geom/pointf.go

package geom

import (
	"math"
)

// PointF is an X, Y coordinate pair (floating point).
type PointF struct {
	X, Y float64
}

// ZeroPtF is initialized on (0, 0).
var ZeroPtF = PointF{X: 0, Y: 0}

// PtF is a shorthand function to create a point.
func PtF(x, y float64) PointF {
	return PointF{X: x, Y: y}
}

// Add adds q as a vector to p.
func (p PointF) Add(q PointF) PointF {
	return PointF{p.X + q.X, p.Y + q.Y}
}

// Add2D adds x and y to X and Y of point p and returns the sum.
func (p PointF) Add2D(x, y float64) PointF {
	return PtF(p.X+x, p.Y+y)
}

// AngleTo calculates the angle [0..2*Pi) from point p to point q.
func (p PointF) AngleTo(q PointF) float64 {
	a := math.Atan((p.Y - q.Y) / (p.X - q.X))
	if q.X < p.X {
		return a + math.Pi
	}
	if a < 0 {
		a += 2 * math.Pi
	}
	return a
}

// Atan2 returns the arc tangent of y/x.
func (p PointF) Atan2() float64 {
	return Atan2(p.Y, p.X)
}

// Distance calculates the distance between points p and q.
func (p PointF) Distance(q PointF) float64 {
	return Sqrt(p.Distance2(q))
}

// Distance2 calculates the squared distance between points p and q.
func (p PointF) Distance2(q PointF) float64 {
	dx := q.X - p.X
	dy := q.Y - p.Y
	return dx*dx + dy*dy
}

// DistanceToLine calculates the distance to the line segment a, b.
func (p PointF) DistanceToLine(a, b PointF) float64 {
	dx1, dy1 := (a.X - p.X), (a.Y - p.Y)
	dx2, dy2 := (b.X - a.X), (b.Y - a.Y)
	t := -((dx1*dx2 + dy1*dy2) / (dx2*dx2 + dy2*dy2))
	if 0 <= t && t <= 1 {
		return Abs(dx2*dy1-dy2*dx1) / Sqrt(dx2*dx2+dy2*dy2)
	}
	d1, d2 := Sqrt(Sq(b.X-p.X)+Sq(b.Y-p.Y)), Sqrt(dx1*dx1+dy1*dy1)
	if d1 < d2 {
		return d1
	}
	return d2
}

// DistanceToLines calculates the smallest distance to the line segments of q.
func (p PointF) DistanceToLines(q PointsF) float64 {
	n := len(q)
	if n == 0 {
		return NaN()
	}
	if n == 1 {
		return p.Distance(q[0])
	}
	min := p.DistanceToLine(q[0], q[1])
	for i := range q {
		if i < 2 {
			continue
		}
		d := p.DistanceToLine(q[i-1], q[i])
		if d < min {
			min = d
		}
	}
	return min
}

// DistanceToPolygon calculates the smallest distance to the polygon q.
func (p PointF) DistanceToPolygon(q PolygonF) float64 {
	if len(q.Points) == 0 {
		return NaN()
	}
	return p.DistanceToLines(append(q.Points, q.Points[0]))
}

// Div divides the X and Y values of point p with t and returns the result.
func (p PointF) Div(t float64) PointF {
	return PtF(p.X/t, p.Y/t)
}

// Dot returns the dot product of p and q.
func (p PointF) Dot(q PointF) float64 {
	return p.X*q.X + p.Y*q.Y
}

// In tests if the point p is inside the rectangle r.
func (p PointF) In(r RectangleF) bool {
	if p.X < r.Min.X || p.X >= r.Max.X || p.Y < r.Min.Y || p.Y >= r.Max.Y {
		return false
	}
	return true
}

// InPolygon tests is the point p is inside the polygon q.
func (p PointF) InPolygon(q PolygonF) bool {
	var n = len(q.Points)
	var c = false

	var i = 0
	var j = n - 1
	for i < n {
		if ((q.Points[i].Y >= p.Y) != (q.Points[j].Y >= p.Y)) &&
			(p.X <= (q.Points[j].X-q.Points[i].X)*(p.Y-q.Points[i].Y)/(q.Points[j].Y-q.Points[i].Y)+q.Points[i].X) {
			c = !c
		}
		j = i
		i++
	}
	return c
}

// Invert changes the sign of the components.
func (p PointF) Invert() PointF {
	return PointF{-p.X, -p.Y}
}

// Len returns the length of the vector.
func (p PointF) Len() float64 {
	return Sqrt(p.X*p.X + p.Y*p.Y)
}

// Mul multiplies the X and Y values of point p with t and returns the result.
func (p PointF) Mul(t float64) PointF {
	return PtF(p.X*t, p.Y*t)
}

// Mul2D multiplies the X and Y values of point p with x and y and returns the result.
func (p PointF) Mul2D(x, y float64) PointF {
	return PtF(p.X*x, p.Y*y)
}

// Norm returns the normalized vector of x and y.
func (p PointF) Norm() PointF {
	return p.Mul(1 / p.Len())
}

// Rect returns a rectangle starting from point p to given point q
func (p PointF) Rect(q PointF) RectangleF {
	return RectangleF{Min: p, Max: q}
}

// Rect2D returns a rectangle starting from point p to given coordinate (x, y)
func (p PointF) Rect2D(x, y float64) RectangleF {
	return RectangleF{Min: p, Max: PtF(x, y)}
}

// RectRel returns a rectangle starting from point p with the given size.
func (p PointF) RectRel(size PointF) RectangleF {
	return RectRelF(p.X, p.Y, size.X, size.Y)
}

// RectRel2D returns a rectangle starting from point p with the given width and height
func (p PointF) RectRel2D(width, height float64) RectangleF {
	return RectRelF(p.X, p.Y, width, height)
}

// Sub subtracts q as a vector from p.
func (p PointF) Sub(q PointF) PointF {
	return PointF{p.X - q.X, p.Y - q.Y}
}

// ToF32 transforms the point p into a PointF32.
func (p PointF) ToF32() PointF32 {
	return PointF32{float32(p.X), float32(p.Y)}
}

// ToInt transforms the point p into a Point.
func (p PointF) ToInt() Point {
	return Point{int(p.X), int(p.Y)}
}

// XY returns the X and Y component of the coordinate.
func (p PointF) XY() (float64, float64) { return p.X, p.Y }

// MaxPtF returns the point that is at the largest X & Y position of a and b.
func MaxPtF(a, b PointF) PointF {
	return PtF(Max(a.X, b.X), Max(a.Y, b.Y))
}

// MinPtF returns the point that is at the smallest X & Y position of a and b.
func MinPtF(a, b PointF) PointF {
	return PtF(Min(a.X, b.X), Min(a.Y, b.Y))
}