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Geometry & geospatial

Transforms and robust predicates, computational geometry, CAD surfaces, spatial indexes, map projections and geocoding.

Transforms & predicates

The small exact pieces every geometry pipeline needs.

homogeneous transforms

Planned.

Quaternion rotations

low

Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.

compose 16 mul + 12 add; to matrix about 30 flops; nlerp O(1) with one sqrt; slerp O(1) with acos and sin

exact geometric predicates

Planned.

ray primitive intersection

Planned.

kabsch rmsd alignment

Planned.

Computational geometry

Hulls, triangulations, polygon operations and simplification.

convex hull quickhull

Planned.

delaunay triangulation

Planned.

voronoi diagrams

Planned.

polygon clipping

Planned.

polygon tessellation

Planned.

point in polygon

Planned.

line simplification

Planned.

label placement collision

Planned.

CAD & surfaces

Exact solid and surface modelling.

b rep topology

Planned.

nurbs

Planned.

solid boolean operations

Planned.

surface surface intersection

Planned.

geometric constraint solving

Planned.

Spatial indexes

Finding nearby things fast.

k-d tree

low

A binary tree that splits k-dimensional points by one coordinate per level, giving fast nearest-neighbour and box queries on static low-dimensional data.

build O(N log N) or O(N) per level via quickselect; nearest O(log N) expected in low dimension, worst case O(N); box query O(N^(1-1/k) + T)

R-tree

low

A balanced tree of nested bounding boxes that indexes rectangles and points, answering window and nearest-neighbour queries by pruning whole subtrees.

search O(log_M N) when boxes overlap little, worst case O(N); insert O(log_M N); STR bulk load O(N log N)

quadtree octree

Planned.

space filling curves

Planned.

Geospatial cell index (geohash, S2, H3)

low

Map a lat/lon to a 64-bit cell id on a hierarchical grid, so "near" becomes an integer range scan in any ordinary sorted index.

point to id O(levels), a few ns; box query = k range scans, k grows with the box perimeter in cells

healpix sky pixelization

Planned.

Maps & projections

Distances on the Earth, projections and map tiles.

Geodesic distance (haversine, Vincenty, Karney)

low

Shortest-path distance between two lat/lon points on the Earth: haversine on a sphere (about 0.5% error), Vincenty or Karney on the WGS84 ellipsoid (sub-millimetre).

O(1) per pair; haversine order of 30 ns, Vincenty order of 240 ns (iterative), Karney similar and always converges

map projections

Planned.

map tile pyramid

Planned.

vector tile encoding

Planned.

kriging spatial interpolation

Planned.

orthorectification

Planned.

Geocoding & map matching

Turning addresses and GPS traces into places on the map.

address geocoding

Planned.

address parsing

Planned.

address interpolation

Planned.

map matching hmm

Planned.