diff --git a/rdp/rdp.go b/rdp/rdp.go
index 759309e..86be545 100644
--- a/rdp/rdp.go
+++ b/rdp/rdp.go
@@ -15,7 +15,7 @@ type Point struct {
 // Note: The resulting slice is a reslice of given points (it shares the same underlying array) for efficiency.
 // It works similar to append, so the input points should not be used after this call, use only the returned value.
 func Simplify(points []Point, epsilon float64) []Point {
-	if len(points) < 2 {
+	if len(points) <= 2 {
 		return points
 	}
 
@@ -38,19 +38,31 @@ func Simplify(points []Point, epsilon float64) []Point {
 		return append(points[:0], first, last)
 	}
 
-	firstHalf, lastHalf := points[:index], points[index:]
+	// Move index to avoids infinite recursive as slice input
+	// for next operation is never changed if we keep it as is.
+	if index == 0 || index == len(points) {
+		index++
+	}
+
+	left, right := points[:index], points[index:]
 
-	return append(Simplify(firstHalf, epsilon), Simplify(lastHalf, epsilon)...)
+	return append(Simplify(left, epsilon), Simplify(right, epsilon)...)
 }
 
 // perpendicularDistance calculates the perpendicular distance from a point to a line segment
 func perpendicularDistance(p, start, end Point) float64 {
 	if start.X == end.X && start.Y == end.Y {
-		return euclidean(start, end)
+		// Find distance between p and (start or end)
+		return euclidean(p, start)
 	}
-	numerator := math.Abs((end.Y-start.Y)*p.X - (end.X-start.X)*p.Y + end.X*start.Y - end.Y*start.X)
-	denominator := euclidean(start, end)
-	return numerator / denominator
+
+	// Standard Form: Ax + Bx + C = 0
+	A := end.Y - start.Y
+	B := start.X - end.X
+	C := (end.X * start.Y) - (start.X * end.Y)
+
+	// d = | Ax + By + C = 0 | / ✓(A²+B²)
+	return math.Abs(A*p.X+B*p.Y+C) / math.Sqrt(A*A+B*B)
 }
 
 // euclidean calculates the distance between two points.
diff --git a/rdp/rdp_test.go b/rdp/rdp_test.go
index 4df9db8..b0404a5 100644
--- a/rdp/rdp_test.go
+++ b/rdp/rdp_test.go
@@ -6,6 +6,7 @@ import (
 	"flag"
 	"fmt"
 	"io"
+	"math"
 	"math/rand"
 	"os"
 	"strconv"
@@ -85,6 +86,45 @@ func TestSimplify(t *testing.T) {
 	}
 }
 
+func TestPerpendicularDistance(t *testing.T) {
+	tt := []struct {
+		name  string
+		p     Point
+		start Point
+		end   Point
+		d     float64
+		prec  float64
+	}{
+		{
+			name:  "valid result",
+			p:     Point{X: 5, Y: 6},
+			start: Point{X: 0, Y: -1.3333333333333333},
+			end:   Point{X: 2, Y: 0},
+			d:     3.328,
+			prec:  1000,
+		},
+		{
+			name:  "zero result",
+			p:     Point{X: 5, Y: 6},
+			start: Point{X: 2, Y: 0},
+			end:   Point{X: 2, Y: 0},
+			d:     6.708, // euclidean((5,6), (2,0))
+			prec:  1000,
+		},
+	}
+
+	for i, tc := range tt {
+		t.Run(fmt.Sprintf("[%d] %s", i, tc.name), func(t *testing.T) {
+			d := perpendicularDistance(tc.p, tc.start, tc.end)
+			d = math.Round(d*tc.prec) / tc.prec
+			tc.d = math.Round(tc.d*tc.prec) / tc.prec
+			if d != tc.d {
+				t.Fatalf("expected: %g, got: %g", tc.d, d)
+			}
+		})
+	}
+}
+
 var update = flag.Bool("update", false, "update the test file")
 
 func BenchmarkSimplify(b *testing.B) {