Add Bezier path

diff --git a/gdx/src/com/badlogic/gdx/math/Bezier.java b/gdx/src/com/badlogic/gdx/math/Bezier.java
new file mode 100644 (file)
index 0000000..3cc94f8
--- /dev/null
+++ b/gdx/src/com/badlogic/gdx/math/Bezier.java
@@ -0,0 +1,117 @@
+/*******************************************************************************
+ * Copyright 2011 See AUTHORS file.
+ * 
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ * 
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ * 
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ ******************************************************************************/
+
+package com.badlogic.gdx.math;
+
+import com.badlogic.gdx.utils.Array;
+import com.badlogic.gdx.utils.GdxRuntimeException;
+
+/** Implementation of the Bezier curve.
+ * @author Xoppa */
+public class Bezier<T extends Vector<T>> implements Path<T> {
+       // TODO implement Serializable
+       
+       /** Simple linear interpolation 
+        * @param out The {@link Vector} to set to the result.
+        * @param t The location (ranging 0..1) on the line.
+        * @param p0 The start point.
+        * @param p1 The end point.
+        * @return The value specified by out for chaining */
+       public static <T extends Vector<T>> T linear(final T out, final float t, final T p0, final T p1) {
+               return out.set(p0).mul(1f - t).add(p1.tmp().mul(t)); // Could just use lerp...
+       }
+       
+       /** Quadratic Bezier curve 
+        * @param out The {@link Vector} to set to the result.
+        * @param t The location (ranging 0..1) on the curve.
+        * @param p0 The first bezier point.
+        * @param p1 The second bezier point.
+        * @param p2 The third bezier point.
+        * @return The value specified by out for chaining */
+       public static <T extends Vector<T>> T quadratic(final T out, final float t, final T p0, final T p1, final T p2) {
+               final float dt = 1f - t;
+               return out.set(p0).mul(dt*dt).add(p1.tmp().mul(2*dt*t)).add(p2.tmp().mul(t*t));
+       }
+       
+       /** Cubic Bezier curve
+        * @param out The {@link Vector} to set to the result.
+        * @param t The location (ranging 0..1) on the curve.
+        * @param p0 The first bezier point.
+        * @param p1 The second bezier point.
+        * @param p2 The third bezier point.
+        * @param p3 The fourth bezier point.
+        * @return The value specified by out for chaining */
+       public static <T extends Vector<T>> T cubic(final T out, final float t, final T p0, final T p1, final T p2, final T p3) {
+               final float dt = 1f - t;
+               final float dt2 = dt * dt;
+               final float t2 = t * t;
+               return out.set(p0).mul(dt2*dt).add(p1.tmp().mul(3*dt2*t)).add(p2.tmp().mul(3*dt*t2)).add(p3.tmp().mul(t2*t));
+       }
+       
+       public Array<T> points = new Array<T>();
+       
+       public Bezier() {       }
+       public Bezier(final T... points) {
+               set(points);
+       }
+       public Bezier(final T[] points, final int offset, final int length) {
+               set(points, offset, length);
+       }
+       public Bezier(final Array<T> points, final int offset, final int length) {
+               set(points, offset, length);
+       }
+       
+       public Bezier set(final T... points) {
+               return set(points, 0, points.length);
+       }
+       public Bezier set(final T[] points, final int offset, final int length) {
+               if (length < 2 || length > 4)
+                       throw new GdxRuntimeException("Only first, second and third degree Bezier curves are supported.");
+               this.points.clear();
+               this.points.addAll(points, offset, length);
+               return this;
+       }
+       public Bezier set(final Array<T> points, final int offset, final int length) {
+               if (length < 2 || length > 4)
+                       throw new GdxRuntimeException("Only first, second and third degree Bezier curves are supported.");
+               this.points.clear();
+               this.points.addAll(points, offset, length);
+               return this;
+       }
+       
+       public T valueAt(final T out, final float t) {
+               final int n = points.size; 
+               if (n == 2)
+                       linear(out, t, points.get(0), points.get(1));
+               else if (n == 3)
+                       quadratic(out, t, points.get(0), points.get(1), points.get(2));
+               else if (n == 4)
+                       cubic(out, t, points.get(0), points.get(1), points.get(2), points.get(3));
+               return out;
+       }
+       
+       public float approximate(final T v) {
+               // TODO: make a real approximate method
+               T p1 = points.get(0);
+               T p2 = points.get(points.size-1);
+               T p3 = v;
+               float l1 = p1.dst(p2);
+               float l2 = p3.dst(p2);
+               float l3 = p3.dst(p1);
+               float s = (l2*l2 + l1*l1 - l3*l3) / (2*l1);
+               return MathUtils.clamp((l1-s)/l1, 0f, 1f);
+       }
+}