Vector Math

Two-dimensional floating point vectors (Vec2) are ubiquitous in Oort and are used to represent positions, velocities, accelerations, etc.

API reference for Vec2

Cartesian coordinate system

Angles in the Cartesian coordinate system

Quick reference:

• vec2(x: f64, y: f64) → Vec2: Create a vector.
• v.x, v.y → f64: Get a component of a vector.
• v1 +- v2 → Vec2: Basic arithmetic between vectors.
• v */ f64 → Vec2: Basic arithmetic between vectors and scalars.
• -v → Vec2: Negate a vector.
• v.length() → f64: Length.
• v.normalize() → Vec2: Normalize to a unit vector.
• v.rotate(angle: f64) → Vec2: Rotate counter-clockwise.
• v.angle() → f64: Angle of a vector.
• v1.dot(v2: Vec2) → f64: Dot product.
• v1.cross(v2: Vec2) → f64: Cross product.
• v1.distance(v2: Vec2) → f64: Distance between two points.

Vec2 is a two-dimensional floating point vector, so it has x and y fields with type f64. This is convenient for storing positions, velocities, accelerations, etc, because operations can work on both components at the same time. For example: vec2(a, b) + vec2(c, d) == vec2(a + c, b + d). Here's a list of how the basic operations expand:

• vec2(a, b) + vec2(c, d) == vec2(a + c, b + d)
• vec2(a, b) - vec2(c, d) == vec2(a - c, b - d)
• vec2(a, b) * c == vec2(a * c, b * c)
• -vec2(a, b) == vec2(-a, -b)

You can get the length of a vector with the length() method, and the distance between two vectors with v1.distance(v2).

All angles are in radians, and are relative to the positive X axis. For example:

• vec2(1.0, 0.0).angle() == 0.0 // Pointing east
• vec2(0.0, 1.0).angle() == PI / 2.0 // Pointing north
• vec2(1.0, 0.0).rotate(PI / 2.0) == PI / 2.0 // Pointing north

Examples:

// Accelerate towards position "p"
accelerate(p - position());

// Get the angle between your ship and another position "p"
let angle = (p - position()).angle();

// Turn to point at "angle"
turn(angle_diff(heading(), angle));