Orb

Documentation

Geometry, vectors, grids and graphs

Every operator a .lolo program can call, from the canonical registry the compiler bakes.

On this page

Namespaces on this page: geo/, graph/, grid/, vec/.

geo/

`geo/aabb-overlap`

Axis-aligned bounding box overlap test

lolo

(geo/aabb-overlap a b)

Parameters

Name	Type	Description
`a`	`object`	First bounding box
`b`	`object`	Second bounding box

Returns: boolean

Example

lolo

(geo/aabb-overlap {"x":0,"y":0,"w":10,"h":10} {"x":5,"y":5,"w":10,"h":10}) // => true

`geo/circle-overlap`

Circle overlap test: distance(centers) <= a.r+b.r

lolo

(geo/circle-overlap a b)

Parameters

Name	Type	Description
`a`	`object`	First circle
`b`	`object`	Second circle

Returns: boolean

Example

lolo

(geo/circle-overlap {"x":0,"y":0,"r":3} {"x":4,"y":0,"r":2}) // => true

`geo/point-in-circle`

Point containment in circle (inclusive)

lolo

(geo/point-in-circle point circle)

Parameters

Name	Type	Description
`point`	`object`	Point coordinates
`circle`	`object`	Circle (center and radius)

Returns: boolean

Example

lolo

(geo/point-in-circle {"x":1,"y":1} {"x":0,"y":0,"r":2}) // => true

`geo/point-in-rect`

Point containment in rect (inclusive bounds)

lolo

(geo/point-in-rect point rect)

Parameters

Name	Type	Description
`point`	`object`	Point coordinates
`rect`	`object`	Rectangle bounds

Returns: boolean

Example

lolo

(geo/point-in-rect {"x":5,"y":5} {"x":0,"y":0,"w":10,"h":10}) // => true

`geo/rect-circle-overlap`

Rect-circle overlap via closest point on rect to circle center

lolo

(geo/rect-circle-overlap rect circle)

Parameters

Name	Type	Description
`rect`	`object`	Rectangle bounds
`circle`	`object`	Circle (center and radius)

Returns: boolean

Example

lolo

(geo/rect-circle-overlap {"x":0,"y":0,"w":10,"h":10} {"x":12,"y":5,"r":3}) // => true

`geo/reflect`

Reflect vector v across normal n (assumed normalized)

lolo

(geo/reflect v n)

Parameters

Name	Type	Description
`v`	`object`	Vector to reflect
`n`	`object`	Surface normal

Returns: vector

Example

lolo

(geo/reflect {"x":1,"y":-1} {"x":0,"y":1})

`geo/segment-intersect`

Intersection point of two segments, or null when parallel/none

lolo

(geo/segment-intersect seg1 seg2)

Parameters

Name	Type	Description
`seg1`	`array`	First segment endpoints
`seg2`	`array`	Second segment endpoints

Returns: point | null

Example

lolo

(geo/segment-intersect {"x1":0,"y1":0,"x2":4,"y2":4} {"x1":0,"y1":4,"x2":4,"y2":0})

graph/

`graph/add-self-loops`

Add self-loop edges to graph

lolo

(graph/add-self-loops graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to augment

Returns: graph

Example

lolo

(graph/add-self-loops ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]])

`graph/batch`

Batch multiple graphs into one

lolo

(graph/batch graphs)

Parameters

Name	Type	Description
`graphs`	`array`	Graphs to batch

Returns: graph

Example

lolo

(graph/batch [["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]]])

`graph/degree`

Get node degree tensor

lolo

(graph/degree graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to query

Returns: tensor

Example

lolo

(graph/degree ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]])

`graph/edge-features`

Get edge feature matrix

lolo

(graph/edge-features graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to query

Returns: tensor

Example

lolo

(graph/edge-features ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]])

`graph/edge-index`

Get edge index tensor

lolo

(graph/edge-index graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to query

Returns: tensor

Example

lolo

(graph/edge-index ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]])

`graph/from-adjacency`

Build graph from adjacency matrix and features

lolo

(graph/from-adjacency adjacency features)

Parameters

Name	Type	Description
`adjacency`	`object`	Adjacency matrix
`features`	`object`	Node features

Returns: graph

Example

lolo

(graph/from-adjacency [[0,1],[1,0]] [[1.0],[2.0]])

`graph/from-edge-list`

Build graph from edge list and features

lolo

(graph/from-edge-list edges features)

Parameters

Name	Type	Description
`edges`	`array`	Edge list
`features`	`object`	Node features

Returns: graph

Example

lolo

(graph/from-edge-list [[0,1]] [[1.0],[2.0]])

`graph/from-entities`

Build PyG graph from entity collections

lolo

(graph/from-entities entities)

Parameters

Name	Type	Description
`entities`	`array`	Entity collection

Returns: graph

Example

lolo

(graph/from-entities [{"age":30,"score":0.5},{"age":25,"score":0.7}])

`graph/k-hop`

K-hop neighborhood subgraph

lolo

(graph/k-hop graph nodeId k)

Parameters

Name	Type	Description
`graph`	`object`	Graph to traverse
`nodeId`	`string`	Starting node ID
`k`	`number`	Hop distance

Returns: graph

Example

lolo

(graph/k-hop ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]] 0 2)

`graph/node-features`

Get node feature matrix

lolo

(graph/node-features graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to query

Returns: tensor

Example

lolo

(graph/node-features ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]])

`graph/num-edges`

Get edge count

lolo

(graph/num-edges graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to query

Returns: number

Example

lolo

(graph/num-edges ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]]) // => 2

`graph/num-nodes`

Get node count

lolo

(graph/num-nodes graph)

Parameters

Name	Type	Description
`graph`	`object`	Graph to query

Returns: number

Example

lolo

(graph/num-nodes ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]]) // => 2

`graph/subgraph`

Extract subgraph by node mask

lolo

(graph/subgraph graph mask)

Parameters

Name	Type	Description
`graph`	`object`	Graph to subset
`mask`	`array`	Node selection mask

Returns: graph

Example

lolo

(graph/subgraph ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]] [true,false])

`graph/to-undirected`

Convert directed graph to undirected

lolo

(graph/to-undirected graph)

Parameters

Name	Type	Description
`graph`	`object`	Directed graph

Returns: graph

Example

lolo

(graph/to-undirected ["graph/from-adjacency",[[0,1],[1,0]],[[1.0],[2.0]]])

grid/

`grid/cells-in-radius`

All cells within Euclidean radius r (row-major order)

lolo

(grid/cells-in-radius center radius)

Parameters

Name	Type	Description
`center`	`object`	Center cell
`radius`	`number`	Euclidean radius

Returns: array

Example

lolo

(grid/cells-in-radius {"x":0,"y":0} 1)

`grid/distance`

Chebyshev distance max(|dx|,|dy|)

lolo

(grid/distance a b)

Parameters

Name	Type	Description
`a`	`object`	First cell
`b`	`object`	Second cell

Returns: number

Example

lolo

(grid/distance {"x":0,"y":0} {"x":3,"y":2}) // => 3

`grid/from-world`

World point to grid cell (floor)

lolo

(grid/from-world point cellSize)

Parameters

Name	Type	Description
`point`	`object`	World coordinates
`cellSize`	`number`	Cell size in world units

Returns: cell

Example

lolo

(grid/from-world {"x":80,"y":112} 32)

`grid/in-bounds`

Whether cell lies within a w×h grid

lolo

(grid/in-bounds cell width height)

Parameters

Name	Type	Description
`cell`	`object`	Cell to check
`width`	`number`	Grid width
`height`	`number`	Grid height

Returns: boolean

Example

lolo

(grid/in-bounds {"x":2,"y":3} 5 5) // => true

`grid/iso-to-screen`

Isometric cell to screen point

lolo

(grid/iso-to-screen cell tileW tileH)

Parameters

Name	Type	Description
`cell`	`object`	Isometric cell
`tileW`	`number`	Tile width
`tileH`	`number`	Tile height

Returns: point

Example

lolo

(grid/iso-to-screen {"x":1,"y":0} 64 32)

`grid/line`

Bresenham line cells from a to b, inclusive, in step order

lolo

(grid/line a b)

Parameters

Name	Type	Description
`a`	`object`	Starting cell
`b`	`object`	Ending cell

Returns: array

Example

lolo

(grid/line {"x":0,"y":0} {"x":2,"y":2})

`grid/manhattan-distance`

Manhattan distance |dx|+|dy|

lolo

(grid/manhattan-distance p1 p2)

Parameters

Name	Type	Description
`p1`	`object`	First point
`p2`	`object`	Second point

Returns: number

Example

lolo

(grid/manhattan-distance {"x":0,"y":0} {"x":3,"y":2}) // => 5

`grid/neighbors`

Adjacent cells in order N,E,S,W (+NE,SE,SW,NW if diagonal)

lolo

(grid/neighbors cell)

Parameters

Name	Type	Description
`cell`	`object`	Grid cell coordinates

Returns: array

Example

lolo

(grid/neighbors {"x":1,"y":1})

`grid/screen-to-iso`

Screen point to isometric cell coordinates

lolo

(grid/screen-to-iso x y z)

Parameters

Name	Type	Description
`x`	`number`	Screen x coordinate
`y`	`number`	Screen y coordinate
`z`	`number`	Scale or depth

Returns: point

Example

lolo

(grid/screen-to-iso 640 360 1)

`grid/to-world`

Cell to world-space center point

lolo

(grid/to-world x y)

Parameters

Name	Type	Description
`x`	`number`	Cell x coordinate
`y`	`number`	Cell y coordinate

Returns: point

Example

lolo

(grid/to-world 10 15) // => 150

vec/

`vec/add`

Componentwise vector addition a+b

lolo

(vec/add a b)

Parameters

Name	Type	Description
`a`	`vector`	First vector
`b`	`vector`	Second vector

Returns: vector

Example

lolo

(vec/add [1 2 3] [4 5 6]) // => [5 7 9]

`vec/angle`

Heading atan2(y,x) (1 arg) or angle between two vectors (2 args), radians

lolo

(vec/angle v other)

Parameters

Name	Type	Description
`v`	`vector`	Vector or heading
`other`	`vector`	Other vector (variadic)

Returns: number

Example

lolo

(vec/angle [1 1]) // => 0.785

`vec/clamp-length`

Clamp magnitude to max (preserves direction)

lolo

(vec/clamp-length v max_length)

Parameters

Name	Type	Description
`v`	`vector`	Vector to clamp
`max_length`	`number`	Maximum magnitude

Returns: vector

Example

lolo

(vec/clamp-length [10 10] 12) // => [8.485 8.485]

`vec/cross`

3D cross product → vector; 2D → scalar ax·by-ay·bx

lolo

(vec/cross a b)

Parameters

Name	Type	Description
`a`	`vector`	First vector
`b`	`vector`	Second vector

Returns: vector | number

Example

lolo

(vec/cross [1 0 0] [0 1 0]) // => [0 0 1]

`vec/distance`

Euclidean distance length(sub(a,b))

lolo

(vec/distance a b)

Parameters

Name	Type	Description
`a`	`vector`	First point
`b`	`vector`	Second point

Returns: number

Example

lolo

(vec/distance [0 0] [3 4]) // => 5

`vec/distance-sq`

Squared distance length-sq(sub(a,b))

lolo

(vec/distance-sq a b)

Parameters

Name	Type	Description
`a`	`vector`	First point
`b`	`vector`	Second point

Returns: number

Example

lolo

(vec/distance-sq [0 0] [3 4]) // => 25

`vec/dot`

Dot product ax·bx+ay·by(+az·bz)

lolo

(vec/dot a b)

Parameters

Name	Type	Description
`a`	`vector`	First vector
`b`	`vector`	Second vector

Returns: number

Example

lolo

(vec/dot [1 2 3] [4 5 6]) // => 32

`vec/length`

Vector magnitude sqrt(dot(a,a))

lolo

(vec/length v)

Parameters

Name	Type	Description
`v`	`vector`	Vector

Returns: number

Example

lolo

(vec/length [3 4]) // => 5

`vec/length-sq`

Squared magnitude dot(a,a)

lolo

(vec/length-sq v)

Parameters

Name	Type	Description
`v`	`vector`	Vector

Returns: number

Example

lolo

(vec/length-sq [3 4]) // => 25

`vec/lerp`

Componentwise linear interpolation a+(b-a)*t

lolo

(vec/lerp a b t)

Parameters

Name	Type	Description
`a`	`vector`	Start vector
`b`	`vector`	End vector
`t`	`number`	Interpolation factor

Returns: vector

Example

lolo

(vec/lerp [0 0] [10 10] 0.5) // => [5 5]

`vec/normalize`

Unit vector a/len; zero-length → zero vector (same dim)

lolo

(vec/normalize v)

Parameters

Name	Type	Description
`v`	`vector`	Vector to normalize

Returns: vector

Example

lolo

(vec/normalize [3 4]) // => [0.6 0.8]

`vec/rotate`

2D rotate by rad (z preserved): x'=x·cos-y·sin, y'=x·sin+y·cos

lolo

(vec/rotate v rad)

Parameters

Name	Type	Description
`v`	`vector`	Vector to rotate
`rad`	`number`	Rotation in radians

Returns: vector

Example

lolo

(vec/rotate [1 0] 1.57) // => [0 1]

`vec/scale`

Componentwise scalar multiply a*k

lolo

(vec/scale v k)

Parameters

Name	Type	Description
`v`	`vector`	Vector to scale
`k`	`number`	Scale factor

Returns: vector

Example

lolo

(vec/scale [1 2 3] 2) // => [2 4 6]

`vec/sub`

Componentwise vector subtraction a-b

lolo

(vec/sub a b)

Parameters

Name	Type	Description
`a`	`vector`	First vector
`b`	`vector`	Second vector

Returns: vector

Example

lolo

(vec/sub [5 7 9] [1 2 3]) // => [4 5 6]

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