geom/trianglef.go

package geom

import (
	"math"
)

// TriangleF is defined by three points that describe a 2D triangle.
type TriangleF struct {
	Points [3]PointF
}

// TrF is a shorthand method to create a TriangleF.
func TrF(q, r, s PointF) TriangleF {
	return TriangleF{Points: [3]PointF{q, r, s}}
}

// Add translates the triangle by point p.
func (t TriangleF) Add(p PointF) TriangleF {
	return TriangleF{Points: [3]PointF{
		t.Points[0].Add(p),
		t.Points[1].Add(p),
		t.Points[2].Add(p),
	}}
}

// Center gives the average of the three points.
func (t TriangleF) Center() PointF {
	return t.Points[0].Add(t.Points[1]).Add(t.Points[2]).Mul(1. / 3)
}

// Contains tests if point p lies in the triangle.
func (t TriangleF) Contains(p PointF) bool {
	u, v, w := t.Points[0], t.Points[1], t.Points[2]
	const eps = 1e-9
	q := 1 / (-v.Y*w.X + u.Y*(-v.X+w.X) + u.X*(v.Y-w.Y) + v.X*w.Y)
	r := (u.Y*w.X - u.X*w.Y + (w.Y-u.Y)*p.X + (u.X-w.X)*p.Y) * q
	s := (u.X*v.Y - u.Y*v.X + (u.Y-v.Y)*p.X + (v.X-u.X)*p.Y) * q
	if r < -eps || r > 1+eps || s < -eps || s > 1+eps || r+s > 1+eps {
		return false
	}
	return true
}

// Inset insets all the points of the triangle towards the center of the triangle with distance f.
func (t TriangleF) Inset(f float64) TriangleF {
	center := t.Center()
	inset := func(p PointF) PointF {
		centered := p.Sub(center)
		length := p.Distance(center)
		factor := (length - f) / length
		return center.Add(centered.Mul(factor))
	}
	return TriangleF{Points: [3]PointF{
		inset(t.Points[0]),
		inset(t.Points[1]),
		inset(t.Points[2]),
	}}
}

// Mul multiplies all the points of the triangle with f.
func (t TriangleF) Mul(f float64) TriangleF {
	return TriangleF{Points: [3]PointF{
		t.Points[0].Mul(f),
		t.Points[1].Mul(f),
		t.Points[2].Mul(f),
	}}
}

// SmallestAngle returns the smallest/sharpest angle of the triangle.
func (t TriangleF) SmallestAngle() float64 {
	u, v, w := t.Points[0], t.Points[1], t.Points[2]
	q := math.Acos(w.Sub(u).Norm().Dot(v.Sub(u).Norm()))
	r := math.Acos(u.Sub(v).Norm().Dot(w.Sub(v).Norm()))
	s := math.Acos(v.Sub(w).Norm().Dot(u.Sub(w).Norm()))
	return math.Min(q, math.Min(r, s))
}

// Winding determines the winding of the triangle.
func (t TriangleF) Winding() Winding {
	u, v := t.Points[1].Sub(t.Points[0]), t.Points[2].Sub(t.Points[1])
	if u.X*v.Y-u.Y*v.X > 0 {
		return WindingClockwise
	}
	return WindingCounterClockwise
}

// Winding describes the order of points.
type Winding bool

const (
	WindingClockwise        Winding = false
	WindingCounterClockwise Winding = true
)