Code style cleanup from #12.

- Moved all curve-related classes into a new package.
- Added some fields and methods to Curve abstract class.
- Removed the old (no longer used) Bezier subclass.
- Changed Error throwing to ErrorHandler.error() calls.
- Formatted code.

Also fixed a crash when reaching the ranking screen with the "Auto" mod active.

Signed-off-by: Jeffrey Han <itdelatrisu@gmail.com>

src/itdelatrisu/opsu/objects/curves/Bezier2.java

@@ -0,0 +1,121 @@
+/*
+ * opsu! - an open-source osu! client
+ * Copyright (C) 2014, 2015 Jeffrey Han
+ *
+ * opsu! is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * opsu! is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with opsu!.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+package itdelatrisu.opsu.objects.curves;
+
+/**
+ * Representation of a Bezier curve with the distance between each point calculated.
+ */
+public class Bezier2 {
+	/** The control points of the Bezier curve. */
+	private Vec2f[] points;
+
+	/** Points along the curve of the Bezier curve. */
+	private Vec2f[] curve;
+
+	/** Distances between a point of the curve and the last point. */
+	private float[] curveDis;
+
+	/** The number of points along the curve. */
+	private int ncurve;
+
+	/** The total distances of this Bezier. */
+	private float totalDistance;
+
+	/**
+	 * Constructor.
+	 * @param points the control points
+	 */
+	public Bezier2(Vec2f[] points) {
+		this.points = points;
+
+		// approximate by finding the length of all points
+		// (which should be the max possible length of the curve)
+		float approxlength = 0;
+		for (int i = 0; i < points.length - 1; i++)
+			approxlength += points[i].cpy().sub(points[i + 1]).len();
+
+		// subdivide the curve
+		this.ncurve = (int) (approxlength / 4);
+		this.curve = new Vec2f[ncurve];
+		for (int i = 0; i < ncurve; i++)
+			curve[i] = pointAt(i / (float) ncurve);
+
+		// find the distance of each point from the previous point
+		this.curveDis = new float[ncurve];
+		this.totalDistance = 0;
+		for (int i = 0; i < ncurve; i++) {
+			curveDis[i] = (i == 0) ? 0 : curve[i].cpy().sub(curve[i - 1]).len();
+			totalDistance += curveDis[i];
+		}
+//		System.out.println("New Bezier2 "+points.length+" "+approxlength+" "+totalDistance());
+	}
+
+	/**
+	 * Returns the point on the Bezier curve at a value t.
+	 * @param t the t value [0, 1]
+	 * @return the point [x, y]
+	 */
+	public Vec2f pointAt(float t) {
+		Vec2f c = new Vec2f();
+		int n = points.length - 1;
+		for (int i = 0; i <= n; i++) {
+			c.x += points[i].x * bernstein(i, n, t);
+			c.y += points[i].y * bernstein(i, n, t);
+		}
+		return c;
+	}
+
+	/**
+	 * Returns the points along the curve of the Bezier curve.
+	 */
+	public Vec2f[] getCurve() { return curve; }
+
+	/**
+	 * Returns the distances between a point of the curve and the last point.
+	 */
+	public float[] getCurveDistances() { return curveDis; }
+
+	/**
+	 * Returns the number of points along the curve.
+	 */
+	public int points() { return ncurve; }
+
+	/**
+	 * Returns the total distances of this Bezier curve.
+	 */
+	public float totalDistance() { return totalDistance; }
+
+	/**
+	 * Calculates the factorial of a number.
+	 */
+	private static long factorial(int n) {
+		return (n <= 1 || n > 20) ? 1 : n * factorial(n - 1);
+	}
+
+	/**
+	 * Calculates the Bernstein polynomial.
+	 * @param i the index
+	 * @param n the degree of the polynomial (i.e. number of points)
+	 * @param t the t value [0, 1]
+	 */
+	private static double bernstein(int i, int n, float t) {
+		return factorial(n) / (factorial(i) * factorial(n - i)) *
+		       Math.pow(t, i) * Math.pow(1 - t, n - i);
+	}
+}