Core Concepts: 2. Vector and Angle types

Cadova uses Vector2D and Vector3D to represent positions, sizes, and displacements in 2D and 3D space. They appear throughout the API, for example, when specifying the size of a Box or Rectangle, or when applying transformations. Vector and angle types are used extensively to represent geometry in 2D and 3D space. These types are lightweight, expressive, and designed to make geometric modeling feel natural in Swift.

Cadova uses millimeters as the default unit for distances and coordinates. All measurements are expressed as Double values, but the vector types themselves are unitless — they can be used to represent any kind of numerical value. For example, a Vector3D might represent a size in millimeters, a displacement in space, or even a scaling factor.

Vector Types

Cadova provides two main vector types:

• Vector2D — for 2D space
• Vector3D — for 3D space

Both types work similarly and support:

• Arithmetic operations (+, -, *, /)
• Dot products (⋅) and cross products (×, only for Vector3D)
• Scalar multiplication and division
• Array literal initialization

Creating Vectors

You can initialize a vector in several ways:

let v1 = Vector2D(x: 10, y: 20)
let v2: Vector2D = [10, 20]

let v3 = Vector3D(x: 5, y: 15, z: -3)
let v4: Vector3D = [5, 15, -3]

You can also construct vectors using .x(...), .y(...), and .z(...) factory methods for convenience. These set the specified axis and leave all others as zero:

let vertical: Vector2D = .y(100)
let forward: Vector3D = .z(30)

Arithmetic

Vectors support component-wise arithmetic:

let a: Vector2D = [10, 20]
let b: Vector2D = [5, 4]
let sum = a + b       // [15, 24]

You can also mix vector and scalar values:

let offset = a - 5    // [5, 15]
let doubled = 2 * b   // [10, 8]

Dot and Cross Products

Cadova provides two common geometric operations on vectors. The dot product (⋅) returns a scalar value and measures alignment between vectors. The cross product (×) returns a vector perpendicular to two inputs, and is only available for Vector3D.

let a: Vector2D = [1, 0]
let b: Vector2D = [0, 1]
let dot = a ⋅ b       // 0

let xAxis: Vector3D = [1, 0, 0]
let yAxis: Vector3D = [0, 1, 0]
let zAxis = xAxis × yAxis   // [0, 0, 1]

Angle

Angles in Cadova are represented by the Angle type. Angles are unitless. You create them using degrees, radians, or full turns, but once created, an Angle simply represents a rotation, not a particular unit. The most natural and preferred way to create angles is by using the ° suffix operator:

let rightAngle = 90°

You can also create angles using degrees, radians, or full turns:

let a1 = Angle(degrees: 90)
let a2 = Angle(radians: .pi / 2)
let a3 = Angle(turns: 0.25)

Angles support arithmetic and comparisons:

let total = 90° + 45°
let diff = a1 - a2
if diff < 5° {
    print("Close enough")
}

Angles also have computed properties for conversion:

let a = 180°
print(a.radians)   // 3.141592...
print(a.turns)     // 0.5

Normalization is available via .normalized, which maps any angle to the range -180°...180°.