modified from side drawing to point drawing

PinwheelTiling/PinwheelTilingPath.cs

@@ -1,4 +1,5 @@
-using Avalonia.Controls.Selection;
+using System.Reflection.Metadata;
+using Avalonia.Controls.Selection;
 using LeoTurtle;
 
 namespace PinwheelTiling;
@@ -23,27 +24,106 @@ public static class PinwheelTilingPath
         const double sideA = 40.0D;
         const double sideB = 80.0D;
         double sideC = CalculateHyptonuse(sideA, sideB);
-        MakeTriangle(turtle, sideA, sideB, sideC);
+        
+        _endPoint = new Point(_startPoint.X + sideB, _startPoint.Y + sideA);
+        Triangle triangle = MakeTriangle(_startPoint, _endPoint);
+        Triangle[] subdivision = GetSubdivision(triangle);
+        
+        DrawSubdivision(turtle, subdivision);
     }
 
-    // TODO - implement your algorithm
+    private static Triangle MakeTriangle(Point startingPoint,
-    private static void MakeTriangle(SmartTurtle turtle, double sideA, double sideB, double sideC)
+                                         Point endingPoint)
     {
+        Point pointA = startingPoint;
+        Point pointB = endingPoint;
+        Point pointC = new Point(endingPoint.X, startingPoint.Y);
+
+        return new Triangle(pointA, pointB, pointC);
+    }
+    
+    private static Triangle[] GetSubdivision(Triangle triangle)
+    {
+        double sideA = triangle.B.Y - triangle.C.Y;
+        double sideB = triangle.C.X - triangle.A.X;
+        double sideC = CalculateHyptonuse(sideA, sideB);
+        Point startingPoint = new Point(triangle.A.X, triangle.A.Y);
+        Point endingPoint = new Point(triangle.B.X, triangle.B.Y);
+        
+        //calculate parent sides
         double height = CalculateHeight(sideA, sideB, sideC);
         double sideE = height / 2;
-        double sideF = CalculateHyptonuse(sideE, height);
+        //double sideF = CalculateHyptonuse(sideE, height);
-        _endPoint = new Point(_startPoint.X + sideB, _startPoint.Y + sideA);
         
-        //Draw it now
+        //calculate additional sides that are part of the parent triangle
-        DrawTriangle(turtle, sideA, sideB, sideC, height, sideE, sideF);
+        double sideB1 = sideB / 2;
+        double sideC1 = Math.Sqrt(Math.Pow(sideA, 2) - Math.Pow(height, 2));
+        //double sideC2;
+        double sideC3 = Math.Sqrt(Math.Pow(sideB1, 2) - Math.Pow(sideE, 2));
+
+        //calculate additional sides that are |not part/not important at all| for the parent triangle
+        double heightOfTriangle0 = CalculateHeight(sideC1, height, sideA);
+        double heightOfTriangle1 = CalculateHeight(sideE, height, sideB1);
+        double heightOfTriangle2 = CalculateHeight(sideE, sideC3, sideB1);
+        double sideB1SegmentOfTriangle1 = Math.Sqrt(Math.Pow(sideE, 2) - Math.Pow(heightOfTriangle1, 2));
+        double sideB1SegmentOfTriangle2 = Math.Sqrt(Math.Pow(sideE, 2) - Math.Pow(heightOfTriangle2, 2));
+        double heightOfAllExceptTriangle0 = CalculateHeight(height, sideC - sideC1, sideB);
+        double sideB1SegmentOfAllTrianglesExcept0
+            = Math.Sqrt(Math.Pow(sideC - sideC1, 2) - Math.Pow(heightOfAllExceptTriangle0, 2));
+        
+        //create Points
+        Point pointA = startingPoint;
+        Point pointB = endingPoint;
+        Point pointC = new Point(endingPoint.X, startingPoint.Y);
+        Point pointD = new Point(startingPoint.X + sideB1SegmentOfAllTrianglesExcept0, startingPoint.Y + heightOfAllExceptTriangle0);
+        Point pointE = new Point(startingPoint.X + sideB1 - sideB1SegmentOfTriangle2, startingPoint.Y + heightOfTriangle2);
+        Point pointF = new Point(startingPoint.X + sideB1, startingPoint.Y);
+        Point pointH = new Point(startingPoint.X + sideB - sideB1SegmentOfTriangle1, startingPoint.Y + heightOfTriangle1);
+
+        Triangle triangle0 = new Triangle(pointC, pointB, pointD);
+        Triangle triangle1 = new Triangle(pointF, pointC, pointH);
+        Triangle triangle2 = new Triangle(pointA, pointF, pointE);
+        Triangle triangle3 = new Triangle(pointF, pointD, pointH);
+        Triangle triangle4 = new Triangle(pointD, pointF, pointE);
+
+        Triangle[] subdivisionTriangles = { triangle0, triangle1, triangle2, triangle3, triangle4 };
+
+        return subdivisionTriangles;
 
         double CalculateHeight(double a, double b, double c)
         {
+            //using Heron's formula
             double s = (a + b + c) / 2;
             return (2 / c) * Math.Sqrt(s * (s - a) * (s - b) * (s - c));
         }
     }
 
+    private static void DrawSubdivision(SmartTurtle turtle, Triangle[] subdivision)
+    {
+        foreach (var triangle in subdivision)      
+        {
+            DrawSimpleTriangle(turtle, triangle);
+        }
+    }
+
+    private static void DrawSimpleTriangle(SmartTurtle turtle, Triangle triangle)
+    {
+        turtle.Teleport(triangle.A.X, triangle.A.Y);
+        
+        double sideAB = DistanceBetweenPoints(triangle.A, triangle.B);
+        double sideBC = DistanceBetweenPoints(triangle.B, triangle.C);
+        double sideCA = DistanceBetweenPoints(triangle.C, triangle.A);
+        
+        turtle.LookAt(triangle.B.X, triangle.B.Y);
+        turtle.MoveForward(sideAB);
+    
+        turtle.LookAt(triangle.C.X, triangle.C.Y);
+        turtle.MoveForward(sideBC);
+    
+        turtle.LookAt(triangle.A.X, triangle.A.Y);
+        turtle.MoveForward(sideCA);
+    }
+
     private static void DrawTriangle(SmartTurtle turtle, double a, double b, double c, double h, double e, double f)
     {
         //Draw base triangle