! S_can = {x ∈ Z³ : x₀² + x₁² + x₂² = 1} | |
| //! Solutions: {(±1,0,0), (0,±1,0), (0,0,±1)} | |
| use crate::Point; | |
| /// Verify membership in canonical sphere. | |
| pub fn is_on_sphere(p: &Point) -> bool { | |
| p.0 * p.0 + p.1 * p.1 + p.2 * p.2 == 1 | |
| } | |
| /// All six canonical points | |
| pub fn canonical_points() -> [Point; 6] { | |
| [ | |
| Point(1, 0, 0), | |
| Point(-1, 0, 0), | |
| Point(0, 1, 0), | |
| Point(0, -1, 0), | |
| Point(0, 0, 1), | |
| Point(0, 0, -1), | |
| ] | |
| } | |
| /// Encode point to 3-byte array (little-endian signed integers) | |
| pub fn encode(p: &Point) -> [u8; 3] { | |
| [ | |
| (p.0 as i8) as u8, | |
| (p.1 as i8) as u8, | |
| (p.2 as i8) as u8, | |
| ] | |
| } | |
| /// Decode point from 3-byte array | |
| pub fn decode(bytes: &[u8; 3]) -> Point { | |
| Point( | |
| bytes[0] as i8 as i32, | |
| bytes[1] as i8 as i32, | |
| bytes[2] as i8 as i32, | |
| ) | |
| } | |
| mod tests { | |
| use super::*; | |
| fn canonical_on_sphere() { | |
| for p in canonical_points() { | |
| assert!(is_on_sphere(&p)); | |
| } | |
| } | |
| fn six_solutions() { | |
| assert_eq!(canonical_points().len(), 6); | |
| } | |
| fn round_trip() { | |
| for p in canonical_points() { | |
| let encoded = encode(&p); | |
| let decoded = decode(&encoded); | |
| assert_eq!(p, decoded); | |
| } | |
| } | |
| fn invalid_rejected() { | |
| assert!(!is_on_sphere(&Point(1, 1, 0))); | |
| assert!(!is_on_sphere(&Point(2, 0, 0))); | |
| assert!(!is_on_sphere(&Point(0, 0, 0))); | |
| } | |
| } | |