Refactor Plane. Add validity check.

src/GShark.Test.XUnit/Core/TrigonometryTests.cs

@@ -32,7 +32,7 @@ public void It_Returns_True_If_Three_Points_Are_Collinear()
             Point3 pt3 = new Point3( 51.299, 37.950, 0.0);
 
             // Assert
-            Trigonometry.AreThreePointsCollinear(pt1, pt2, pt3, GeoSharkMath.MinTolerance).Should().BeTrue();
+            Trigonometry.ArePointsCollinear(pt1, pt2, pt3, GeoSharkMath.MinTolerance).Should().BeTrue();
         }
 
         [Fact]
@@ -44,7 +44,7 @@ public void It_Returns_False_If_Three_Points_Are_Not_Collinear()
             Point3 pt3 = new Point3( 51.299, 37.950, 0.0);
 
             // Assert
-            Trigonometry.AreThreePointsCollinear(pt1, pt2, pt3, GeoSharkMath.MinTolerance).Should().BeFalse();
+            Trigonometry.ArePointsCollinear(pt1, pt2, pt3, GeoSharkMath.MinTolerance).Should().BeFalse();
         }
 
         [Theory]

src/GShark.Test.XUnit/Geometry/PlaneTests.cs

@@ -37,6 +37,19 @@ public void It_Initializes_A_Plane()
             plane.Origin.Equals(origin).Should().BeTrue();
         }
 
+        [Fact]
+        public void It_Checks_If_Plane_Is_Valid()
+        {
+            //Arrange
+            var validPlane = new Plane(new Point3(5, 5, 5), new Vector3(10, 0, 0), new Vector3(0, 5, 0));
+            var invalidPlane = new Plane(validPlane);
+            invalidPlane.XAxis = new Vector3(5,5,5);
+
+            //Assert
+            validPlane.IsValid.Should().BeTrue();
+            invalidPlane.IsValid.Should().BeFalse();
+        }
+
         [Fact]
         public void It_Trows_An_Exception_If_The_Three_Point_Are_Collinear()
         {
@@ -54,7 +67,7 @@ public void It_Trows_An_Exception_If_The_Three_Point_Are_Collinear()
         }
 
         [Fact]
-        public void It_Creates_A_Plane_By_Tree_Points()
+        public void It_Creates_A_Plane_By_Three_Points()
         {
             // Arrange
             var pt1 = new Point3(20, 20, 0);
@@ -92,7 +105,7 @@ public void It_Returns_A_Flipped_Plane()
         {
             // Arrange
             var plane = Plane.PlaneXY;
-            var expectedPlane = new Plane(Plane.PlaneXY.Origin, -plane.XAxis, plane.YAxis);
+            var expectedPlane = new Plane(Plane.PlaneXY.Origin, plane.YAxis, plane.XAxis);
 
             // Act
             Plane flippedPlane = plane.Flip();

src/GShark.Test.XUnit/Operation/FittingTests.cs

@@ -85,7 +85,7 @@ public void Returns_A_Sets_Of_Interpolated_Beziers_From_A_Collection_Of_Points()
             crvs.Count.Should().Be(4);
             for (int i = 0; i < crvs.Count - 1; i++)
             {
-               bool areCollinear = Trigonometry.AreThreePointsCollinear(crvs[i].LocationPoints[2], crvs[i].LocationPoints[3],
+               bool areCollinear = Trigonometry.ArePointsCollinear(crvs[i].LocationPoints[2], crvs[i].LocationPoints[3],
                     crvs[i + 1].LocationPoints[1]);
                areCollinear.Should().BeTrue();
             }

src/GShark/Core/Trigonometry.cs

@@ -46,7 +46,7 @@ public static bool ArePointsCoplanar(IList<Point3> points)
         /// <param name="pt3">Third point.</param>
         /// <param name="tol">Tolerance ser per default as 1e-6</param>
         /// <returns>True if the three points are collinear.</returns>
-        public static bool AreThreePointsCollinear(Point3 pt1, Point3 pt2, Point3 pt3, double tol = 1e-6)
+        public static bool ArePointsCollinear(Point3 pt1, Point3 pt2, Point3 pt3, double tol = GeoSharkMath.MaxTolerance)
         {
             // Find the area of the triangle without using square root and multiply it for 0.5
             // http://www.stumblingrobot.com/2016/05/01/use-cross-product-compute-area-triangles-given-vertices/

src/GShark/Geometry/Plane.cs

@@ -19,9 +19,9 @@ public class Plane : IEquatable<Plane>, ITransformable<Plane>
         /// <param name="direction">The vector representing the normal of the plane.</param>
         public Plane(Point3 origin, Vector3 direction)
         {
-            ZAxis = direction.Unitize();
-            XAxis = Vector3.XAxis.PerpendicularTo(ZAxis).Unitize();
-            YAxis = Vector3.CrossProduct(ZAxis, XAxis).Unitize();
+            var normal = direction.Unitize();
+            XAxis = Vector3.XAxis.PerpendicularTo(normal).Unitize();
+            YAxis = Vector3.CrossProduct(normal, XAxis).Unitize();
             Origin = origin;
         }
 
@@ -33,7 +33,7 @@ public Plane(Point3 origin, Vector3 direction)
         /// <param name="pt3">Third point representing the y direction.</param>
         public Plane(Point3 pt1, Point3 pt2, Point3 pt3)
         {
-            if(LinearAlgebra.Orientation(pt1, pt2, pt3) == 0)
+            if(Trigonometry.ArePointsCollinear(pt1, pt2, pt3))
             {
                 throw new Exception("Plane cannot be created, the tree points must not be collinear");
             }
@@ -45,7 +45,6 @@ public Plane(Point3 pt1, Point3 pt2, Point3 pt3)
             Origin = pt1;
             XAxis = dir1.Unitize();
             YAxis = Vector3.CrossProduct(normal, dir1).Unitize();
-            ZAxis = normal.Unitize();
         }
 
         /// <summary>
@@ -59,7 +58,19 @@ public Plane(Point3 origin, Vector3 xDirection, Vector3 yDirection)
             Origin = origin;
             XAxis = xDirection.IsUnitVector ? xDirection : xDirection.Unitize();
             YAxis = yDirection.IsUnitVector ? yDirection : yDirection.Unitize();
-            ZAxis = Vector3.CrossProduct(XAxis, YAxis);
+
+        }
+
+        /// <summary>
+        /// Constructs a plane from another plane.
+        /// </summary>
+        /// <param name="plane">Input plane.</param>
+        public Plane(Plane plane)
+        {
+            Origin = plane.Origin;
+            XAxis = plane.XAxis;
+            YAxis = plane.YAxis;
+
         }
 
         /// <summary>
@@ -78,29 +89,53 @@ public Plane(Point3 origin, Vector3 xDirection, Vector3 yDirection)
         public static Plane PlaneZX => new Plane(Point3.Origin, Vector3.ZAxis, Vector3.XAxis);
 
         /// <summary>
-        /// Gets the normal of the plan.
+        /// Gets a plane whose components are Unset.
+        /// </summary>
+        public static Plane Unset => new Plane(Point3.Unset, Vector3.Unset, Vector3.Unset);
+
+        /// <summary>
+        /// Gets the normal of the plane.
         /// </summary>
         public Vector3 Normal => ZAxis;
 
         /// <summary>
         /// Gets the origin of the plane.
         /// </summary>
-        public Point3 Origin { get; }
+        public Point3 Origin { get; set; }
 
         /// <summary>
         /// Gets the XAxis of the plane.
         /// </summary>
-        public Vector3 XAxis { get; }
+        public Vector3 XAxis { get; set; }
 
         /// <summary>
         /// Gets the YAxis of the plane.
         /// </summary>
-        public Vector3 YAxis { get; }
+        public Vector3 YAxis { get; set; }
 
         /// <summary>
         /// Gets the ZAxis of the plane.
         /// </summary>
-        public Vector3 ZAxis { get; }
+        public Vector3 ZAxis => Vector3.CrossProduct(XAxis, YAxis).Unitize();
+
+        /// <summary>
+        /// Returns true if origin and axis vectors are valid and orthogonal.
+        /// </summary>
+        public bool IsValid
+        {
+            get
+            {
+                //check all axes and origin are valid
+                var areAxesValid = Origin.IsValid && XAxis.IsValid && YAxis.IsValid && ZAxis.IsValid;
+
+                //check that vectors are orthogonal
+                var areAxesOrthogonal = Vector3.DotProduct(XAxis, YAxis) == 0 && Vector3.DotProduct(YAxis, ZAxis) == 0;
+
+                if (areAxesValid && areAxesOrthogonal) return true;
+
+                return false;
+            }
+        }
 
         /// <summary>
         /// Finds the closest point on a plane.
@@ -160,13 +195,14 @@ public Point3 PointAt(double u, double v)
         }
 
         /// <summary>
-        /// Swapping out the X and Y axes and inverting the Z axis.
+        /// Flip plane by swapping X and Y axes.
         /// </summary>
         /// <returns>The flipped plane.</returns>
         public Plane Flip()
         {
-            //ToDo flip by reversing X, Y, or swapping X and Y.
-            return  new Plane(Origin, -XAxis, YAxis);
+                var xAxis = YAxis;
+                var yAxis = XAxis;
+                return  new Plane(Origin, xAxis, yAxis);
         }
 
         /// <summary>

src/GShark/Operation/Tessellation.cs

@@ -92,7 +92,7 @@ public static (List<double> tValues, List<Point3> pts) CurveAdaptiveSampleRange(
             Vector3 diff2 = pt1 - pt2;
 
             if ((Vector3.DotProduct(diff, diff) < setTolerance && Vector3.DotProduct(diff2, diff2) > setTolerance)
-                || !Trigonometry.AreThreePointsCollinear(pt1, pt2, pt3, setTolerance))
+                || !Trigonometry.ArePointsCollinear(pt1, pt2, pt3, setTolerance))
             {
                 // Get the exact middle value or a random value start + (end - start) * (0.45 + 0.1 * random.NextDouble());
                 double tMiddle = start + (end - start) * 0.5;