cubic 2D

Curve/CubicBezierCurve2D.cs

@@ -0,0 +1,57 @@
+using Microsoft.Xna.Framework;
+using MoonTools.Core.Curve.Extensions;
+
+namespace MoonTools.Core.Curve
+{
+    public struct CubicBezierCurve2D
+    {
+        public Vector2 p0;
+        public Vector2 p1;
+        public Vector2 p2;
+        public Vector2 p3;
+
+        public CubicBezierCurve2D(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3)
+        {
+            this.p0 = p0;
+            this.p1 = p1;
+            this.p2 = p2;
+            this.p3 = p3;
+        }
+
+        public Vector2 Point(float t) => Point(p0, p1, p2, p3, t);
+        public Vector2 Point(float t, float minT, float maxT) => Point(p0, p1, p2, p3, t, minT, maxT);
+        public Vector2 Velocity(float t) => Velocity(p0, p1, p2, p3, t);
+        public Vector2 Velocity(float t, float minT, float maxT) => Velocity(p0, p1, p2, p3, TimeHelper.Normalized(t, minT, maxT));
+        public static Vector2 Point(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, float t)
+        {
+            return CubicBezierCurve3D.Point(
+                new Vector3(p0.X, p0.Y, 0),
+                new Vector3(p1.X, p1.Y, 0),
+                new Vector3(p2.X, p2.Y, 0),
+                new Vector3(p3.X, p3.Y, 0),
+                t
+            ).XY();
+        }
+
+        public static Vector2 Point(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, float t, float minT, float maxT)
+        {
+            return Point(p0, p1, p2, p3, TimeHelper.Normalized(t, minT, maxT));
+        }
+
+        public static Vector2 Velocity(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, float t)
+        {
+            return CubicBezierCurve3D.Velocity(
+                new Vector3(p0.X, p0.Y, 0),
+                new Vector3(p1.X, p1.Y, 0),
+                new Vector3(p2.X, p2.Y, 0),
+                new Vector3(p3.X, p3.Y, 0),
+                t
+            ).XY();
+        }
+
+        public static Vector2 Velocity(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, float t, float minT, float maxT)
+        {
+            return Velocity(p0, p1, p2, p3, TimeHelper.Normalized(t, minT, maxT));
+        }
+    }
+}

Curve/CubicBezierCurve3D.cs

@@ -21,9 +21,9 @@ namespace MoonTools.Core.Curve
 
         public Vector3 Point(float t, float minT, float maxT) => Point(p0, p1, p2, p3, t, minT, maxT);
 
-        public Vector3 Velocity(float t) => FirstDerivative(p0, p1, p2, p3, t);
+        public Vector3 Velocity(float t) => Velocity(p0, p1, p2, p3, t);
 
-        public Vector3 Velocity(float t, float minT, float maxT) => FirstDerivative(p0, p1, p2, p3, t, minT, maxT);
+        public Vector3 Velocity(float t, float minT, float maxT) => Velocity(p0, p1, p2, p3, t, minT, maxT);
 
         public static Vector3 Point(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
         {
@@ -37,10 +37,10 @@ namespace MoonTools.Core.Curve
 
         public static Vector3 Point(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t, float minT, float maxT)
         {
-            return Point(p0, p1, p2, p3, Normalized(t, minT, maxT));
+            return Point(p0, p1, p2, p3, TimeHelper.Normalized(t, minT, maxT));
         }
 
-        public static Vector3 FirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
+        public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t)
         {
             if (t < 0 || t > 1) { throw new System.ArgumentException($"{t} is an invalid value. Must be between 0 and 1"); }
 
@@ -49,11 +49,9 @@ namespace MoonTools.Core.Curve
                     3f * t * t * (p3 - p2);
         }
 
-        public static Vector3 FirstDerivative(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t, float minT, float maxT)
+        public static Vector3 Velocity(Vector3 p0, Vector3 p1, Vector3 p2, Vector3 p3, float t, float minT, float maxT)
         {
-            return FirstDerivative(p0, p1, p2, p3, Normalized(t, minT, maxT));
+            return Velocity(p0, p1, p2, p3, TimeHelper.Normalized(t, minT, maxT));
         }
-
-        private static float Normalized(float t, float minT, float maxT) => ((t - minT)) / (maxT - minT);
     }
 }

Curve/Extensions.cs

@@ -0,0 +1,9 @@
+using Microsoft.Xna.Framework;
+
+namespace MoonTools.Core.Curve.Extensions
+{
+    public static class Vector2Extensions
+    {
+        public static Vector2 XY(this Vector3 vector) => new Vector2(vector.X, vector.Y);
+    }
+}

Curve/Helper.cs

@@ -0,0 +1,7 @@
+namespace MoonTools.Core.Curve
+{
+    public static class TimeHelper
+    {
+        public static float Normalized(float t, float minT, float maxT) => ((t - minT)) / (maxT - minT);
+    }
+}

Test/CubicBezierCurve2D.cs

@@ -0,0 +1,127 @@
+using NUnit.Framework;
+using FluentAssertions;
+
+using MoonTools.Core.Curve;
+using Microsoft.Xna.Framework;
+
+namespace Tests
+{
+    public class CubicBezierCurve2DTests
+    {
+        [Test]
+        public void Point()
+        {
+            var p0 = new Vector2(-4, -4);
+            var p1 = new Vector2(-2, 4);
+            var p2 = new Vector2(2, -4);
+            var p3 = new Vector2(4, 4);
+
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 0.5f).Should().BeEquivalentTo(new Vector2(0, 0));
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 0.5f).Should().BeEquivalentTo(new Vector2(0, 0));
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 0.25f).Should().BeEquivalentTo(new Vector2(-2.1875f, -0.5f));
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 0.75f).Should().BeEquivalentTo(new Vector2(2.1875f, 0.5f));
+        }
+
+        [Test]
+        public void PointNormalized()
+        {
+            var p0 = new Vector2(-4, -4);
+            var p1 = new Vector2(-2, 4);
+            var p2 = new Vector2(2, -4);
+            var p3 = new Vector2(4, 4);
+
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 3, 2, 4).Should().BeEquivalentTo(new Vector2(0, 0));
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 2, 1, 5).Should().BeEquivalentTo(new Vector2(-2.1875f, -0.5f));
+            CubicBezierCurve2D.Point(p0, p1, p2, p3, 11, 2, 14).Should().BeEquivalentTo(new Vector2(2.1875f, 0.5f));
+        }
+
+        [Test]
+        public void Velocity()
+        {
+            var p0 = new Vector2(-4, -4);
+            var p1 = new Vector2(-2, 4);
+            var p2 = new Vector2(2, -4);
+            var p3 = new Vector2(4, 4);
+
+            CubicBezierCurve2D.Velocity(p0, p1, p2, p3, 0.5f).Should().BeEquivalentTo(new Vector2(9, 0));
+            CubicBezierCurve2D.Velocity(p0, p1, p2, p3, 0.25f).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+            CubicBezierCurve2D.Velocity(p0, p1, p2, p3, 0.75f).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+        }
+
+        [Test]
+        public void VelocityNormalized()
+        {
+            var p0 = new Vector2(-4, -4);
+            var p1 = new Vector2(-2, 4);
+            var p2 = new Vector2(2, -4);
+            var p3 = new Vector2(4, 4);
+
+            CubicBezierCurve2D.Velocity(p0, p1, p2, p3, 3, 2, 4).Should().BeEquivalentTo(new Vector2(9, 0));
+            CubicBezierCurve2D.Velocity(p0, p1, p2, p3, 2, 1, 5).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+            CubicBezierCurve2D.Velocity(p0, p1, p2, p3, 11, 2, 14).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+        }
+    }
+
+    public class CubicBezierCurve2DStructTests
+    {
+        [Test]
+        public void Point()
+        {
+            var myCurve = new CubicBezierCurve2D(
+                new Vector2(-4, -4),
+                new Vector2(-2, 4),
+                new Vector2(2, -4),
+                new Vector2(4, 4)
+            );
+
+            myCurve.Point(0.5f).Should().BeEquivalentTo(new Vector2(0, 0));
+            myCurve.Point(0.25f).Should().BeEquivalentTo(new Vector2(-2.1875f, -0.5f));
+            myCurve.Point(0.75f).Should().BeEquivalentTo(new Vector2(2.1875f, 0.5f));
+        }
+
+        [Test]
+        public void PointNormalized()
+        {
+            var myCurve = new CubicBezierCurve2D(
+                new Vector2(-4, -4),
+                new Vector2(-2, 4),
+                new Vector2(2, -4),
+                new Vector2(4, 4)
+            );
+
+            myCurve.Point(3, 2, 4).Should().BeEquivalentTo(new Vector2(0, 0));
+            myCurve.Point(2, 1, 5).Should().BeEquivalentTo(new Vector2(-2.1875f, -0.5f));
+            myCurve.Point(11, 2, 14).Should().BeEquivalentTo(new Vector2(2.1875f, 0.5f));
+        }
+
+        [Test]
+        public void Velocity()
+        {
+            var myCurve = new CubicBezierCurve2D(
+                new Vector2(-4, -4),
+                new Vector2(-2, 4),
+                new Vector2(2, -4),
+                new Vector2(4, 4)
+            );
+
+            myCurve.Velocity(0.5f).Should().BeEquivalentTo(new Vector2(9, 0));
+            myCurve.Velocity(0.25f).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+            myCurve.Velocity(0.75f).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+        }
+
+        [Test]
+        public void VelocityNormalized()
+        {
+            var myCurve = new CubicBezierCurve2D(
+                new Vector2(-4, -4),
+                new Vector2(-2, 4),
+                new Vector2(2, -4),
+                new Vector2(4, 4)
+            );
+
+            myCurve.Velocity(3, 2, 4).Should().BeEquivalentTo(new Vector2(9, 0));
+            myCurve.Velocity(2, 1, 5).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+            myCurve.Velocity(11, 2, 14).Should().BeEquivalentTo(new Vector2(8.25f, 6f));
+        }
+    }
+}

Test/CubicBezierCurve3D.cs

@@ -36,29 +36,29 @@ namespace Tests
         }
 
         [Test]
-        public void FirstDerivative()
+        public void Velocity()
         {
             var p0 = new Vector3(-4, -4, -3);
             var p1 = new Vector3(-2, 4, 0);
             var p2 = new Vector3(2, -4, 3);
             var p3 = new Vector3(4, 4, 0);
 
-            CubicBezierCurve3D.FirstDerivative(p0, p1, p2, p3, 0.5f).Should().BeEquivalentTo(new Vector3(9, 0, 4.5f));
+            CubicBezierCurve3D.Velocity(p0, p1, p2, p3, 0.5f).Should().BeEquivalentTo(new Vector3(9, 0, 4.5f));
-            CubicBezierCurve3D.FirstDerivative(p0, p1, p2, p3, 0.25f).Should().BeEquivalentTo(new Vector3(8.25f, 6f, 7.875f));
+            CubicBezierCurve3D.Velocity(p0, p1, p2, p3, 0.25f).Should().BeEquivalentTo(new Vector3(8.25f, 6f, 7.875f));
-            CubicBezierCurve3D.FirstDerivative(p0, p1, p2, p3, 0.75f).Should().BeEquivalentTo(new Vector3(8.25f, 6f, -1.125f));
+            CubicBezierCurve3D.Velocity(p0, p1, p2, p3, 0.75f).Should().BeEquivalentTo(new Vector3(8.25f, 6f, -1.125f));
         }
 
         [Test]
-        public void FirstDerivativeNormalized()
+        public void VelocityNormalized()
         {
             var p0 = new Vector3(-4, -4, -3);
             var p1 = new Vector3(-2, 4, 0);
             var p2 = new Vector3(2, -4, 3);
             var p3 = new Vector3(4, 4, 0);
 
-            CubicBezierCurve3D.FirstDerivative(p0, p1, p2, p3, 3, 2, 4).Should().BeEquivalentTo(new Vector3(9, 0, 4.5f));
+            CubicBezierCurve3D.Velocity(p0, p1, p2, p3, 3, 2, 4).Should().BeEquivalentTo(new Vector3(9, 0, 4.5f));
-            CubicBezierCurve3D.FirstDerivative(p0, p1, p2, p3, 2, 1, 5).Should().BeEquivalentTo(new Vector3(8.25f, 6f, 7.875f));
+            CubicBezierCurve3D.Velocity(p0, p1, p2, p3, 2, 1, 5).Should().BeEquivalentTo(new Vector3(8.25f, 6f, 7.875f));
-            CubicBezierCurve3D.FirstDerivative(p0, p1, p2, p3, 11, 2, 14).Should().BeEquivalentTo(new Vector3(8.25f, 6f, -1.125f));
+            CubicBezierCurve3D.Velocity(p0, p1, p2, p3, 11, 2, 14).Should().BeEquivalentTo(new Vector3(8.25f, 6f, -1.125f));
         }
     }