Geometria

A collection of definitions and algorithms for working with 2- and 3- dimensional geometries in Swift.

(README.md is still in construction.)

Type definitions

N-dimensional
Primitive	Illustration	Geometria type	Remarks
Axis-aligned bounding-box		AABB.swift	Defined as two point vectors describing the minimal and maximal coordinates contained within the AABB.
Ray (unit vector direction)		DirectionalRay.swift	Defined as a starting point vector and a unit vector describing the direction of the ray. Conceptually it extends to infinity in only one of its two ends (pointed to by its direction unit vector).
N-dimensional Ellipsoid		Ellipsoid.swift	Defined as a center point vector and an axis vector.
Hyperplane		Hyperplane.swift	Defined as a point vector on the plane and a unit vector orthogonal to the hyperplane’s surface. Defines a split between two half-spaces of the space it is contained within. Is considered a convex, volumetric space that can be intersected against lines and contain points.
Line		Line.swift	Defined as a pair of point vectors on the line. Conceptually it extends to infinity at both ends.
Line segment		LineSegment.swift	Defined as start and end point vectors on the line. Conceptually it is contained only within the limits of start <-> end.
N-dimensional capsule		NCapsule.swift	Defined as a line segment containing two point vectors describing the span of the capsule’s body, and a scalar radius that defines the maximal distance to the line segment points must be to be considered as contained within the capsule. Specializes as a Stadium in 2D and Capsule in 3D.
Hyperrectangle		NRectangle.swift	Defined as an origin (top-left in two dimensions) point vector and an N-dimensional size vector.
N-sphere		NSphere.swift	Defined as a center point vector and a scalar radius.
N-dimensional cube (Hypercube)		NSquare.swift	Generalized for any dimension. Defined as an origin point (top-left in two dimensions) and a scalar value that describes the span of the cube, in each dimension. Forms a square in 2D, and a cube in 3D.
Plane		PointNormalPlane.swift	Defined as a point vector on the plane and a unit vector orthogonal to the plane’s surface.
Ray (two-point)		Ray.swift	Defined as a pair of points start and b describing the two points the ray crosses before projecting to infinity. Similar in definition to a line and line segment, but extends in one direction to infinity.
Triangle		Triangle.swift	Defined as a set of three point vectors.

GeometriaClipping

An extra library dependency exported called GeometriaClipping can be used to generate boolean geometry from input geometries composed of line and circular arc simplexes.

The operations supported are the following:

2-dimensional
Operation	Illustration	GeometriaClipping type
Union		Union2Parametric.swift
Intersection		Intersection2Parametric.swift
Subtraction		Subtraction2Parametric.swift
Exclusive disjunction or Symmetric Difference		ExclusiveDisjunction2Parametric.swift