From 3d8e58a61c2ad7d6e2eb32eefddc99f8272dcb32 Mon Sep 17 00:00:00 2001
From: Derek McQuay <derekmcquay@gmail.com>
Date: Sat, 27 Aug 2016 18:55:26 -0700
Subject: [PATCH] added function to get intersection of two lines

---
 point.go      | 33 ++++++++++++++++++++++++++++++++-
 point_test.go | 23 +++++++++++++++++++++++
 2 files changed, 55 insertions(+), 1 deletion(-)

diff --git a/point.go b/point.go
index ce2881e..02ec13f 100644
--- a/point.go
+++ b/point.go
@@ -1,6 +1,9 @@
 package rect
 
-import "math"
+import (
+	"fmt"
+	"math"
+)
 
 type Point struct {
 	X, Y float64
@@ -25,6 +28,34 @@ func onLine(rp1, rp2, p Point) bool {
 	return false
 }
 
+func lineHelper(l line) (float64, float64, float64) {
+	a := l.pt2.Y - l.pt1.Y
+	b := l.pt1.X - l.pt2.X
+	c := a*l.pt1.X + b*l.pt1.Y
+	return a, b, c
+}
+
+func lineIntersection(l1, l2 line) (Point, error) {
+	a1, b1, c1 := lineHelper(l1)
+	a2, b2, c2 := lineHelper(l2)
+	det := a1*b2 - a2*b1
+
+	if det != 0 {
+		x := ((b2*c1 - b1*c2) / det)
+		y := ((a1*c2 - a2*c1) / det)
+		minx1, maxx1 := math.Min(l1.pt1.X, l1.pt2.X), math.Max(l1.pt1.X, l1.pt2.X)
+		miny1, maxy1 := math.Min(l1.pt1.Y, l1.pt2.Y), math.Max(l1.pt1.Y, l1.pt2.Y)
+		minx2, maxx2 := math.Min(l2.pt1.X, l2.pt2.X), math.Max(l2.pt1.X, l2.pt2.X)
+		miny2, maxy2 := math.Min(l2.pt1.Y, l2.pt2.Y), math.Max(l2.pt1.Y, l2.pt2.Y)
+		if minx1 <= x && x <= maxx1 && miny1 <= y && y <= maxy1 {
+			if minx2 <= x && x <= maxx2 && miny2 <= y && y <= maxy2 {
+				return Point{x, y}, nil
+			}
+		}
+	}
+	return Point{}, fmt.Errorf("lines do not intersect")
+}
+
 func lineOnLine(l1, l2 line) bool {
 	if onLine(l1.pt1, l1.pt2, l2.pt1) && onLine(l1.pt1, l1.pt2, l2.pt2) {
 		return true
diff --git a/point_test.go b/point_test.go
index ede848b..954c82f 100644
--- a/point_test.go
+++ b/point_test.go
@@ -50,3 +50,26 @@ func TestOnLine(t *testing.T) {
 
 	}
 }
+
+func TestLineIntersection(t *testing.T) {
+	var lineIntersectionTest = []struct {
+		l        []line
+		expected Point
+	}{
+		{[]line{line{Point{0, 0}, Point{2, 2}}, line{Point{2, 0}, Point{0, 2}}}, Point{1, 1}},
+		{[]line{line{Point{0, 0}, Point{-2, -2}}, line{Point{-2, 0}, Point{0, -2}}}, Point{-1, -1}},
+		{[]line{line{Point{0, 0}, Point{-2, -2}}, line{Point{1, 0}, Point{1, -7}}}, Point{0, 0}},
+		{[]line{line{Point{5, 8}, Point{8, 5}}, line{Point{3, 7}, Point{7, 3}}}, Point{0, 0}},
+	}
+	for _, rt := range lineIntersectionTest {
+		actual := lineIntersection(rt.l[0], rt.l[1])
+		if actual != rt.expected {
+			t.Errorf(
+				"failed spiral:\n\texpected: %f\n\t  actual: %f",
+				rt.expected,
+				actual,
+			)
+		}
+
+	}
+}