Added TriangleF.

Renamed Add to Extend on PolygonF{,32}.
Add now translates a polygon.

math.go

@@ -6,6 +6,9 @@ func emulate32(f float32, fn func(float64) float64) float32 {
 	return float32(fn(float64(f)))
 }
 
+// Pi constant https://oeis.org/A000796
+const Pi = math.Pi
+
 // Abs returns the absolute value.
 func Abs(f float64) float64 {
 	return math.Abs(f)
@@ -21,11 +24,21 @@ func Atan(f float64) float64 {
 	return math.Atan(f)
 }
 
+// Atan2 returns the arc tangent of y/x.
+func Atan2(y, x float64) float64 {
+	return math.Atan2(y, x)
+}
+
 // Atan32 returns the arc tangent of f.
 func Atan32(f float32) float32 {
 	return float32(math.Atan(float64(f)))
 }
 
+// Atan232 returns the arc tangent of y/x.
+func Atan232(y, x float32) float32 {
+	return float32(math.Atan2(float64(y), float64(x)))
+}
+
 // Ceil rounds f up to an natural number.
 func Ceil(f float64) float64 {
 	return math.Ceil(f)

point.go

@@ -64,6 +64,11 @@ func (p Point) DistInt(q Point) int {
 	return ints.SubAbs(p.X, q.X) + ints.SubAbs(p.Y, q.Y)
 }
 
+// Dot returns the dot product of p and q.
+func (p Point) Dot(q Point) int {
+	return p.X*p.X + p.Y*p.Y
+}
+
 // In tests if the point p is inside the rectangle r.
 func (p Point) In(r Rectangle) bool {
 	if p.X < r.Min.X || p.X >= r.Max.X || p.Y < r.Min.Y || p.Y >= r.Max.Y {
@@ -80,11 +85,16 @@ func (p Point) Less(q Point) bool {
 	return p.Y < q.Y
 }
 
-// Mul multiplier the X and Y values of point p with t and returns the result.
+// Mul multiplies the X and Y values of point p with t and returns the result.
 func (p Point) Mul(t int) Point {
 	return Pt(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 Point) Mul2D(x, y int) Point {
+	return Pt(p.X*x, p.Y*y)
+}
+
 // Norm returns the point with both X and Y normalized.
 func (p Point) Norm() Point {
 	return Pt(ints.Norm(p.X), ints.Norm(p.Y))

pointf.go

@@ -39,9 +39,14 @@ func (p PointF) AngleTo(q PointF) float64 {
 	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 math.Sqrt(p.Distance2(q))
+	return Sqrt(p.Distance2(q))
 }
 
 // Distance2 calculates the squared distance between points p and q.
@@ -101,6 +106,11 @@ 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 {
@@ -132,11 +142,26 @@ func (p PointF) Invert() PointF {
 	return PointF{-p.X, -p.Y}
 }
 
-// Mul multiplier the X and Y values of point p with t and returns the result.
+// 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}

pointf32.go

@@ -39,9 +39,14 @@ func (p PointF32) AngleTo(q PointF32) float32 {
 	return a
 }
 
+// Atan2 returns the arc tangent of y/x.
+func (p PointF32) Atan2() float32 {
+	return Atan232(p.Y, p.X)
+}
+
 // Distance calculates the distance between points p and q.
 func (p PointF32) Distance(q PointF32) float32 {
-	return float32(math.Sqrt(float64(p.Distance2(q))))
+	return Sqrt32(p.Distance2(q))
 }
 
 // Distance2 calculates the squared distance between points p and q.
@@ -101,6 +106,11 @@ func (p PointF32) Div(t float32) PointF32 {
 	return PtF32(p.X/t, p.Y/t)
 }
 
+// Dot returns the dot product of p and q.
+func (p PointF32) Dot(q PointF32) float32 {
+	return p.X*q.X + p.Y*q.Y
+}
+
 // In tests if the point p is inside the rectangle r.
 func (p PointF32) In(r RectangleF32) bool {
 	if p.X < r.Min.X || p.X >= r.Max.X || p.Y < r.Min.Y || p.Y >= r.Max.Y {
@@ -132,11 +142,26 @@ func (p PointF32) Invert() PointF32 {
 	return PointF32{-p.X, -p.Y}
 }
 
-// Mul multiplier the X and Y values of point p with t and returns the result.
+// Len returns the length of the vector.
+func (p PointF32) Len() float32 {
+	return Sqrt32(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 PointF32) Mul(t float32) PointF32 {
 	return PtF32(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 PointF32) Mul2D(x, y float32) PointF32 {
+	return PtF32(p.X*x, p.Y*y)
+}
+
+// Norm returns the normalized vector of x and y.
+func (p PointF32) Norm() PointF32 {
+	return p.Mul(1 / p.Len())
+}
+
 // Rect returns a rectangle starting from point p to given point q
 func (p PointF32) Rect(q PointF32) RectangleF32 {
 	return RectangleF32{Min: p, Max: q}

polygonf.go

@@ -1,5 +1,7 @@
 package geom
 
+import "log"
+
 // PointsF is a set of points.
 type PointsF []PointF
 
@@ -11,10 +13,97 @@ type PolygonF struct {
 	Points PointsF
 }
 
-// Add creates a new polyqon based on p with one or more extra points q.
-func (p PolygonF) Add(q ...PointF) PolygonF {
+// Add adds q as a vector to all points in p.
+func (p PolygonF) Add(q PointF) PolygonF {
+	var r = p.copy()
+	for i, pt := range r.Points {
+		r.Points[i] = pt.Add(q)
+	}
+	return r
+}
+
+func (p PolygonF) copy() PolygonF {
+	var q = PolygonF{make(PointsF, len(p.Points))}
+	copy(q.Points, p.Points)
+	return q
+}
+
+// Extend creates a new polygon based on p with one or more extra points q.
+func (p PolygonF) Extend(q ...PointF) PolygonF {
 	var t = PolygonF{make(PointsF, len(p.Points)+len(q))}
 	copy(t.Points, p.Points)
 	copy(t.Points[len(p.Points):], q)
 	return t
 }
+
+// Mul multiplies the points of polygon p with t and returns the result.
+func (p PolygonF) Mul(t float64) PolygonF {
+	var q = p.copy()
+	for i, pt := range q.Points {
+		q.Points[i] = pt.Mul(t)
+	}
+	return q
+}
+
+// Triangulate triangulates the polygon p.
+func (p PolygonF) Triangulate() []TriangleF {
+	var triangles []TriangleF
+	points := p.copy().Points[:]
+	n := len(points)
+
+	if n > 0 && points[0] == points[n-1] { // remove first point if polygon is closed
+		points = points[1:]
+		n--
+	}
+
+	triangle := func(i int) TriangleF {
+		return TrF(points[(i+n-1)%n], points[i], points[(i+1)%n])
+	}
+	ear := func(i int) (TriangleF, bool) {
+		t := triangle(i)
+		if t.Winding() == WindingCounterClockwise {
+			return TriangleF{}, false
+		}
+		for j := 0; j < n-3; j++ {
+			p := points[(i+2+j)%n]
+			if t.Contains(p) {
+				return TriangleF{}, false
+			}
+		}
+		return t, true
+	}
+
+	for n >= 3 {
+		leastSharp := -1
+		var leastSharpAngle float64
+		for i := range points {
+			if t, ok := ear(i); ok {
+				sharpAngle := t.SmallestAngle()
+				if leastSharp < 0 || sharpAngle > leastSharpAngle {
+					leastSharp = i
+					leastSharpAngle = sharpAngle
+				}
+			}
+		}
+		if leastSharp < 0 {
+			if n >= 3 {
+				log.Println("not fully triangulated")
+			}
+			break
+		}
+		triangles = append(triangles, triangle(leastSharp))
+		points = append(points[:leastSharp], points[leastSharp+1:]...)
+		n = len(points)
+	}
+	return triangles
+}
+
+// Reverse reverses the order of the points of polygon p.
+func (p PolygonF) Reverse() PolygonF {
+	n := len(p.Points)
+	var q = PolygonF{make(PointsF, n)}
+	for i := 0; i < n/2; i++ {
+		q.Points[i], q.Points[n-i-1] = p.Points[n-i-1], p.Points[i]
+	}
+	return q
+}

polygonf32.go

@@ -11,10 +11,34 @@ type PolygonF32 struct {
 	Points PointsF32
 }
 
-// Add creates a new polyqon based on p with one or more extra points q.
-func (p PolygonF32) Add(q ...PointF32) PolygonF32 {
+// Add adds q as a vector to all points in p.
+func (p PolygonF32) Add(q PointF32) PolygonF32 {
+	var r = p.copy()
+	for i, pt := range r.Points {
+		r.Points[i] = pt.Add(q)
+	}
+	return r
+}
+
+func (p PolygonF32) copy() PolygonF32 {
+	var q = PolygonF32{make(PointsF32, len(p.Points))}
+	copy(q.Points, p.Points)
+	return q
+}
+
+// Extend creates a new polygon based on p with one or more extra points q.
+func (p PolygonF32) Extend(q ...PointF32) PolygonF32 {
 	var t = PolygonF32{make(PointsF32, len(p.Points)+len(q))}
 	copy(t.Points, p.Points)
 	copy(t.Points[len(p.Points):], q)
 	return t
 }
+
+// Mul multiplies the points of polygon p with t and returns the result.
+func (p PolygonF32) Mul(t float32) PolygonF32 {
+	var q = p.copy()
+	for i, pt := range q.Points {
+		q.Points[i] = pt.Mul(t)
+	}
+	return q
+}

trianglef.go

@@ -0,0 +1,93 @@
+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
+)

trianglef_test.go

@@ -0,0 +1,12 @@
+package geom
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func TestTriangleFSmallestAngle(t *testing.T) {
+	triangle := TrF(PtF(0, 0), PtF(0, 1), PtF(1, 1))
+	assert.InEpsilon(t, .25*Pi, triangle.SmallestAngle(), 1e-9)
+}