Vec2d.scala

import scala.math.sqrt
import scala.util.Random

trait Vec2d {
  def x: Double

  def y: Double

  def -(that: Point): Point = Point(this.x - that.x, this.y - that.y)

  def +(that: Point): Point = Point(this.x + that.x, this.y + that.y)

  def *(that: Point): Double = this.x * that.x + this.y * that.y

  def cross(that: Point): Double = this.x * that.y - this.y * that.x

  def *(that: Double): Point = Point(this.x * that, this.y * that)

  def /(that: Double): Point = Point(this.x / that, this.y / that)

  def sqnorm = x * x + y * y

  def norm = sqrt(sqnorm)
}


case class Point(override val x: Double, override val y: Double) extends Vec2d

object Point {
  def nextGaussian = Point(Random.nextGaussian, Random.nextGaussian)

  def nextUniform = Point(Random.nextDouble, Random.nextDouble)
}

case class Line(override val x: Double, override val y: Double) extends Vec2d {
  def distance(p: Point) = {
    val lp = Point(x, y)
    val proj = lp * (lp * p) / lp.sqnorm
    (proj - lp) * lp / lp.norm
  }

  def apply(ix: Double) = {
    y + x * (x - ix) / y
  }
}

object Line {
  def apply(p: Point): Line = Line(p.x, p.y)
}