feat: 添加贝塞尔曲线 Ease

EleCho.WpfSuite/Animations/BezierEaseBase.cs

@@ -0,0 +1,12 @@
+using System.Windows.Media.Animation;
+
+namespace EleCho.WpfSuite
+{
+    public abstract class BezierEaseBase : IEasingFunction
+    {
+        protected abstract double GetSampleRate(double time);
+        protected abstract double GetSampleValue(double rate);
+
+        public double Ease(double normalizedTime) => GetSampleValue(GetSampleRate(normalizedTime));
+    }
+}

EleCho.WpfSuite/Animations/CubicBezierEase.cs

@@ -0,0 +1,139 @@
+using System;
+using System.Windows.Media.Animation;
+
+namespace EleCho.WpfSuite
+{
+
+    public class CubicBezierEase : BezierEaseBase
+    {
+        private double x1;
+        private double y1;
+        private double x2;
+        private double y2;
+
+        /// <summary>
+        /// X value of control point 1
+        /// </summary>
+        public double X1
+        {
+            get => x1; set
+            {
+                if (value < 0 || value > 1)
+                    throw new ArgumentOutOfRangeException();
+
+                x1 = value;
+            }
+        }
+
+        /// <summary>
+        /// Y value of control point 1
+        /// </summary>
+        public double Y1 { get => y1; set => y1 = value; }
+
+        /// <summary>
+        /// X value of control point 2
+        /// </summary>
+        public double X2
+        {
+            get => x2; set
+            {
+                if (value < 0 || value > 1)
+                    throw new ArgumentOutOfRangeException();
+
+                x2 = value;
+            }
+        }
+
+        /// <summary>
+        /// Y value of control point 2
+        /// </summary>
+        public double Y2 { get => y2; set => y2 = value; }
+
+        private double MathCbrt(double num)
+        {
+            return num < 0 ? -Math.Pow(-num, 1d / 3) : Math.Pow(num, 1d / 3);
+        }
+        private double PickAppropriateRate(double cp1, double cp2, double p, params double[] rates)
+        {
+            double result = double.NaN;
+            double diffNow = double.MaxValue;
+            foreach (var rate in rates)
+                if (!double.IsNaN(rate) && Math.Abs(GetSamplePoint(cp1, cp2, rate) - p) < diffNow)
+                    result = rate;
+            return result;
+        }
+        private double GetSampleRate(double cp1, double cp2, double p)
+        {
+            // 警告, 这里是魔法, 是求根公式
+
+            double
+                a = 3 * cp1 - 3 * cp2 + 1,
+                b = -6 * cp1 + 3 * cp2,
+                c = 3 * cp1,
+                d = -p;
+            double
+                A = b * b - 3 * a * c,
+                B = b * c - 9 * a * d,
+                C = c * c - 3 * b * d;
+            double
+                delta = B * B - 4 * A * C;
+            if (A == B)
+            {
+                double x = -c / b; // -b/3a -c/b -3d/c
+                double rst = x;
+                return rst;
+            }
+            else if (delta > 0)
+            {
+                //double I = double.NaN;
+                double
+                    y1 = A * b + 3 * a * ((-B + Math.Sqrt(delta)) / 2),
+                    y2 = A * b + 3 * a * ((-B - Math.Sqrt(delta)) / 2);
+                double
+                    xtmp1 = MathCbrt(y1) + MathCbrt(y2); //,
+                                                         //xtmp2 = Cubic(y1) - Cubic(y2);
+                double   // what the fuck is I? virtual number wtf... impossible for now (((
+                    x1 = (-b - xtmp1) / (3 * a); //,
+                                                 //x2 = (-2 * b + xtmp1 + Math.Sqrt(3) * xtmp2 * I) / (6 * a),
+                                                 //x3 = (-2 * b + xtmp1 - Math.Sqrt(3) * xtmp2 * I) / (6 * a);
+                double rst = x1;
+                return rst;
+            }
+            else if (delta == 0)
+            {
+                double k = B / A;
+                double
+                    x1 = -b / a + k,
+                    x2 = -k / 2;
+                double rst = PickAppropriateRate(cp1, cp2, p, x1, x2);
+                return rst;
+            }
+            else  // delta < 0
+            {
+                double
+                    t = (2 * A * b - 3 * a * B) / (2 * A * Math.Sqrt(A)),
+                    sita = Math.Acos(t);
+                double
+                    x1 = (-b - 2 * Math.Sqrt(A) * Math.Cos(sita / 3)) / (3 * a),
+                    x2 = (-b + Math.Sqrt(A) * (Math.Cos(sita / 3) + Math.Sqrt(3) * Math.Sin(sita / 3))) / (3 * a),
+                    x3 = (-b + Math.Sqrt(A) * (Math.Cos(sita / 3) - Math.Sqrt(3) * Math.Sin(sita / 3))) / (3 * a);
+                double rst = PickAppropriateRate(cp1, cp2, p, x1, x2, x3);
+                return rst;
+            }
+        }
+        private double GetSamplePoint(double cp1, double cp2, double rate)
+        {
+            return 3d * cp1 * rate * (1d - rate) * (1d - rate) + 3d * cp2 * rate * rate * (1d - rate) + rate * rate * rate;
+            // return 3 * cp1 * rate - 3 * cp1 * 2 * rate * rate + 3 * cp1 * rate * rate * rate + 3 * cp2 * rate * rate - 3 * cp2 * rate * rate * rate + rate * rate * rate;
+        }
+
+        protected override double GetSampleRate(double time)
+        {
+            return GetSampleRate(X1, X2, time);
+        }
+        protected override double GetSampleValue(double rate)
+        {
+            return GetSamplePoint(Y1, Y2, rate);
+        }
+    }
+}

EleCho.WpfSuite/Animations/QuadraticBezierEase.cs

@@ -0,0 +1,64 @@
+using System;
+
+namespace EleCho.WpfSuite
+{
+    public class QuadraticBezierEase : BezierEaseBase
+    {
+        private double x;
+        private double y;
+
+        /// <summary>
+        /// X value of control point
+        /// </summary>
+        public double X { get => x; set => x = value; }
+
+        /// <summary>
+        /// Y value of control point
+        /// </summary>
+        public double Y { get => y; set => y = value; }
+
+        private double GetSamplePoint(double cp, double rate)
+        {
+            return 2 * rate * (1 - rate) * cp + rate * rate * 1;
+        }
+        private double PickAppropriateRate(double cp, double p, params double[] rates)
+        {
+            double result = double.NaN;
+            double diffNow = double.MaxValue;
+            foreach (var rate in rates)
+                if (rate >= 0 && rate <= 1 && Math.Abs(GetSamplePoint(cp, rate) - p) < diffNow)
+                    result = rate;
+            return result;
+        }
+        private double GetSampleRate(double cp, double p)
+        {
+            double
+                a = 1 - 2 * cp,
+                b = 2 * cp,
+                c = -p;
+            double
+                delta = b * b - 4 * a * c;
+            if (delta > 0)
+            {
+                double
+                    x1 = (-b + Math.Sqrt(delta)) / (2 * a),
+                    x2 = (-b - Math.Sqrt(delta)) / (2 * a);
+                double rst = PickAppropriateRate(cp, p, x1, x2);
+                return rst;
+            }
+            else if (delta == 0)
+            {
+                double
+                    x = -b / (2 * a);
+                return x;
+            }
+            else
+            {
+                throw new Exception("Fuck");
+            }
+        }
+
+        protected override double GetSampleRate(double time) => GetSampleRate(this.X, time);
+        protected override double GetSampleValue(double rate) => GetSamplePoint(this.X, rate);
+    }
+}