From 31895ea2c11d9bc0a76353ac441915338b2938e4 Mon Sep 17 00:00:00 2001
From: Guido Maciocci <guidomaciocci@gmail.com>
Date: Mon, 15 Nov 2021 23:52:27 +1100
Subject: [PATCH] Adds check for surface planarity.

---
 .../Geometry/NurbsSurfaceTests.cs             | 27 +++++++++++++++++++
 src/GShark/Core/Trigonometry.cs               | 11 ++++----
 src/GShark/Geometry/NurbsSurface.cs           | 11 ++++++++
 3 files changed, 44 insertions(+), 5 deletions(-)

diff --git a/src/GShark.Test.XUnit/Geometry/NurbsSurfaceTests.cs b/src/GShark.Test.XUnit/Geometry/NurbsSurfaceTests.cs
index 19da6d7e..a85440d6 100644
--- a/src/GShark.Test.XUnit/Geometry/NurbsSurfaceTests.cs
+++ b/src/GShark.Test.XUnit/Geometry/NurbsSurfaceTests.cs
@@ -269,6 +269,33 @@ public void Returns_True_If_Surface_Is_Close()
             surface.IsClosed(SurfaceDirection.V).Should().BeTrue();
         }
 
+        [Fact]
+        public void Returns_True_If_Surface_Is_Planar()
+        {
+            //Arrange
+            var planarSurface = NurbsSurface.FromCorners(
+                new Point3(0, 0, 0),
+                new Point3(10, 0, 0),
+                new Point3(10,5,0),
+                new Point3(0,5,0)
+            );
+            
+            var nonPlanarSurface = NurbsSurface.FromCorners(
+                new Point3(0, 0, 0),
+                new Point3(10, 0, 5),
+                new Point3(10, 5, 0),
+                new Point3(0, 5, 5)
+            );
+
+            //Act
+            var isPlanarSurfacePlanar = planarSurface.IsPlanar();
+            var isNonPlanarSurfacePlanar = nonPlanarSurface.IsPlanar();
+
+            //Assert
+            isPlanarSurfacePlanar.Should().BeTrue();
+            isNonPlanarSurfacePlanar.Should().BeFalse();
+        }
+
         [Theory]
         [InlineData(0.1, 0.1, new double[] { 0.2655, 1, 2.442 })]
         [InlineData(0.5, 0.5, new double[] { 4.0625, 5, 4.0625 })]
diff --git a/src/GShark/Core/Trigonometry.cs b/src/GShark/Core/Trigonometry.cs
index d4bc0feb..89e86a72 100644
--- a/src/GShark/Core/Trigonometry.cs
+++ b/src/GShark/Core/Trigonometry.cs
@@ -11,14 +11,15 @@ namespace GShark.Core
     public class Trigonometry
     {
         /// <summary>
-        /// Determines if the provide points are on the same plane.
+        /// Determines if the provide points are on the same plane within specified tolerance.
         /// </summary>
-        /// <param name="points">Provided points.</param>
-        /// <returns>Whether the point are coplanar.</returns>
-        public static bool ArePointsCoplanar(IList<Point3> points)
+        /// <param name="points">Points to check.</param>
+        /// <param name="tolerance">Tolerance.</param>
+        /// <returns>True if all points are coplanar.</returns>
+        public static bool ArePointsCoplanar(IList<Point3> points, double tolerance = GSharkMath.Epsilon)
         {
             // https://en.wikipedia.org/wiki/Triple_product
-            if (points.Count < 3)
+            if (points.Count <= 3)
             {
                 return true;
             }
diff --git a/src/GShark/Geometry/NurbsSurface.cs b/src/GShark/Geometry/NurbsSurface.cs
index 43cc1c14..2de0a7f7 100644
--- a/src/GShark/Geometry/NurbsSurface.cs
+++ b/src/GShark/Geometry/NurbsSurface.cs
@@ -108,6 +108,17 @@ public bool IsClosed(SurfaceDirection direction)
             return pts2d.All(pts => pts[0].DistanceTo(pts.Last()) < GSharkMath.Epsilon);
         }
 
+
+        /// <summary>
+        /// Checks is surface is planar within specified tolerance.
+        /// </summary>
+        /// <param name="tolerance"></param>
+        /// <returns></returns>
+        public bool IsPlanar(double tolerance = GSharkMath.Epsilon)
+        {
+            return Trigonometry.ArePointsCoplanar(ControlPointLocations.SelectMany(pt => pt).ToList(), tolerance);
+        }
+
         /// <summary>
         /// Constructs a NURBS surface from four corners.<br/>
         /// If the corners are ordered ccw the normal of the surface will point up otherwise, if corners ordered cw the normal will point down.<br/>