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Tidy up Slider class.
This commit is contained in:
Dean Herbert
parent
2947121e48
commit
a0503bd13f
148
osu.Game.Mode.Osu/Objects/BezierApproximator.cs
Normal file
148
osu.Game.Mode.Osu/Objects/BezierApproximator.cs
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@ -0,0 +1,148 @@
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using System.Collections.Generic;
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using OpenTK;
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namespace osu.Game.Modes.Osu.Objects
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{
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public class BezierApproximator
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{
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private int count;
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private List<Vector2> controlPoints;
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private Vector2[] subdivisionBuffer1;
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private Vector2[] subdivisionBuffer2;
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private const float TOLERANCE = 0.5f;
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private const float TOLERANCE_SQ = TOLERANCE * TOLERANCE;
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public BezierApproximator(List<Vector2> controlPoints)
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{
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this.controlPoints = controlPoints;
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count = controlPoints.Count;
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subdivisionBuffer1 = new Vector2[count];
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subdivisionBuffer2 = new Vector2[count * 2 - 1];
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}
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/// <summary>
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/// Make sure the 2nd order derivative (approximated using finite elements) is within tolerable bounds.
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/// NOTE: The 2nd order derivative of a 2d curve represents its curvature, so intuitively this function
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/// checks (as the name suggests) whether our approximation is _locally_ "flat". More curvy parts
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/// need to have a denser approximation to be more "flat".
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/// </summary>
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/// <param name="controlPoints">The control points to check for flatness.</param>
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/// <returns>Whether the control points are flat enough.</returns>
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private static bool IsFlatEnough(Vector2[] controlPoints)
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{
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for (int i = 1; i < controlPoints.Length - 1; i++)
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if ((controlPoints[i - 1] - 2 * controlPoints[i] + controlPoints[i + 1]).LengthSquared > TOLERANCE_SQ)
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return false;
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return true;
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}
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/// <summary>
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/// Subdivides n control points representing a bezier curve into 2 sets of n control points, each
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/// describing a bezier curve equivalent to a half of the original curve. Effectively this splits
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/// the original curve into 2 curves which result in the original curve when pieced back together.
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/// </summary>
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/// <param name="controlPoints">The control points to split.</param>
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/// <param name="l">Output: The control points corresponding to the left half of the curve.</param>
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/// <param name="r">Output: The control points corresponding to the right half of the curve.</param>
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private void Subdivide(Vector2[] controlPoints, Vector2[] l, Vector2[] r)
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{
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Vector2[] midpoints = subdivisionBuffer1;
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for (int i = 0; i < count; ++i)
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midpoints[i] = controlPoints[i];
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for (int i = 0; i < count; i++)
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{
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l[i] = midpoints[0];
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r[count - i - 1] = midpoints[count - i - 1];
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for (int j = 0; j < count - i - 1; j++)
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midpoints[j] = (midpoints[j] + midpoints[j + 1]) / 2;
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}
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}
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/// <summary>
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/// This uses <a href="https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm">De Casteljau's algorithm</a> to obtain an optimal
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/// piecewise-linear approximation of the bezier curve with the same amount of points as there are control points.
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/// </summary>
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/// <param name="controlPoints">The control points describing the bezier curve to be approximated.</param>
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/// <param name="output">The points representing the resulting piecewise-linear approximation.</param>
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private void Approximate(Vector2[] controlPoints, List<Vector2> output)
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{
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Vector2[] l = subdivisionBuffer2;
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Vector2[] r = subdivisionBuffer1;
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Subdivide(controlPoints, l, r);
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for (int i = 0; i < count - 1; ++i)
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l[count + i] = r[i + 1];
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output.Add(controlPoints[0]);
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for (int i = 1; i < count - 1; ++i)
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{
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int index = 2 * i;
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Vector2 p = 0.25f * (l[index - 1] + 2 * l[index] + l[index + 1]);
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output.Add(p);
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}
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}
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/// <summary>
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/// Creates a piecewise-linear approximation of a bezier curve, by adaptively repeatedly subdividing
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/// the control points until their approximation error vanishes below a given threshold.
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/// </summary>
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/// <param name="controlPoints">The control points describing the curve.</param>
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/// <returns>A list of vectors representing the piecewise-linear approximation.</returns>
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public List<Vector2> CreateBezier()
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{
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List<Vector2> output = new List<Vector2>();
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if (count == 0)
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return output;
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Stack<Vector2[]> toFlatten = new Stack<Vector2[]>();
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Stack<Vector2[]> freeBuffers = new Stack<Vector2[]>();
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// "toFlatten" contains all the curves which are not yet approximated well enough.
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// We use a stack to emulate recursion without the risk of running into a stack overflow.
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// (More specifically, we iteratively and adaptively refine our curve with a
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// <a href="https://en.wikipedia.org/wiki/Depth-first_search">Depth-first search</a>
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// over the tree resulting from the subdivisions we make.)
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toFlatten.Push(controlPoints.ToArray());
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Vector2[] leftChild = subdivisionBuffer2;
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while (toFlatten.Count > 0)
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{
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Vector2[] parent = toFlatten.Pop();
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if (IsFlatEnough(parent))
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{
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// If the control points we currently operate on are sufficiently "flat", we use
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// an extension to De Casteljau's algorithm to obtain a piecewise-linear approximation
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// of the bezier curve represented by our control points, consisting of the same amount
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// of points as there are control points.
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Approximate(parent, output);
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freeBuffers.Push(parent);
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continue;
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}
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// If we do not yet have a sufficiently "flat" (in other words, detailed) approximation we keep
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// subdividing the curve we are currently operating on.
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Vector2[] rightChild = freeBuffers.Count > 0 ? freeBuffers.Pop() : new Vector2[count];
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Subdivide(parent, leftChild, rightChild);
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// We re-use the buffer of the parent for one of the children, so that we save one allocation per iteration.
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for (int i = 0; i < count; ++i)
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parent[i] = leftChild[i];
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toFlatten.Push(rightChild);
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toFlatten.Push(parent);
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}
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output.Add(controlPoints[count - 1]);
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return output;
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}
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}
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}
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@ -1,9 +1,7 @@
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//Copyright (c) 2007-2016 ppy Pty Ltd <contact@ppy.sh>.
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//Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
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using System.Collections.Generic;
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using osu.Game.Database;
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using OpenTK;
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using osu.Game.Beatmaps;
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using System;
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@ -25,188 +23,6 @@ namespace osu.Game.Modes.Osu.Objects
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public SliderCurve Curve;
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}
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public class SliderCurve
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{
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public double Length;
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public List<Vector2> Path;
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public CurveTypes CurveType;
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private List<Vector2> calculatedPath;
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public void Calculate()
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{
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switch (CurveType)
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{
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case CurveTypes.Linear:
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calculatedPath = Path;
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break;
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default:
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var bezier = new BezierApproximator(Path);
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calculatedPath = bezier.CreateBezier();
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break;
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}
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}
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public Vector2 PositionAt(double progress)
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{
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progress = MathHelper.Clamp(progress, 0, 1);
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double index = progress * (calculatedPath.Count - 1);
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int flooredIndex = (int)index;
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Vector2 pos = calculatedPath[flooredIndex];
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if (index != flooredIndex)
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pos += (calculatedPath[flooredIndex + 1] - pos) * (float)(index - flooredIndex);
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return pos;
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}
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}
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public class BezierApproximator
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{
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private int count;
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private List<Vector2> controlPoints;
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private Vector2[] subdivisionBuffer1;
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private Vector2[] subdivisionBuffer2;
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private const float TOLERANCE = 0.5f;
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private const float TOLERANCE_SQ = TOLERANCE * TOLERANCE;
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public BezierApproximator(List<Vector2> controlPoints)
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{
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this.controlPoints = controlPoints;
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count = controlPoints.Count;
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subdivisionBuffer1 = new Vector2[count];
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subdivisionBuffer2 = new Vector2[count * 2 - 1];
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}
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/// <summary>
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/// Make sure the 2nd order derivative (approximated using finite elements) is within tolerable bounds.
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/// NOTE: The 2nd order derivative of a 2d curve represents its curvature, so intuitively this function
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/// checks (as the name suggests) whether our approximation is _locally_ "flat". More curvy parts
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/// need to have a denser approximation to be more "flat".
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/// </summary>
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/// <param name="controlPoints">The control points to check for flatness.</param>
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/// <returns>Whether the control points are flat enough.</returns>
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private static bool IsFlatEnough(Vector2[] controlPoints)
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{
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for (int i = 1; i < controlPoints.Length - 1; i++)
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if ((controlPoints[i - 1] - 2 * controlPoints[i] + controlPoints[i + 1]).LengthSquared > TOLERANCE_SQ)
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return false;
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return true;
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}
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/// <summary>
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/// Subdivides n control points representing a bezier curve into 2 sets of n control points, each
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/// describing a bezier curve equivalent to a half of the original curve. Effectively this splits
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/// the original curve into 2 curves which result in the original curve when pieced back together.
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/// </summary>
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/// <param name="controlPoints">The control points to split.</param>
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/// <param name="l">Output: The control points corresponding to the left half of the curve.</param>
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/// <param name="r">Output: The control points corresponding to the right half of the curve.</param>
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private void Subdivide(Vector2[] controlPoints, Vector2[] l, Vector2[] r)
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{
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Vector2[] midpoints = subdivisionBuffer1;
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for (int i = 0; i < count; ++i)
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midpoints[i] = controlPoints[i];
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for (int i = 0; i < count; i++)
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{
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l[i] = midpoints[0];
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r[count - i - 1] = midpoints[count - i - 1];
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for (int j = 0; j < count - i - 1; j++)
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midpoints[j] = (midpoints[j] + midpoints[j + 1]) / 2;
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}
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}
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/// <summary>
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/// This uses <a href="https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm">De Casteljau's algorithm</a> to obtain an optimal
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/// piecewise-linear approximation of the bezier curve with the same amount of points as there are control points.
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/// </summary>
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/// <param name="controlPoints">The control points describing the bezier curve to be approximated.</param>
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/// <param name="output">The points representing the resulting piecewise-linear approximation.</param>
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private void Approximate(Vector2[] controlPoints, List<Vector2> output)
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{
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Vector2[] l = subdivisionBuffer2;
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Vector2[] r = subdivisionBuffer1;
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Subdivide(controlPoints, l, r);
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for (int i = 0; i < count - 1; ++i)
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l[count + i] = r[i + 1];
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output.Add(controlPoints[0]);
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for (int i = 1; i < count - 1; ++i)
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{
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int index = 2 * i;
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Vector2 p = 0.25f * (l[index - 1] + 2 * l[index] + l[index + 1]);
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output.Add(p);
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}
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}
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/// <summary>
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/// Creates a piecewise-linear approximation of a bezier curve, by adaptively repeatedly subdividing
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/// the control points until their approximation error vanishes below a given threshold.
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/// </summary>
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/// <param name="controlPoints">The control points describing the curve.</param>
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/// <returns>A list of vectors representing the piecewise-linear approximation.</returns>
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public List<Vector2> CreateBezier()
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{
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List<Vector2> output = new List<Vector2>();
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if (count == 0)
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return output;
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Stack<Vector2[]> toFlatten = new Stack<Vector2[]>();
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Stack<Vector2[]> freeBuffers = new Stack<Vector2[]>();
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// "toFlatten" contains all the curves which are not yet approximated well enough.
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// We use a stack to emulate recursion without the risk of running into a stack overflow.
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// (More specifically, we iteratively and adaptively refine our curve with a
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// <a href="https://en.wikipedia.org/wiki/Depth-first_search">Depth-first search</a>
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// over the tree resulting from the subdivisions we make.)
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toFlatten.Push(controlPoints.ToArray());
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Vector2[] leftChild = subdivisionBuffer2;
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while (toFlatten.Count > 0)
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{
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Vector2[] parent = toFlatten.Pop();
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if (IsFlatEnough(parent))
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{
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// If the control points we currently operate on are sufficiently "flat", we use
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// an extension to De Casteljau's algorithm to obtain a piecewise-linear approximation
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// of the bezier curve represented by our control points, consisting of the same amount
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// of points as there are control points.
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Approximate(parent, output);
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freeBuffers.Push(parent);
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continue;
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}
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// If we do not yet have a sufficiently "flat" (in other words, detailed) approximation we keep
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// subdividing the curve we are currently operating on.
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Vector2[] rightChild = freeBuffers.Count > 0 ? freeBuffers.Pop() : new Vector2[count];
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Subdivide(parent, leftChild, rightChild);
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// We re-use the buffer of the parent for one of the children, so that we save one allocation per iteration.
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for (int i = 0; i < count; ++i)
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parent[i] = leftChild[i];
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toFlatten.Push(rightChild);
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toFlatten.Push(parent);
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}
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output.Add(controlPoints[count - 1]);
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return output;
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}
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}
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public enum CurveTypes
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{
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Catmull,
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44
osu.Game.Mode.Osu/Objects/SliderCurve.cs
Normal file
44
osu.Game.Mode.Osu/Objects/SliderCurve.cs
Normal file
@ -0,0 +1,44 @@
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using System.Collections.Generic;
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using OpenTK;
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namespace osu.Game.Modes.Osu.Objects
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{
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public class SliderCurve
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{
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public double Length;
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public List<Vector2> Path;
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public CurveTypes CurveType;
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private List<Vector2> calculatedPath;
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public void Calculate()
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{
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switch (CurveType)
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{
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case CurveTypes.Linear:
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calculatedPath = Path;
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break;
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default:
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var bezier = new BezierApproximator(Path);
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calculatedPath = bezier.CreateBezier();
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break;
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}
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}
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public Vector2 PositionAt(double progress)
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{
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progress = MathHelper.Clamp(progress, 0, 1);
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double index = progress * (calculatedPath.Count - 1);
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int flooredIndex = (int)index;
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Vector2 pos = calculatedPath[flooredIndex];
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if (index != flooredIndex)
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pos += (calculatedPath[flooredIndex + 1] - pos) * (float)(index - flooredIndex);
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return pos;
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}
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}
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}
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@ -41,6 +41,7 @@
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<Reference Include="System.Xml" />
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</ItemGroup>
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<ItemGroup>
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<Compile Include="Objects\BezierApproximator.cs" />
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<Compile Include="Objects\Drawables\DrawableOsuHitObject.cs" />
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<Compile Include="Objects\Drawables\Pieces\ApproachCircle.cs" />
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<Compile Include="Objects\Drawables\Pieces\CirclePiece.cs" />
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@ -53,6 +54,7 @@
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<Compile Include="Objects\Drawables\Pieces\RingPiece.cs" />
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<Compile Include="Objects\Drawables\Pieces\Triangles.cs" />
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<Compile Include="Objects\OsuHitObjectParser.cs" />
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<Compile Include="Objects\SliderCurve.cs" />
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<Compile Include="OsuScore.cs" />
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<Compile Include="OsuScoreProcessor.cs" />
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<Compile Include="UI\OsuComboCounter.cs" />
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