diff --git a/BezierKit.podspec b/BezierKit.podspec
index 65f52a85..b1f354cf 100644
--- a/BezierKit.podspec
+++ b/BezierKit.podspec
@@ -5,7 +5,7 @@
 
 Pod::Spec.new do |s|
   s.name         = "BezierKit"
-  s.version      = "0.1.11"
+  s.version      = "0.1.12"
   s.summary      = "comprehensive Bezier curve library written in Swift"
   s.homepage     = "https://github.com/hfutrell/BezierKit"
   s.license      = "MIT"
diff --git a/BezierKit/BezierKitTests/PathTests.swift b/BezierKit/BezierKitTests/PathTests.swift
index ee3c4fd9..74da4451 100644
--- a/BezierKit/BezierKitTests/PathTests.swift
+++ b/BezierKit/BezierKitTests/PathTests.swift
@@ -418,6 +418,7 @@ class PathTests: XCTestCase {
             CGPoint(x: 1, y: 1),
             CGPoint(x: 2, y: 1),
             CGPoint(x: 0, y: 3),
+            CGPoint(x: 0, y: 0)
         ]
         let cgPath = CGMutablePath()
         cgPath.addLines(between: points)
@@ -437,6 +438,14 @@ class PathTests: XCTestCase {
         XCTAssertEqual(result.subpaths.count, 1)
         XCTAssertTrue(componentsEqualAsideFromElementOrdering(result.subpaths[0], expectedResult.subpaths[0]))
         
+        // check also that the algorithm works when the first point falls *inside* the path
+        let cgPathAlt = CGMutablePath()
+        cgPathAlt.addLines(between: Array(points[3..<points.count]) + Array(points[1...3]))
+        let pathAlt = Path(cgPath: cgPathAlt)
+
+        let resultAlt = pathAlt.crossingsRemoved()
+        XCTAssertEqual(resultAlt.subpaths.count, 1)
+        XCTAssertTrue(componentsEqualAsideFromElementOrdering(resultAlt.subpaths[0], expectedResult.subpaths[0]))
     }
     
     func testCrossingsRemovedNoCrossings() {
diff --git a/BezierKit/Library/AugmentedGraph.swift b/BezierKit/Library/AugmentedGraph.swift
index e3dbfcdc..8f161952 100644
--- a/BezierKit/Library/AugmentedGraph.swift
+++ b/BezierKit/Library/AugmentedGraph.swift
@@ -172,14 +172,16 @@ internal class PathLinkedListRepresentation {
             // determine the initial winding count (winding count before first vertex)
             var initialWinding = 0
             if useRelativeWinding {
+                var minimumWinding = Int.max
                 self.forEachVertexInComponent(atIndex: i) { v in
                     guard v.isIntersection else {
                         return
                     }
-                    if v.intersectionInfo.nextWinding < -initialWinding {
-                        initialWinding = v.intersectionInfo.nextWinding
+                    if v.intersectionInfo.nextWinding < minimumWinding {
+                        minimumWinding = v.intersectionInfo.nextWinding
                     }
                 }
+                initialWinding = -minimumWinding
             }
             else {
                 initialWinding = path.windingCount(lists[i][0].emitPrevious().compute(0.5))
diff --git a/README.md b/README.md
index 618f3100..45607222 100644
--- a/README.md
+++ b/README.md
@@ -46,7 +46,7 @@ To integrate BezierKit into your Xcode project using CocoaPods, add it to your t
 
 ```ruby
 target '<Your Target Name>' do
-    pod 'BezierKit', '>= 0.1.11'
+    pod 'BezierKit', '>= 0.1.12'
 end
 ```