Merge pull request #290 from GSharker/dev/mibi/derivativeAt

Added derivativeAt.

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

@@ -238,6 +238,30 @@ public void It_Returns_The_Closest_Parameter_On_A_Circle(double[] ptToTest, doub
             // Assert
             parameter.Should().BeApproximately(expectedParameter, GSharkMath.MaxTolerance);
         }
+
+        [Fact]
+        public void It_Returns_The_Derivatives_At_Given_Parameter()
+        {
+            // Arrange
+            Point3 expectedDerv0 = new Point3(69.253451, 22.768104, 1.732159);
+            Vector3 expectedDerv1 = new Vector3(13.388719, -99.325852, 25.95035);
+            Vector3 expectedDerv2 = new Vector3(645.009827, 80.060471, -26.349577);
+            Vector3 expectedDerv3 = new Vector3(-528.565438, 3921.227465, -1024.478763);
+
+            // Act
+            Vector3 derv0 = _circle3D.DerivativeAt(0.15, 0);
+            Vector3 derv1 = _circle3D.DerivativeAt(0.15, 1);
+            Vector3 derv2 = _circle3D.DerivativeAt(0.15, 2);
+            Vector3 derv3 = _circle3D.DerivativeAt(0.15, 3);
+            Point3 pt = _circle3D.Center + derv0;
+
+            // Assert
+            // The zero derivative is the vector identify the point on the circle.
+            expectedDerv0.EpsilonEquals(pt, GSharkMath.MaxTolerance).Should().BeTrue();
+            expectedDerv1.IsParallelTo(derv1).Should().NotBe(0);
+            expectedDerv2.IsParallelTo(derv2).Should().NotBe(0);
+            expectedDerv3.IsParallelTo(derv3).Should().NotBe(0);
+        }
     }
 }
 

src/GShark/Geometry/Circle.cs

@@ -123,6 +123,51 @@ public virtual BoundingBox GetBoundingBox()
             return new BoundingBox(min, max);
         }
 
+        /// <summary>
+        /// Determines the value of the Nth derivative at a parameter.
+        /// </summary>
+        /// <param name="t">Parameter to evaluate derivative. A parameter between 0.0 to 1.0.</param>
+        /// <param name="derivative">Which order of derivative is wanted. Valid values are 0,1,2,3.</param>
+        /// <returns>The derivative of the circle at the given parameter.</returns>
+        public Vector3 DerivativeAt(double t, int derivative = 0)
+        {
+            if (t < 0.0)
+            {
+                t = 0.0;
+            }
+
+            if (t > 1.0)
+            {
+                t = 1.0;
+            }
+
+            double theta = Domain.T0 + (Domain.T1 - Domain.T0) * t;
+
+            double r0 = 0;
+            double r1 = 0;
+            switch (derivative % 4)
+            {
+                case 0:
+                    r0 = Radius * Math.Cos(theta);
+                    r1 = Radius * Math.Sin(theta);
+                    break;
+                case 1:
+                    r0 = Radius * -Math.Sin(theta);
+                    r1 = Radius * Math.Cos(theta);
+                    break;
+                case 2:
+                    r0 = Radius * -Math.Cos(theta);
+                    r1 = Radius * -Math.Sin(theta);
+                    break;
+                case 3:
+                    r0 = Radius * Math.Sin(theta);
+                    r1 = Radius * -Math.Cos(theta);
+                    break;
+            }
+
+            return r0 * Plane.XAxis + r1 * Plane.YAxis;
+        }
+
         /// <summary>
         /// Evaluates the point at the parameter t on the circular curve.
         /// </summary>
@@ -187,13 +232,8 @@ public Vector3 TangentAt(double t)
             }
 
             double theta = Domain.T0 + (Domain.T1 - Domain.T0) * t;
-
-            double r1 = Radius * (-Math.Sin(theta));
-            double r2 = Radius * (Math.Cos(theta));
-
-            Vector3 vector = Plane.XAxis * r1 + Plane.YAxis * r2;
-
-            return vector.Unitize();
+            Vector3 derivative = DerivativeAt(theta, 1);
+            return derivative.Unitize();
         }
 
         /// <summary>