Import std.math.geometry

std.math.geometry

Rectangles, boxes, spheres, rays, planes, and frustums, and the tests between them.

The shapes for finding what's where: Rect in 2D, and AABB, Sphere, Ray, Plane, and Frustum in 3D, with Contains, Intersects, and Raycast. A shape holds the points on its edges. A Raycast gives how far along the ray it first meets the shape, in lengths of the ray's Direction, so a Direction of length 1 makes it a distance; 0 for a ray that starts inside, and Null for one that misses.

std/math/geometry.fb

Types

`Rect` struct

Public Struct Rect Implements Equatable, Printable

A rectangle in 2D, from its corner with the smallest X and Y, of a Width and Height that aren't negative.

Examples


Local a = Rect(0, 0, 10, 10)
Local b = Rect(5, 5, 10, 10)
Expect(a.Intersects(b))
Expect(a.Intersection(b) == Rect(5, 5, 5, 5))
Expect(a.Union(b) == Rect(0, 0, 15, 15))
Expect(a.Contains(Vec2(2, 3)) && !a.Contains(Vec2(12, 3)))

std/math/geometry.fb, line 30

Public Field X: Float field #

Its left edge, the smallest X it has.
Public Field Y: Float field #

Its top edge, the smallest Y it has.
Public Field Width: Float field #

How wide it is, which isn't negative.
Public Field Height: Float field #

How high it is, which isn't negative.
Public Static Method FromCorners(a: Vec2, b: Vec2): Rect static method #

The rectangle from one corner to the other, whichever way around they are.
Public Static Method FromCenter(center: Vec2, size: Vec2): Rect static method #

The rectangle of the size, with its center at the point.
Public Property Min: Vec2 property #

The corner with the smallest X and Y.
Public Property Max: Vec2 property #

The corner with the largest X and Y.
Public Property Center: Vec2 property #

The point in its middle.
Public Property Size: Vec2 property #

Its Width and Height, as a Vec2.
Public Property Area: Float property #

Its Width times its Height.
Public Method Contains(point: Vec2): Bool method #

Whether the point is in the rectangle or on its edge.
Public Method Contains(other: Rect): Bool method #

Whether the other rectangle is all in this one.
Public Method Intersects(other: Rect): Bool method #

Whether the two have a point in common, an edge's included.
Public Method Intersection(other: Rect): Rect? method #

The rectangle where the two overlap, or Null where they don't meet.
Public Method Union(other: Rect): Rect method #

The smallest rectangle that holds both.
Public Method Grow(amount: Float): Rect method #

The rectangle with each edge moved out by amount, or in by a negative one. Shrunk past nothing, a side is 0 long, at the center.
Public Method ToString(): String method #

Its parts, as "Rect(0, 0, 10, 5)".

`AABB` struct

Public Struct AABB Implements Equatable, Printable

An axis-aligned box in 3D, from its corner with the smallest x, y, and z to the one with the largest.

Examples


Local box = AABB(Vec3(-1, -1, -1), Vec3(1, 1, 1))
Local ray = Ray(Vec3(0, 0, 5), Vec3(0, 0, -1))
Expect(box.Raycast(ray) == 4.0)
Expect(ray.At(4) == Vec3(0, 0, 1))
Expect(box.Contains(Vec3(0.5, 0, 0)) && !box.Contains(Vec3(2, 0, 0)))

std/math/geometry.fb, line 133

Public Field Min: Vec3 field #

Its corner with the smallest x, y, and z.
Public Field Max: Vec3 field #

Its corner with the largest x, y, and z.
Public Static Method FromCenter(center: Vec3, size: Vec3): AABB static method #

The box of the size, with its center at the point.
@PanicsAtCaller Public Static Method FromPoints(points: Vec3[]): AABB static method #

The smallest box that holds every point. No points panics.
Public Property Center: Vec3 property #

The point in its middle.
Public Property Size: Vec3 property #

How wide, high, and deep it is.
Public Property Extents: Vec3 property #

Half the size: how far each face is from the center.
Public Method Contains(point: Vec3): Bool method #

Whether the point is in the box or on its surface.
Public Method Contains(other: AABB): Bool method #

Whether the other box is all in this one.
Public Method Intersects(other: AABB): Bool method #

Whether the two have a point in common, a face's included.
Public Method Intersects(sphere: Sphere): Bool method #

Whether the sphere and the box have a point in common.
Public Method ClosestPoint(point: Vec3): Vec3 method #

The point in the box nearest the one given: that point itself when it's inside.
Public Method Raycast(ray: Ray): Float? method #

How far along the ray it first meets the box, by its slabs, one axis at a time.
Public Method Union(other: AABB): AABB method #

The smallest box that holds both.
Public Method Union(point: Vec3): AABB method #

The smallest box that holds this one and the point.
Public Method Grow(amount: Float): AABB method #

The box with each face moved out by amount, or in by a negative one. Shrunk past nothing, an axis is 0 long, at the center.
Public Method Transform(m: Mat4): AABB method #

The smallest box that holds this one transformed by the matrix, as an object's box is moved into the world.
Public Method ToString(): String method #

Its parts, as "AABB((0, 0, 0), (1, 1, 1))".

`Sphere` struct

Public Struct Sphere Implements Equatable, Printable

A ball: the points no further from its Center than its Radius.

Examples


Local ball = Sphere(Vec3(0, 0, 0), 1)
Expect(ball.Contains(Vec3(0.5, 0, 0)))
Expect(ball.Raycast(Ray(Vec3(0, 0, 5), Vec3(0, 0, -1))) == 4.0)

std/math/geometry.fb, line 265

Public Field Center: Vec3 field #

The point in its middle.
Public Field Radius: Float field #

How far its surface is from its Center.
Public Method Contains(point: Vec3): Bool method #

Whether the point is in the sphere or on its surface, by squares in Doubles, which no Float's square overflows.
Public Method Intersects(other: Sphere): Bool method #

Whether the two have a point in common, by squares in Doubles.
Public Method Intersects(box: AABB): Bool method #

Whether the box and the sphere have a point in common.
Public Method Raycast(ray: Ray): Float? method #

How far along the ray it first meets the sphere, worked out in Doubles from where the ray comes nearest the center, as Ray Tracing Gems' chapter 7 has it, so a sphere far off or small, or a short Direction, loses nothing to rounding.
Public Method ToString(): String method #

Its parts, as "Sphere((0, 0, 0), 1)".

`Ray` struct

Public Struct Ray Implements Equatable, Printable

A half-line, from its Origin along its Direction.

Examples


Expect(Ray(Vec3(0, 0, 0), Vec3(1, 0, 0)).At(3) == Vec3(3, 0, 0))

std/math/geometry.fb, line 336

Public Field Origin: Vec3 field #

Where it starts.
Public Field Direction: Vec3 field #

Which way it goes, and how far each length of it along the ray is.
Public Method At(distance: Float): Vec3 method #

The point so far along the ray, in lengths of its Direction.
Public Method ToString(): String method #

Its parts, as "Ray((0, 0, 0), (0, 0, -1))".

`Plane` struct

Public Struct Plane Implements Equatable, Printable

A flat surface without end, of the points p where Dot(Normal, p) is Distance, with a Normal of length 1. The side the Normal points to is in front.

Examples


Local ground = Plane.FromPointNormal(Vec3(0, 0, 0), Vec3(0, 1, 0))
Expect(ground.SignedDistance(Vec3(3, 2, 1)) == 2.0)
Expect(ground.Raycast(Ray(Vec3(0, 5, 0), Vec3(0, -1, 0))) == 5.0)

std/math/geometry.fb, line 361

Public Field Normal: Vec3 field #

Which way it faces, of length 1.
Public Field Distance: Float field #

Its distance from the origin along its Normal: Dot(Normal, p) for each point p on it.
@PanicsAtCaller Public Static Method FromPointNormal(point: Vec3, normal: Vec3): Plane static method #

The plane through the point, facing the way the normal does. A zero normal panics.
@PanicsAtCaller Public Static Method FromPoints(a: Vec3, b: Vec3, c: Vec3): Plane static method #

The plane through the three points, facing the side they go counterclockwise around. Three on a line panic.
Public Method SignedDistance(point: Vec3): Float method #

How far the point is in front of the plane, negative behind it.
Public Method ClosestPoint(point: Vec3): Vec3 method #

The point on the plane nearest the one given.
Public Method Raycast(ray: Ray): Float? method #

How far along the ray it meets the plane, from either side, 0 for a ray that starts on it, whichever way it goes. A ray along it misses.
Public Method ToString(): String method #

Its parts, as "Plane((0, 1, 0), 0)".

`Frustum` struct

Public Struct Frustum Implements Equatable, Printable

What a camera sees: the six planes of its projection, each facing in.

Examples


Local camera = Mat4.Perspective(Deg(90), 1, 0.1, 100) *
               Mat4.LookAt(Vec3(0, 0, 5), Vec3(0, 0, 0), Vec3(0, 1, 0))
Local view = Frustum.FromMatrix(camera)
Expect(view.Contains(Vec3(0, 0, 0)))
Expect(!view.Contains(Vec3(0, 0, 10)))
Expect(view.Intersects(Sphere(Vec3(0, 0, 0), 1)))

std/math/geometry.fb, line 419

Public Field Left: Plane field #

Its left plane, facing in.
Public Field Right: Plane field #

Its right plane, facing in.
Public Field Bottom: Plane field #

Its bottom plane, facing in.
Public Field Top: Plane field #

Its top plane, facing in.
Public Field Near: Plane field #

Its near plane, facing in.
Public Field Far: Plane field #

Its far plane, facing in.
Public Static Method FromMatrix(m: Mat4): Frustum static method #

The frustum of a projection times a view matrix, as Mat4.Perspective and LookAt make them, with depth from 0 to 1, in the space the view matrix takes from: the world's, for a camera.
Public Method Contains(point: Vec3): Bool method #

Whether the point is inside, or on a plane.
Public Method Intersects(sphere: Sphere): Bool method #

Whether the sphere is inside, or partly: False only when it's all behind a plane.
Public Method Intersects(box: AABB): Bool method #

Whether the box is inside, or partly: False only when it's all behind a plane, so a box just past a corner of the frustum can be True, as culling allows.
Public Method ToString(): String method #

Its six planes, left, right, bottom, top, near, and far, as "Frustum(Plane(...), ...)".

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std.math.geometry

Types

Rect struct

Examples

AABB struct

Examples

Sphere struct

Examples

Ray struct

Examples

Plane struct

Examples

Frustum struct

Examples

`Rect` struct

`AABB` struct

`Sphere` struct

`Ray` struct

`Plane` struct

`Frustum` struct