vector/geometry.go

package vector

import (
	"math"
)

// A and B represent two opposite corners of axis-aligned boundin box
type AABB2d struct {
	A Point2d `json:"A"`
	B Point2d `json:"B"`
}

type Polygon2d struct {
	Points  []Vector2d `json:"points"`
	Normals []Vector2d `json:"normals"`
	Origin  Point2d    `json:"origin"`
}

func (p Polygon2d) Edge(i int) (Point2d, Vector2d) {
	p1 := Point2d{}
	p2 := Point2d{}

	if i == len(p.Points)-1 {
		p1 = p.Origin.Add(p.Points[i])
		p2 = p.Origin.Add(p.Points[0])
	} else {
		p1 = p.Origin.Add(p.Points[i])
		p2 = p.Origin.Add(p.Points[i+1])
	}
	return p1, p2.Sub(p1)
}

type Vector2d struct {
	X float64 `json:"x"`
	Y float64 `json:"y"`
}

type Point2d struct {
	X float64 `json:"x"`
	Y float64 `json:"y"`
}

const Epsilon = 1e-7
const Rad2deg = 180 / math.Pi
const Deg2rad = math.Pi / 180

func (p1 Point2d) Sub(p2 Point2d) Vector2d {
	return Vector2d{p1.X - p2.X, p1.Y - p2.Y}
}

func (p Point2d) Add(v Vector2d) Point2d {
	return Point2d{p.X + v.X, p.Y + v.Y}
}

func (v Vector2d) Mag() float64 {
	return math.Abs(math.Sqrt(v.X*v.X + v.Y*v.Y))
}

func (v Vector2d) MagSquared() float64 {
	return math.Abs(v.X*v.X + v.Y*v.Y)
}

func (v Vector2d) PopPop() float64 {
	return v.Mag()
}

func (v Vector2d) Scale(s float64) Vector2d {
	return Vector2d{v.X * s, v.Y * s}
}

func (v1 Vector2d) Cross(v2 Vector2d) float64 {
	return v1.X*v2.Y - v1.Y*v2.X
}

func (v1 Vector2d) Dot(v2 Vector2d) float64 {
	return (v1.X * v2.X) + (v1.Y * v2.Y)
}

func (p Point2d) ToVector() Vector2d {
	return Vector2d{p.X, p.Y}
}

func (v Vector2d) ToPoint() Point2d {
	return Point2d{v.X, v.Y}
}

func (v1 Vector2d) Rotate(a float64) Vector2d {
	x := float64(v1.X)*math.Cos(float64(a)) - float64(v1.Y)*math.Sin(float64(a))
	y := float64(v1.X)*math.Sin(float64(a)) + float64(v1.Y)*math.Cos(float64(a))
	return Vector2d{x, y}
}

func PointInRect(p Point2d, r AABB2d) bool {
	return (p.X > r.A.X) && (p.X < r.B.X) && (p.Y > r.A.Y) && (p.Y < r.B.Y)
}

func AASquareAtPoint(p Point2d, edgeLength float64) AABB2d {
	size := edgeLength / 2.0
	return AABB2d{
		A: Point2d{X: p.X - size, Y: p.Y - size},
		B: Point2d{X: p.X + size, Y: p.Y + size}}
}

func (r AABB2d) ToPolygon() Polygon2d {
	p := Polygon2d{}

	p.Origin = r.A
	p.Points = append(p.Points, r.A.Sub(p.Origin))
	p.Points = append(p.Points, Point2d{r.A.X, r.B.Y}.Sub(p.Origin))
	p.Points = append(p.Points, r.B.Sub(p.Origin))
	p.Points = append(p.Points, Point2d{r.B.X, r.A.Y}.Sub(p.Origin))

	return p
}

func OrientedSquare(center Point2d, heading Vector2d, size float64) Polygon2d {
	out := Polygon2d{}
	out.Origin.X = center.X
	out.Origin.Y = center.Y
	x := heading.Normalize().Scale(size)
	y := Vector2d{-x.Y, x.X}
	z := Point2d{}
	out.Points = append(out.Points, z.Add(x).Add(y).ToVector())
	out.Points = append(out.Points, z.Add(y).Sub(x.ToPoint()))
	out.Points = append(out.Points, z.Sub(x.ToPoint()).ToPoint().Sub(y.ToPoint()))
	out.Points = append(out.Points, z.Add(x).Sub(y.ToPoint()))
	return out
}

func (v Vector2d) Normalize() Vector2d {
	if v.X == 0 && v.Y == 0 {
		return v
	}

	m := v.Mag()
	return Vector2d{v.X / m, v.Y / m}
}

func Distance(p1, p2 Point2d) float64 {
	return p1.Sub(p2).Mag()
}

// returns radians
func Angle(v1, v2 Vector2d) float64 {
	x := (v1.Dot(v2) / (v1.Mag() * v2.Mag()))
	angle := math.Acos(float64(x))

	if math.IsNaN(angle) {
		if math.Abs(float64(v1.X-v2.X)) > Epsilon {
			return 180.0
		} else {
			return 0
		}
	}

	// Determine the sign to see what direction
	// the angle should go in
	if v1.Y*v2.X > v1.X*v2.Y {
		angle = angle * -1.0
	}
	return angle
}