diff --git a/geometry.go b/geometry.go
index 4b45afb..f2c0017 100644
--- a/geometry.go
+++ b/geometry.go
@@ -314,38 +314,26 @@ func (l Line) Intersect(k Line) (Vec, bool) {
 		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
 		}
 
-		maxVerticalY := verticalLine.A.Y
-		minVerticalY := verticalLine.B.Y
-		if verticalLine.B.Y > maxVerticalY {
-			maxVerticalY = verticalLine.B.Y
-			minVerticalY = verticalLine.A.Y
-		}
-
-		y := intersectM*l.A.X + intersectB
-		if y > maxVerticalY || y < minVerticalY {
-			// Point is not on the horizontal line
-			return ZV, false
-		}
-
-		return V(l.A.X, y), true
+		y = intersectM*l.A.X + intersectB
+		x = l.A.X
+	} else {
+		// Coordinates of intersect
+		x = (kb - lb) / (lm - km)
+		y = lm*x + lb
 	}
 
-	// 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
@@ -619,6 +607,28 @@ 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.
+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 := edge.Intersect(l); ok {
+			fmt.Println(edge)
+			fmt.Println(l)
+			fmt.Println(intersect)
+			pointMap[intersect] = struct{}{}
+		}
+	}
+
+	points := make([]Vec, 0, len(pointMap))
+	for point := range pointMap {
+		points = append(points, point)
+	}
+	return points
+}
+
 // Vertices returns a slice of the four corners which make up the rectangle.
 func (r Rect) Vertices() [4]Vec {
 	return [4]Vec{
@@ -858,6 +868,12 @@ 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.
+func (c Circle) IntersectionPoints(l Line) []Vec {
+	return []Vec{}
+}
+
 // Matrix is a 2x3 affine matrix that can be used for all kinds of spatial transforms, such
 // as movement, scaling and rotations.
 //
diff --git a/geometry_test.go b/geometry_test.go
index 488a5a3..4f8f8df 100644
--- a/geometry_test.go
+++ b/geometry_test.go
@@ -609,6 +609,35 @@ func TestCircle_Intersect(t *testing.T) {
 	}
 }
 
+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
+	}{
+		// TODO: Add test cases.
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			c := pixel.Circle{
+				Center: tt.fields.Center,
+				Radius: tt.fields.Radius,
+			}
+			if got := c.IntersectionPoints(tt.args.l); !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("Circle.IntersectPoints() = %v, want %v", got, tt.want)
+			}
+		})
+	}
+}
+
 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.
@@ -759,6 +788,52 @@ 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, 2))},
+		// 	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
@@ -1008,6 +1083,13 @@ func TestLine_Intersect(t *testing.T) {
 			want:   pixel.V(5, 5),
 			want1:  true,
 		},
+		{
+			name:   "Lines 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:   "Line intersect with vertical",
 			fields: fields{A: pixel.V(5, 0), B: pixel.V(5, 10)},