Geometry Domain

The Geometry domain creates shapes (Sphere, Ray, Rect) and checks if they touch.

This is the "physical" side of math. While Vector handles movement, Geometry handles stuff.

• "Did I click the button?" (Point vs Rect)
• "Did the bullet hit the player?" (Ray vs Cylinder)
• "Is the tank inside the base?" (Point vs Polygon)

Almost every visual application needs to know when two things collide. This domain gives you standard shapes and highly optimized algorithms to check for intersections instantly.

Overview

use aivi.geometry (Ray, Sphere, intersect)

// A ray firing forwards from origin
ray = Ray(origin: {x:0, y:0, z:0}, dir: {x:0, y:0, z:1})

// A sphere 5 units away
sphere = Sphere(center: {x:0, y:0, z:5}, radius: 1.0)

if intersect(ray, sphere) {
    print("Hit!")
}

Features

Point2 = { x: Float, y: Float }
Point3 = { x: Float, y: Float, z: Float }
Line2 = { origin: Point2, direction: Point2 }
Segment2 = { start: Point2, end: Point2 }
Polygon = { vertices: List Point2 }

Domain Definition

domain Geometry over Point2 = {
  (+) : Point2 -> Point2 -> Point2
  (+) a b = { x: a.x + b.x, y: a.y + b.y }
  
  (-) : Point2 -> Point2 -> Point2
  (-) a b = { x: a.x - b.x, y: a.y - b.y }
}

domain Geometry over Point3 = {
  (+) : Point3 -> Point3 -> Point3
  (+) a b = { x: a.x + b.x, y: a.y + b.y, z: a.z + b.z }
  
  (-) : Point3 -> Point3 -> Point3
  (-) a b = { x: a.x - b.x, y: a.y - b.y, z: a.z - b.z }
}

Helper Functions

Function	Explanation
distance a b Point2 -> Point2 -> Float	Returns the Euclidean distance between two 2D points.
midpoint segment Segment2 -> Point2	Returns the center point of a line segment.
area polygon Polygon -> Float	Returns the signed area (positive for counter-clockwise winding).

Usage Examples

use aivi.geometry

p1 = { x: 0.0, y: 0.0 }
p2 = { x: 3.0, y: 4.0 }

d = distance p1 p2
center = midpoint { start: p1, end: p2 }