Merge pull request #174 from bcvery1/addLine

Add line geometry

geometry.go

@@ -181,6 +181,268 @@ func Lerp(a, b Vec, t float64) Vec {
 	return a.Scaled(1 - t).Add(b.Scaled(t))
 }
 
+// Line is a 2D line segment, between points A and B.
+type Line struct {
+	A, B Vec
+}
+
+// L creates and returns a new Line.
+func L(from, to Vec) Line {
+	return Line{
+		A: from,
+		B: to,
+	}
+}
+
+// Bounds returns the lines bounding box.  This is in the form of a normalized Rect.
+func (l Line) Bounds() Rect {
+	return R(l.A.X, l.A.Y, l.B.X, l.B.Y).Norm()
+}
+
+// Center will return the point at center of the line; that is, the point equidistant from either end.
+func (l Line) Center() Vec {
+	return l.A.Add(l.A.To(l.B).Scaled(0.5))
+}
+
+// Closest will return the point on the line which is closest to the Vec provided.
+func (l Line) Closest(v Vec) Vec {
+	// between is a helper function which determines whether x is greater than min(a, b) and less than max(a, b)
+	between := func(a, b, x float64) bool {
+		min := math.Min(a, b)
+		max := math.Max(a, b)
+		return min < x && x < max
+	}
+
+	// Closest point will be on a line which perpendicular to this line.
+	// If and only if the infinite perpendicular line intersects the segment.
+	m, b := l.Formula()
+
+	// Account for horizontal lines
+	if m == 0 {
+		x := v.X
+		y := l.A.Y
+
+		// check if the X coordinate of v is on the line
+		if between(l.A.X, l.B.X, v.X) {
+			return V(x, y)
+		}
+
+		// Otherwise get the closest endpoint
+		if l.A.To(v).Len() < l.B.To(v).Len() {
+			return l.A
+		}
+		return l.B
+	}
+
+	// Account for vertical lines
+	if math.IsInf(math.Abs(m), 1) {
+		x := l.A.X
+		y := v.Y
+
+		// check if the Y coordinate of v is on the line
+		if between(l.A.Y, l.B.Y, v.Y) {
+			return V(x, y)
+		}
+
+		// Otherwise get the closest endpoint
+		if l.A.To(v).Len() < l.B.To(v).Len() {
+			return l.A
+		}
+		return l.B
+	}
+
+	perpendicularM := -1 / m
+	perpendicularB := v.Y - (perpendicularM * v.X)
+
+	// Coordinates of intersect (of infinite lines)
+	x := (perpendicularB - b) / (m - perpendicularM)
+	y := m*x + b
+
+	// Check if the point lies between the x and y bounds of the segment
+	if !between(l.A.X, l.B.X, x) && !between(l.A.Y, l.B.Y, y) {
+		// Not within bounding box
+		toStart := v.To(l.A)
+		toEnd := v.To(l.B)
+
+		if toStart.Len() < toEnd.Len() {
+			return l.A
+		}
+		return l.B
+	}
+
+	return V(x, y)
+}
+
+// Contains returns whether the provided Vec lies on the line.
+func (l Line) Contains(v Vec) bool {
+	return l.Closest(v) == v
+}
+
+// Formula will return the values that represent the line in the formula: y = mx + b
+// This function will return math.Inf+, math.Inf- for a vertical line.
+func (l Line) Formula() (m, b float64) {
+	// Account for horizontal lines
+	if l.B.Y == l.A.Y {
+		return 0, l.A.Y
+	}
+
+	m = (l.B.Y - l.A.Y) / (l.B.X - l.A.X)
+	b = l.A.Y - (m * l.A.X)
+
+	return m, b
+}
+
+// Intersect will return the point of intersection for the two line segments.  If the line segments do not intersect,
+// this function will return the zero-vector and false.
+func (l Line) Intersect(k Line) (Vec, bool) {
+	// Check if the lines are parallel
+	lDir := l.A.To(l.B)
+	kDir := k.A.To(k.B)
+	if lDir.X == kDir.X && lDir.Y == kDir.Y {
+		return ZV, false
+	}
+
+	// The lines intersect - but potentially not within the line segments.
+	// Get the intersection point for the lines if they were infinitely long, check if the point exists on both of the
+	// segments
+	lm, lb := l.Formula()
+	km, kb := k.Formula()
+
+	// Account for vertical lines
+	if math.IsInf(math.Abs(lm), 1) && math.IsInf(math.Abs(km), 1) {
+		// Both vertical, therefore parallel
+		return ZV, false
+	}
+
+	var x, y float64
+
+	if math.IsInf(math.Abs(lm), 1) || math.IsInf(math.Abs(km), 1) {
+		// One line is vertical
+		intersectM := lm
+		intersectB := lb
+		verticalLine := k
+
+		if math.IsInf(math.Abs(lm), 1) {
+			intersectM = km
+			intersectB = kb
+			verticalLine = l
+		}
+
+		y = intersectM*verticalLine.A.X + intersectB
+		x = verticalLine.A.X
+	} else {
+		// Coordinates of intersect
+		x = (kb - lb) / (lm - km)
+		y = lm*x + lb
+	}
+
+	if l.Contains(V(x, y)) && k.Contains(V(x, y)) {
+		// The intersect point is on both line segments, they intersect.
+		return V(x, y), true
+	}
+
+	return ZV, false
+}
+
+// IntersectCircle will return the shortest Vec such that moving the Line by that Vec will cause the Line and Circle
+// to no longer intesect.  If they do not intersect at all, this function will return a zero-vector.
+func (l Line) IntersectCircle(c Circle) Vec {
+	// Get the point on the line closest to the center of the circle.
+	closest := l.Closest(c.Center)
+	cirToClosest := c.Center.To(closest)
+
+	if cirToClosest.Len() >= c.Radius {
+		return ZV
+	}
+
+	return cirToClosest.Scaled(cirToClosest.Len() - c.Radius)
+}
+
+// IntersectRect will return the shortest Vec such that moving the Line by that Vec will cause  the Line and Rect to
+// no longer intesect.  If they do not intersect at all, this function will return a zero-vector.
+func (l Line) IntersectRect(r Rect) Vec {
+	// Check if either end of the line segment are within the rectangle
+	if r.Contains(l.A) || r.Contains(l.B) {
+		// Use the Rect.Intersect to get minimal return value
+		rIntersect := l.Bounds().Intersect(r)
+		if rIntersect.H() > rIntersect.W() {
+			// Go vertical
+			return V(0, rIntersect.H())
+		}
+		return V(rIntersect.W(), 0)
+	}
+
+	// Check if any of the rectangles' edges intersect with this line.
+	for _, edge := range r.Edges() {
+		if _, ok := l.Intersect(edge); ok {
+			// Get the closest points on the line to each corner, where:
+			//  - the point is contained by the rectangle
+			//  - the point is not the corner itself
+			corners := r.Vertices()
+			closest := ZV
+			closestCorner := corners[0]
+			for _, c := range corners {
+				cc := l.Closest(c)
+				if closest == ZV || (closest.Len() > cc.Len() && r.Contains(cc)) {
+					closest = cc
+					closestCorner = c
+				}
+			}
+
+			return closest.To(closestCorner)
+		}
+	}
+
+	// No intersect
+	return ZV
+}
+
+// Len returns the length of the line segment.
+func (l Line) Len() float64 {
+	return l.A.To(l.B).Len()
+}
+
+// Moved will return a line moved by the delta Vec provided.
+func (l Line) Moved(delta Vec) Line {
+	return Line{
+		A: l.A.Add(delta),
+		B: l.B.Add(delta),
+	}
+}
+
+// Rotated will rotate the line around the provided Vec.
+func (l Line) Rotated(around Vec, angle float64) Line {
+	// Move the line so we can use `Vec.Rotated`
+	lineShifted := l.Moved(around.Scaled(-1))
+
+	lineRotated := Line{
+		A: lineShifted.A.Rotated(angle),
+		B: lineShifted.B.Rotated(angle),
+	}
+
+	return lineRotated.Moved(around)
+}
+
+// Scaled will return the line scaled around the center point.
+func (l Line) Scaled(scale float64) Line {
+	return l.ScaledXY(l.Center(), scale)
+}
+
+// ScaledXY will return the line scaled around the Vec provided.
+func (l Line) ScaledXY(around Vec, scale float64) Line {
+	toA := around.To(l.A).Scaled(scale)
+	toB := around.To(l.B).Scaled(scale)
+
+	return Line{
+		A: around.Add(toA),
+		B: around.Add(toB),
+	}
+}
+
+func (l Line) String() string {
+	return fmt.Sprintf("Line(%v, %v)", l.A, l.B)
+}
+
 // Rect is a 2D rectangle aligned with the axes of the coordinate system. It is defined by two
 // points, Min and Max.
 //
@@ -243,6 +505,18 @@ func (r Rect) Area() float64 {
 	return r.W() * r.H()
 }
 
+// Edges will return the four lines which make up the edges of the rectangle.
+func (r Rect) Edges() [4]Line {
+	corners := r.Vertices()
+
+	return [4]Line{
+		{A: corners[0], B: corners[1]},
+		{A: corners[1], B: corners[2]},
+		{A: corners[2], B: corners[3]},
+		{A: corners[3], B: corners[0]},
+	}
+}
+
 // Center returns the position of the center of the Rect.
 func (r Rect) Center() Vec {
 	return Lerp(r.Min, r.Max, 0.5)
@@ -329,6 +603,50 @@ func (r Rect) IntersectCircle(c Circle) Vec {
 	return c.IntersectRect(r).Scaled(-1)
 }
 
+// IntersectLine will return the shortest Vec such that if the Rect is moved by the Vec returned, the Line and Rect no
+// longer intersect.
+func (r Rect) IntersectLine(l Line) Vec {
+	return l.IntersectRect(r).Scaled(-1)
+}
+
+// IntersectionPoints returns all the points where the Rect intersects with the line provided.  This can be zero, one or
+// two points, depending on the location of the shapes.  The points of intersection will be returned in order of
+// closest-to-l.A to closest-to-l.B.
+func (r Rect) IntersectionPoints(l Line) []Vec {
+	// Use map keys to ensure unique points
+	pointMap := make(map[Vec]struct{})
+
+	for _, edge := range r.Edges() {
+		if intersect, ok := l.Intersect(edge); ok {
+			pointMap[intersect] = struct{}{}
+		}
+	}
+
+	points := make([]Vec, 0, len(pointMap))
+	for point := range pointMap {
+		points = append(points, point)
+	}
+
+	// Order the points
+	if len(points) == 2 {
+		if points[1].To(l.A).Len() < points[0].To(l.A).Len() {
+			return []Vec{points[1], points[0]}
+		}
+	}
+
+	return points
+}
+
+// Vertices returns a slice of the four corners which make up the rectangle.
+func (r Rect) Vertices() [4]Vec {
+	return [4]Vec{
+		r.Min,
+		V(r.Min.X, r.Max.Y),
+		r.Max,
+		V(r.Max.X, r.Min.Y),
+	}
+}
+
 // Circle is a 2D circle. It is defined by two properties:
 //  - Center vector
 //  - Radius float64
@@ -398,6 +716,12 @@ func (c Circle) Contains(u Vec) bool {
 	return c.Radius >= toCenter.Len()
 }
 
+// Formula returns the values of h and k, for the equation of the circle: (x-h)^2 + (y-k)^2 = r^2
+// where r is the radius of the circle.
+func (c Circle) Formula() (h, k float64) {
+	return c.Center.X, c.Center.Y
+}
+
 // maxCircle will return the larger circle based on the radius.
 func maxCircle(c, d Circle) Circle {
 	if c.Radius < d.Radius {
@@ -476,6 +800,12 @@ func (c Circle) Intersect(d Circle) Circle {
 	}
 }
 
+// IntersectLine will return the shortest Vec such that if the Rect is moved by the Vec returned, the Line and Rect no
+// longer intersect.
+func (c Circle) IntersectLine(l Line) Vec {
+	return l.IntersectCircle(c).Scaled(-1)
+}
+
 // IntersectRect returns a minimal required Vector, such that moving the circle by that vector would stop the Circle
 // and the Rect intersecting.  This function returns a zero-vector if the Circle and Rect do not overlap, and if only
 // the perimeters touch.
@@ -552,6 +882,99 @@ func (c Circle) IntersectRect(r Rect) Vec {
 	}
 }
 
+// IntersectionPoints returns all the points where the Circle intersects with the line provided.  This can be zero, one or
+// two points, depending on the location of the shapes.  The points of intersection will be returned in order of
+// closest-to-l.A to closest-to-l.B.
+func (c Circle) IntersectionPoints(l Line) []Vec {
+	cContainsA := c.Contains(l.A)
+	cContainsB := c.Contains(l.B)
+
+	// Special case for both endpoint being contained within the circle
+	if cContainsA && cContainsB {
+		return []Vec{}
+	}
+
+	// Get closest point on the line to this circles' center
+	closestToCenter := l.Closest(c.Center)
+
+	// If the distance to the closest point is greater than the radius, there are no points of intersection
+	if closestToCenter.To(c.Center).Len() > c.Radius {
+		return []Vec{}
+	}
+
+	// If the distance to the closest point is equal to the radius, the line is tangent and the closest point is the
+	// point at which it touches the circle.
+	if closestToCenter.To(c.Center).Len() == c.Radius {
+		return []Vec{closestToCenter}
+	}
+
+	// Special case for endpoint being on the circles' center
+	if c.Center == l.A || c.Center == l.B {
+		otherEnd := l.B
+		if c.Center == l.B {
+			otherEnd = l.A
+		}
+		intersect := c.Center.Add(c.Center.To(otherEnd).Unit().Scaled(c.Radius))
+		return []Vec{intersect}
+	}
+
+	// This means the distance to the closest point is less than the radius, so there is at least one intersection,
+	// possibly two.
+
+	// If one of the end points exists within the circle, there is only one intersection
+	if cContainsA || cContainsB {
+		containedPoint := l.A
+		otherEnd := l.B
+		if cContainsB {
+			containedPoint = l.B
+			otherEnd = l.A
+		}
+
+		// Use trigonometry to get the length of the line between the contained point and the intersection point.
+		// The following is used to describe the triangle formed:
+		//  - a is the side between contained point and circle center
+		//  - b is the side between the center and the intersection point (radius)
+		//  - c is the side between the contained point and the intersection point
+		// The captials of these letters are used as the angles opposite the respective sides.
+		// a and b are known
+		a := containedPoint.To(c.Center).Len()
+		b := c.Radius
+		// B can be calculated by subtracting the angle of b (to the x-axis) from the angle of c (to the x-axis)
+		B := containedPoint.To(c.Center).Angle() - containedPoint.To(otherEnd).Angle()
+		// Using the Sin rule we can get A
+		A := math.Asin((a * math.Sin(B)) / b)
+		// Using the rule that there are 180 degrees (or Pi radians) in a triangle, we can now get C
+		C := math.Pi - A + B
+		// If C is zero, the line segment is in-line with the center-intersect line.
+		var c float64
+		if C == 0 {
+			c = b - a
+		} else {
+			// Using the Sine rule again, we can now get c
+			c = (a * math.Sin(C)) / math.Sin(A)
+		}
+		// Travelling from the contained point to the other end by length of a will provide the intersection point.
+		return []Vec{
+			containedPoint.Add(containedPoint.To(otherEnd).Unit().Scaled(c)),
+		}
+	}
+
+	// Otherwise the endpoints exist outside of the circle, and the line segment intersects in two locations.
+	// The vector formed by going from the closest point to the center of the circle will be perpendicular to the line;
+	// this forms a right-angled triangle with the intersection points, with the radius as the hypotenuse.
+	// Calculate the other triangles' sides' length.
+	a := math.Sqrt(math.Pow(c.Radius, 2) - math.Pow(closestToCenter.To(c.Center).Len(), 2))
+
+	// Travelling in both directions from the closest point by length of a will provide the two intersection points.
+	first := closestToCenter.Add(closestToCenter.To(l.A).Unit().Scaled(a))
+	second := closestToCenter.Add(closestToCenter.To(l.B).Unit().Scaled(a))
+
+	if first.To(l.A).Len() < second.To(l.A).Len() {
+		return []Vec{first, second}
+	}
+	return []Vec{second, first}
+}
+
 // Matrix is a 2x3 affine matrix that can be used for all kinds of spatial transforms, such
 // as movement, scaling and rotations.
 //

geometry_test.go

@@ -10,6 +10,53 @@ import (
 	"github.com/stretchr/testify/assert"
 )
 
+// closeEnough will shift the decimal point by the accuracy required, truncates the results and compares them.
+// Effectively this compares two floats to a given decimal point.
+//  Example:
+//  closeEnough(100.125342432, 100.125, 2) == true
+//  closeEnough(math.Pi, 3.14, 2) == true
+//  closeEnough(0.1234, 0.1245, 3) == false
+func closeEnough(got, expected float64, decimalAccuracy int) bool {
+	gotShifted := got * math.Pow10(decimalAccuracy)
+	expectedShifted := expected * math.Pow10(decimalAccuracy)
+
+	return math.Trunc(gotShifted) == math.Trunc(expectedShifted)
+}
+
+func TestRect_Edges(t *testing.T) {
+	type fields struct {
+		Min pixel.Vec
+		Max pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		want   [4]pixel.Line
+	}{
+		{
+			name:   "Get edges",
+			fields: fields{Min: pixel.V(0, 0), Max: pixel.V(10, 10)},
+			want: [4]pixel.Line{
+				pixel.L(pixel.V(0, 0), pixel.V(0, 10)),
+				pixel.L(pixel.V(0, 10), pixel.V(10, 10)),
+				pixel.L(pixel.V(10, 10), pixel.V(10, 0)),
+				pixel.L(pixel.V(10, 0), pixel.V(0, 0)),
+			},
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			r := pixel.Rect{
+				Min: tt.fields.Min,
+				Max: tt.fields.Max,
+			}
+			if got := r.Edges(); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Rect.Edges() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
 func TestRect_Resize(t *testing.T) {
 	type rectTestTransform struct {
 		name string
@@ -80,6 +127,40 @@ func TestRect_Resize(t *testing.T) {
 	}
 }
 
+func TestRect_Vertices(t *testing.T) {
+	type fields struct {
+		Min pixel.Vec
+		Max pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		want   [4]pixel.Vec
+	}{
+		{
+			name:   "Get corners",
+			fields: fields{Min: pixel.V(0, 0), Max: pixel.V(10, 10)},
+			want: [4]pixel.Vec{
+				pixel.V(0, 0),
+				pixel.V(0, 10),
+				pixel.V(10, 10),
+				pixel.V(10, 0),
+			},
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			r := pixel.Rect{
+				Min: tt.fields.Min,
+				Max: tt.fields.Max,
+			}
+			if got := r.Vertices(); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Rect.Vertices() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
 func TestMatrix_Unproject(t *testing.T) {
 	const delta = 1e-15
 	t.Run("for rotated matrix", func(t *testing.T) {
@@ -541,20 +622,86 @@ func TestCircle_Intersect(t *testing.T) {
 	}
 }
 
-func TestRect_IntersectCircle(t *testing.T) {
-	// closeEnough will shift the decimal point by the accuracy required, truncates the results and compares them.
-	// Effectively this compares two floats to a given decimal point.
-	//  Example:
-	//  closeEnough(100.125342432, 100.125, 2) == true
-	//  closeEnough(math.Pi, 3.14, 2) == true
-	//  closeEnough(0.1234, 0.1245, 3) == false
-	closeEnough := func(got, expected float64, decimalAccuracy int) bool {
-		gotShifted := got * math.Pow10(decimalAccuracy)
-		expectedShifted := expected * math.Pow10(decimalAccuracy)
-
-		return math.Trunc(gotShifted) == math.Trunc(expectedShifted)
+func TestCircle_IntersectPoints(t *testing.T) {
+	type fields struct {
+		Center pixel.Vec
+		Radius float64
 	}
+	type args struct {
+		l pixel.Line
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   []pixel.Vec
+	}{
+		{
+			name:   "Line intersects circle at two points",
+			fields: fields{Center: pixel.V(2, 2), Radius: 1},
+			args:   args{pixel.L(pixel.V(0, 0), pixel.V(10, 10))},
+			want:   []pixel.Vec{pixel.V(1.292, 1.292), pixel.V(2.707, 2.707)},
+		},
+		{
+			name:   "Line intersects circle at one point",
+			fields: fields{Center: pixel.V(-0.5, -0.5), Radius: 1},
+			args:   args{pixel.L(pixel.V(0, 0), pixel.V(10, 10))},
+			want:   []pixel.Vec{pixel.V(0.207, 0.207)},
+		},
+		{
+			name:   "Line endpoint is circle center",
+			fields: fields{Center: pixel.V(0, 0), Radius: 1},
+			args:   args{pixel.L(pixel.V(0, 0), pixel.V(10, 10))},
+			want:   []pixel.Vec{pixel.V(0.707, 0.707)},
+		},
+		{
+			name:   "Both line endpoints within circle",
+			fields: fields{Center: pixel.V(0, 0), Radius: 1},
+			args:   args{pixel.L(pixel.V(0.2, 0.2), pixel.V(0.5, 0.5))},
+			want:   []pixel.Vec{},
+		},
+		{
+			name:   "Line does not intersect circle",
+			fields: fields{Center: pixel.V(10, 0), Radius: 1},
+			args:   args{pixel.L(pixel.V(0, 0), pixel.V(10, 10))},
+			want:   []pixel.Vec{},
+		},
+		{
+			name:   "Horizontal line intersects circle at two points",
+			fields: fields{Center: pixel.V(5, 5), Radius: 1},
+			args:   args{pixel.L(pixel.V(0, 5), pixel.V(10, 5))},
+			want:   []pixel.Vec{pixel.V(4, 5), pixel.V(6, 5)},
+		},
+		{
+			name:   "Vertical line intersects circle at two points",
+			fields: fields{Center: pixel.V(5, 5), Radius: 1},
+			args:   args{pixel.L(pixel.V(5, 0), pixel.V(5, 10))},
+			want:   []pixel.Vec{pixel.V(5, 4), pixel.V(5, 6)},
+		},
+		{
+			name:   "Left and down line intersects circle at two points",
+			fields: fields{Center: pixel.V(5, 5), Radius: 1},
+			args:   args{pixel.L(pixel.V(10, 10), pixel.V(0, 0))},
+			want:   []pixel.Vec{pixel.V(5.707, 5.707), pixel.V(4.292, 4.292)},
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			c := pixel.Circle{
+				Center: tt.fields.Center,
+				Radius: tt.fields.Radius,
+			}
+			got := c.IntersectionPoints(tt.args.l)
+			for i, v := range got {
+				if !closeEnough(v.X, tt.want[i].X, 2) || !closeEnough(v.Y, tt.want[i].Y, 2) {
+					t.Errorf("Circle.IntersectPoints() = %v, want %v", v, tt.want[i])
+				}
+			}
+		})
+	}
+}
 
+func TestRect_IntersectCircle(t *testing.T) {
 	type fields struct {
 		Min pixel.Vec
 		Max pixel.Vec
@@ -690,3 +837,708 @@ func TestRect_IntersectCircle(t *testing.T) {
 		})
 	}
 }
+
+func TestRect_IntersectionPoints(t *testing.T) {
+	type fields struct {
+		Min pixel.Vec
+		Max pixel.Vec
+	}
+	type args struct {
+		l pixel.Line
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   []pixel.Vec
+	}{
+		{
+			name:   "No intersection points",
+			fields: fields{Min: pixel.V(1, 1), Max: pixel.V(5, 5)},
+			args:   args{l: pixel.L(pixel.V(-5, 0), pixel.V(-2, 2))},
+			want:   []pixel.Vec{},
+		},
+		{
+			name:   "One intersection point",
+			fields: fields{Min: pixel.V(1, 1), Max: pixel.V(5, 5)},
+			args:   args{l: pixel.L(pixel.V(2, 0), pixel.V(2, 3))},
+			want:   []pixel.Vec{pixel.V(2, 1)},
+		},
+		{
+			name:   "Two intersection points",
+			fields: fields{Min: pixel.V(1, 1), Max: pixel.V(5, 5)},
+			args:   args{l: pixel.L(pixel.V(0, 2), pixel.V(6, 2))},
+			want:   []pixel.Vec{pixel.V(1, 2), pixel.V(5, 2)},
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			r := pixel.Rect{
+				Min: tt.fields.Min,
+				Max: tt.fields.Max,
+			}
+			if got := r.IntersectionPoints(tt.args.l); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Rect.IntersectPoints() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Bounds(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		want   pixel.Rect
+	}{
+		{
+			name:   "Positive slope",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			want:   pixel.R(0, 0, 10, 10),
+		},
+		{
+			name:   "Negative slope",
+			fields: fields{A: pixel.V(10, 10), B: pixel.V(0, 0)},
+			want:   pixel.R(0, 0, 10, 10),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.Bounds(); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.Bounds() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Center(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		want   pixel.Vec
+	}{
+		{
+			name:   "Positive slope",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			want:   pixel.V(5, 5),
+		},
+		{
+			name:   "Negative slope",
+			fields: fields{A: pixel.V(10, 10), B: pixel.V(0, 0)},
+			want:   pixel.V(5, 5),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.Center(); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.Center() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Closest(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		v pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Vec
+	}{
+		{
+			name:   "Point on line",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{v: pixel.V(5, 5)},
+			want:   pixel.V(5, 5),
+		},
+		{
+			name:   "Point on next to line",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{v: pixel.V(0, 10)},
+			want:   pixel.V(5, 5),
+		},
+		{
+			name:   "Point on next to vertical line",
+			fields: fields{A: pixel.V(5, 0), B: pixel.V(5, 10)},
+			args:   args{v: pixel.V(6, 5)},
+			want:   pixel.V(5, 5),
+		},
+		{
+			name:   "Point on next to horizontal line",
+			fields: fields{A: pixel.V(0, 5), B: pixel.V(10, 5)},
+			args:   args{v: pixel.V(5, 6)},
+			want:   pixel.V(5, 5),
+		},
+		{
+			name:   "Point far from line",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{v: pixel.V(80, -70)},
+			want:   pixel.V(5, 5),
+		},
+		{
+			name:   "Point on inline with line",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{v: pixel.V(20, 20)},
+			want:   pixel.V(10, 10),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.Closest(tt.args.v); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.Closest() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Contains(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		v pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   bool
+	}{
+		{
+			name:   "Point on line",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{v: pixel.V(5, 5)},
+			want:   true,
+		},
+		{
+			name:   "Point on negative sloped line",
+			fields: fields{A: pixel.V(0, 10), B: pixel.V(10, 0)},
+			args:   args{v: pixel.V(5, 5)},
+			want:   true,
+		},
+		{
+			name:   "Point not on line",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{v: pixel.V(0, 10)},
+			want:   false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.Contains(tt.args.v); got != tt.want {
+				t.Errorf("Line.Contains() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Formula(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		wantM  float64
+		wantB  float64
+	}{
+		{
+			name:   "Getting formula - 45 degs",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			wantM:  1,
+			wantB:  0,
+		},
+		{
+			name:   "Getting formula - 90 degs",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(0, 10)},
+			wantM:  math.Inf(1),
+			wantB:  math.NaN(),
+		},
+		{
+			name:   "Getting formula - 0 degs",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 0)},
+			wantM:  0,
+			wantB:  0,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			gotM, gotB := l.Formula()
+			if gotM != tt.wantM {
+				t.Errorf("Line.Formula() gotM = %v, want %v", gotM, tt.wantM)
+			}
+			if gotB != tt.wantB {
+				if math.IsNaN(tt.wantB) && !math.IsNaN(gotB) {
+					t.Errorf("Line.Formula() gotB = %v, want %v", gotB, tt.wantB)
+				}
+			}
+		})
+	}
+}
+
+func TestLine_Intersect(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		k pixel.Line
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Vec
+		want1  bool
+	}{
+		{
+			name:   "Lines intersect",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{k: pixel.L(pixel.V(0, 10), pixel.V(10, 0))},
+			want:   pixel.V(5, 5),
+			want1:  true,
+		},
+		{
+			name:   "Lines intersect 2",
+			fields: fields{A: pixel.V(5, 1), B: pixel.V(1, 1)},
+			args:   args{k: pixel.L(pixel.V(2, 0), pixel.V(2, 3))},
+			want:   pixel.V(2, 1),
+			want1:  true,
+		},
+		{
+			name:   "Line intersect with vertical",
+			fields: fields{A: pixel.V(5, 0), B: pixel.V(5, 10)},
+			args:   args{k: pixel.L(pixel.V(0, 0), pixel.V(10, 10))},
+			want:   pixel.V(5, 5),
+			want1:  true,
+		},
+		{
+			name:   "Line intersect with horizontal",
+			fields: fields{A: pixel.V(0, 5), B: pixel.V(10, 5)},
+			args:   args{k: pixel.L(pixel.V(0, 0), pixel.V(10, 10))},
+			want:   pixel.V(5, 5),
+			want1:  true,
+		},
+		{
+			name:   "Lines don't intersect",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{k: pixel.L(pixel.V(0, 10), pixel.V(1, 20))},
+			want:   pixel.ZV,
+			want1:  false,
+		},
+		{
+			name:   "Lines don't intersect 2",
+			fields: fields{A: pixel.V(1, 1), B: pixel.V(1, 5)},
+			args:   args{k: pixel.L(pixel.V(-5, 0), pixel.V(-2, 2))},
+			want:   pixel.ZV,
+			want1:  false,
+		},
+		{
+			name:   "Lines don't intersect 3",
+			fields: fields{A: pixel.V(2, 0), B: pixel.V(2, 3)},
+			args:   args{k: pixel.L(pixel.V(1, 5), pixel.V(5, 5))},
+			want:   pixel.ZV,
+			want1:  false,
+		},
+		{
+			name:   "Lines parallel",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{k: pixel.L(pixel.V(0, 1), pixel.V(10, 11))},
+			want:   pixel.ZV,
+			want1:  false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			got, got1 := l.Intersect(tt.args.k)
+			if !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.Intersect() got = %v, want %v", got, tt.want)
+			}
+			if got1 != tt.want1 {
+				t.Errorf("Line.Intersect() got1 = %v, want %v", got1, tt.want1)
+			}
+		})
+	}
+}
+
+func TestLine_IntersectCircle(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		c pixel.Circle
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Vec
+	}{
+		{
+			name:   "Cirle intersects",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{c: pixel.C(pixel.V(6, 4), 2)},
+			want:   pixel.V(0.5857864376269049, -0.5857864376269049),
+		},
+		{
+			name:   "Cirle doesn't intersects",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{c: pixel.C(pixel.V(0, 5), 1)},
+			want:   pixel.ZV,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.IntersectCircle(tt.args.c); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.IntersectCircle() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_IntersectRect(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		r pixel.Rect
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Vec
+	}{
+		{
+			name:   "Line through rect vertically",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(0, 10)},
+			args:   args{r: pixel.R(-1, 1, 5, 5)},
+			want:   pixel.V(-1, 0),
+		},
+		{
+			name:   "Line through rect horizontally",
+			fields: fields{A: pixel.V(0, 1), B: pixel.V(10, 1)},
+			args:   args{r: pixel.R(1, 0, 5, 5)},
+			want:   pixel.V(0, -1),
+		},
+		{
+			name:   "Line through rect diagonally bottom and left edges",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{r: pixel.R(0, 2, 3, 3)},
+			want:   pixel.V(-1, 1),
+		},
+		{
+			name:   "Line through rect diagonally top and right edges",
+			fields: fields{A: pixel.V(10, 0), B: pixel.V(0, 10)},
+			args:   args{r: pixel.R(5, 0, 8, 3)},
+			want:   pixel.V(-2.5, -2.5),
+		},
+		{
+			name:   "Line with not rect intersect",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{r: pixel.R(20, 20, 21, 21)},
+			want:   pixel.ZV,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.IntersectRect(tt.args.r); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.IntersectRect() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Len(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		want   float64
+	}{
+		{
+			name:   "End right-up of start",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(3, 4)},
+			want:   5,
+		},
+		{
+			name:   "End left-up of start",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(-3, 4)},
+			want:   5,
+		},
+		{
+			name:   "End right-down of start",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(3, -4)},
+			want:   5,
+		},
+		{
+			name:   "End left-down of start",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(-3, -4)},
+			want:   5,
+		},
+		{
+			name:   "End same as start",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(0, 0)},
+			want:   0,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.Len(); got != tt.want {
+				t.Errorf("Line.Len() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Rotated(t *testing.T) {
+	// round returns the nearest integer, rounding ties away from zero.
+	// This is required because `math.Round` wasn't introduced until Go1.10
+	round := func(x float64) float64 {
+		t := math.Trunc(x)
+		if math.Abs(x-t) >= 0.5 {
+			return t + math.Copysign(1, x)
+		}
+		return t
+	}
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		around pixel.Vec
+		angle  float64
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Line
+	}{
+		{
+			name:   "Rotating around line center",
+			fields: fields{A: pixel.V(1, 1), B: pixel.V(3, 3)},
+			args:   args{around: pixel.V(2, 2), angle: math.Pi},
+			want:   pixel.L(pixel.V(3, 3), pixel.V(1, 1)),
+		},
+		{
+			name:   "Rotating around x-y origin",
+			fields: fields{A: pixel.V(1, 1), B: pixel.V(3, 3)},
+			args:   args{around: pixel.V(0, 0), angle: math.Pi},
+			want:   pixel.L(pixel.V(-1, -1), pixel.V(-3, -3)),
+		},
+		{
+			name:   "Rotating around line end",
+			fields: fields{A: pixel.V(1, 1), B: pixel.V(3, 3)},
+			args:   args{around: pixel.V(1, 1), angle: math.Pi},
+			want:   pixel.L(pixel.V(1, 1), pixel.V(-1, -1)),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			// Have to round the results, due to floating-point in accuracies.  Results are correct to approximately
+			// 10 decimal places.
+			got := l.Rotated(tt.args.around, tt.args.angle)
+			if round(got.A.X) != tt.want.A.X ||
+				round(got.B.X) != tt.want.B.X ||
+				round(got.A.Y) != tt.want.A.Y ||
+				round(got.B.Y) != tt.want.B.Y {
+				t.Errorf("Line.Rotated() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_Scaled(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		scale float64
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Line
+	}{
+		{
+			name:   "Scaling by 1",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{scale: 1},
+			want:   pixel.L(pixel.V(0, 0), pixel.V(10, 10)),
+		},
+		{
+			name:   "Scaling by >1",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{scale: 2},
+			want:   pixel.L(pixel.V(-5, -5), pixel.V(15, 15)),
+		},
+		{
+			name:   "Scaling by <1",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{scale: 0.5},
+			want:   pixel.L(pixel.V(2.5, 2.5), pixel.V(7.5, 7.5)),
+		},
+		{
+			name:   "Scaling by -1",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{scale: -1},
+			want:   pixel.L(pixel.V(10, 10), pixel.V(0, 0)),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.Scaled(tt.args.scale); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.Scaled() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_ScaledXY(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	type args struct {
+		around pixel.Vec
+		scale  float64
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		args   args
+		want   pixel.Line
+	}{
+		{
+			name:   "Scaling by 1 around origin",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{around: pixel.ZV, scale: 1},
+			want:   pixel.L(pixel.V(0, 0), pixel.V(10, 10)),
+		},
+		{
+			name:   "Scaling by >1 around origin",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{around: pixel.ZV, scale: 2},
+			want:   pixel.L(pixel.V(0, 0), pixel.V(20, 20)),
+		},
+		{
+			name:   "Scaling by <1 around origin",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{around: pixel.ZV, scale: 0.5},
+			want:   pixel.L(pixel.V(0, 0), pixel.V(5, 5)),
+		},
+		{
+			name:   "Scaling by -1 around origin",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(10, 10)},
+			args:   args{around: pixel.ZV, scale: -1},
+			want:   pixel.L(pixel.V(0, 0), pixel.V(-10, -10)),
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.ScaledXY(tt.args.around, tt.args.scale); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Line.ScaledXY() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
+func TestLine_String(t *testing.T) {
+	type fields struct {
+		A pixel.Vec
+		B pixel.Vec
+	}
+	tests := []struct {
+		name   string
+		fields fields
+		want   string
+	}{
+		{
+			name:   "Getting string",
+			fields: fields{A: pixel.V(0, 0), B: pixel.V(1, 1)},
+			want:   "Line(Vec(0, 0), Vec(1, 1))",
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			l := pixel.Line{
+				A: tt.fields.A,
+				B: tt.fields.B,
+			}
+			if got := l.String(); got != tt.want {
+				t.Errorf("Line.String() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}