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Code Issues Releases Wiki Activity

Use framework helper functions for path approximation

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This commit is contained in:
Dean Herbert 2018-11-02 02:43:43 +09:00
parent d78348f178
commit e6ee3dc73e
8 changed files with 8 additions and 347 deletions
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6
osu.Game.Rulesets.Osu/Edit/Masks/SliderMasks/SliderPlacementMask.cs
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@ -8,9 +8,9 @@ using osu.Framework.Allocation;
using osu.Framework.Extensions.IEnumerableExtensions;
using osu.Framework.Graphics;
using osu.Framework.Input.Events;
using osu.Framework.MathUtils;
using osu.Game.Graphics;
using osu.Game.Rulesets.Edit;
using osu.Game.Rulesets.Objects;
using osu.Game.Rulesets.Objects.Types;
using osu.Game.Rulesets.Osu.Edit.Masks.SliderMasks.Components;
using OpenTK;
@ -164,10 +164,10 @@ namespace osu.Game.Rulesets.Osu.Edit.Masks.SliderMasks
{
case 1:
case 2:
result = new LinearApproximator().Approximate(allControlPoints);
result = PathApproximator.ApproximateLinear(allControlPoints);
break;
default:
result = new BezierApproximator().Approximate(allControlPoints);
result = PathApproximator.ApproximateBezier(allControlPoints);
break;
}

145
osu.Game/Rulesets/Objects/BezierApproximator.cs
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@ -1,145 +0,0 @@
// Copyright (c) 2007-2018 ppy Pty Ltd <contact@ppy.sh>.
// Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
using System;
using System.Collections.Generic;
using OpenTK;
namespace osu.Game.Rulesets.Objects
{
public struct BezierApproximator : IApproximator
{
private const float tolerance = 0.25f;
private const float tolerance_sq = tolerance * tolerance;
private int count;
private Vector2[] subdivisionBuffer1;
private Vector2[] subdivisionBuffer2;
/// <summary>
/// Creates a piecewise-linear approximation of a bezier curve, by adaptively repeatedly subdividing
/// the control points until their approximation error vanishes below a given threshold.
/// </summary>
/// <returns>A list of vectors representing the piecewise-linear approximation.</returns>
public List<Vector2> Approximate(ReadOnlySpan<Vector2> controlPoints)
{
List<Vector2> output = new List<Vector2>();
count = controlPoints.Length;
if (count == 0)
return output;
subdivisionBuffer1 = new Vector2[count];
subdivisionBuffer2 = new Vector2[count * 2 - 1];
Stack<Vector2[]> toFlatten = new Stack<Vector2[]>();
Stack<Vector2[]> freeBuffers = new Stack<Vector2[]>();
// "toFlatten" contains all the curves which are not yet approximated well enough.
// We use a stack to emulate recursion without the risk of running into a stack overflow.
// (More specifically, we iteratively and adaptively refine our curve with a
// <a href="https://en.wikipedia.org/wiki/Depth-first_search">Depth-first search</a>
// over the tree resulting from the subdivisions we make.)
toFlatten.Push(controlPoints.ToArray());
Vector2[] leftChild = subdivisionBuffer2;
while (toFlatten.Count > 0)
{
Vector2[] parent = toFlatten.Pop();
if (isFlatEnough(parent))
{
// If the control points we currently operate on are sufficiently "flat", we use
// an extension to De Casteljau's algorithm to obtain a piecewise-linear approximation
// of the bezier curve represented by our control points, consisting of the same amount
// of points as there are control points.
approximate(parent, output);
freeBuffers.Push(parent);
continue;
}
// If we do not yet have a sufficiently "flat" (in other words, detailed) approximation we keep
// subdividing the curve we are currently operating on.
Vector2[] rightChild = freeBuffers.Count > 0 ? freeBuffers.Pop() : new Vector2[count];
subdivide(parent, leftChild, rightChild);
// We re-use the buffer of the parent for one of the children, so that we save one allocation per iteration.
for (int i = 0; i < count; ++i)
parent[i] = leftChild[i];
toFlatten.Push(rightChild);
toFlatten.Push(parent);
}
output.Add(controlPoints[count - 1]);
return output;
}
/// <summary>
/// Make sure the 2nd order derivative (approximated using finite elements) is within tolerable bounds.
/// NOTE: The 2nd order derivative of a 2d curve represents its curvature, so intuitively this function
/// checks (as the name suggests) whether our approximation is _locally_ "flat". More curvy parts
/// need to have a denser approximation to be more "flat".
/// </summary>
/// <param name="controlPoints">The control points to check for flatness.</param>
/// <returns>Whether the control points are flat enough.</returns>
private static bool isFlatEnough(Vector2[] controlPoints)
{
for (int i = 1; i < controlPoints.Length - 1; i++)
if ((controlPoints[i - 1] - 2 * controlPoints[i] + controlPoints[i + 1]).LengthSquared > tolerance_sq * 4)
return false;
return true;
}
/// <summary>
/// Subdivides n control points representing a bezier curve into 2 sets of n control points, each
/// describing a bezier curve equivalent to a half of the original curve. Effectively this splits
/// the original curve into 2 curves which result in the original curve when pieced back together.
/// </summary>
/// <param name="controlPoints">The control points to split.</param>
/// <param name="l">Output: The control points corresponding to the left half of the curve.</param>
/// <param name="r">Output: The control points corresponding to the right half of the curve.</param>
private void subdivide(Vector2[] controlPoints, Vector2[] l, Vector2[] r)
{
Vector2[] midpoints = subdivisionBuffer1;
for (int i = 0; i < count; ++i)
midpoints[i] = controlPoints[i];
for (int i = 0; i < count; i++)
{
l[i] = midpoints[0];
r[count - i - 1] = midpoints[count - i - 1];
for (int j = 0; j < count - i - 1; j++)
midpoints[j] = (midpoints[j] + midpoints[j + 1]) / 2;
}
}
/// <summary>
/// This uses <a href="https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm">De Casteljau's algorithm</a> to obtain an optimal
/// piecewise-linear approximation of the bezier curve with the same amount of points as there are control points.
/// </summary>
/// <param name="controlPoints">The control points describing the bezier curve to be approximated.</param>
/// <param name="output">The points representing the resulting piecewise-linear approximation.</param>
private void approximate(Vector2[] controlPoints, List<Vector2> output)
{
Vector2[] l = subdivisionBuffer2;
Vector2[] r = subdivisionBuffer1;
subdivide(controlPoints, l, r);
for (int i = 0; i < count - 1; ++i)
l[count + i] = r[i + 1];
output.Add(controlPoints[0]);
for (int i = 1; i < count - 1; ++i)
{
int index = 2 * i;
Vector2 p = 0.25f * (l[index - 1] + 2 * l[index] + l[index + 1]);
output.Add(p);
}
}
}
}

63
osu.Game/Rulesets/Objects/CatmullApproximator.cs
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@ -1,63 +0,0 @@
// Copyright (c) 2007-2018 ppy Pty Ltd <contact@ppy.sh>.
// Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
using System;
using System.Collections.Generic;
using OpenTK;
namespace osu.Game.Rulesets.Objects
{
public readonly struct CatmullApproximator : IApproximator
{
/// <summary>
/// The amount of pieces to calculate for each controlpoint quadruplet.
/// </summary>
private const int detail = 50;
/// <summary>
/// Creates a piecewise-linear approximation of a Catmull-Rom spline.
/// </summary>
/// <returns>A list of vectors representing the piecewise-linear approximation.</returns>
public List<Vector2> Approximate(ReadOnlySpan<Vector2> controlPoints)
{
var result = new List<Vector2>((controlPoints.Length - 1) * detail * 2);
for (int i = 0; i < controlPoints.Length - 1; i++)
{
var v1 = i > 0 ? controlPoints[i - 1] : controlPoints[i];
var v2 = controlPoints[i];
var v3 = i < controlPoints.Length - 1 ? controlPoints[i + 1] : v2 + v2 - v1;
var v4 = i < controlPoints.Length - 2 ? controlPoints[i + 2] : v3 + v3 - v2;
for (int c = 0; c < detail; c++)
{
result.Add(findPoint(ref v1, ref v2, ref v3, ref v4, (float)c / detail));
result.Add(findPoint(ref v1, ref v2, ref v3, ref v4, (float)(c + 1) / detail));
}
}
return result;
}
/// <summary>
/// Finds a point on the spline at the position of a parameter.
/// </summary>
/// <param name="vec1">The first vector.</param>
/// <param name="vec2">The second vector.</param>
/// <param name="vec3">The third vector.</param>
/// <param name="vec4">The fourth vector.</param>
/// <param name="t">The parameter at which to find the point on the spline, in the range [0, 1].</param>
/// <returns>The point on the spline at <paramref name="t"/>.</returns>
private Vector2 findPoint(ref Vector2 vec1, ref Vector2 vec2, ref Vector2 vec3, ref Vector2 vec4, float t)
{
float t2 = t * t;
float t3 = t * t2;
Vector2 result;
result.X = 0.5f * (2f * vec2.X + (-vec1.X + vec3.X) * t + (2f * vec1.X - 5f * vec2.X + 4f * vec3.X - vec4.X) * t2 + (-vec1.X + 3f * vec2.X - 3f * vec3.X + vec4.X) * t3);
result.Y = 0.5f * (2f * vec2.Y + (-vec1.Y + vec3.Y) * t + (2f * vec1.Y - 5f * vec2.Y + 4f * vec3.Y - vec4.Y) * t2 + (-vec1.Y + 3f * vec2.Y - 3f * vec3.Y + vec4.Y) * t3);
return result;
}
}
}

90
osu.Game/Rulesets/Objects/CircularArcApproximator.cs
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@ -1,90 +0,0 @@
// Copyright (c) 2007-2018 ppy Pty Ltd <contact@ppy.sh>.
// Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
using System;
using System.Collections.Generic;
using osu.Framework.MathUtils;
using OpenTK;
namespace osu.Game.Rulesets.Objects
{
public readonly struct CircularArcApproximator : IApproximator
{
private const float tolerance = 0.1f;
/// <summary>
/// Creates a piecewise-linear approximation of a circular arc curve.
/// </summary>
/// <returns>A list of vectors representing the piecewise-linear approximation.</returns>
public List<Vector2> Approximate(ReadOnlySpan<Vector2> controlPoints)
{
Vector2 a = controlPoints[0];
Vector2 b = controlPoints[1];
Vector2 c = controlPoints[2];
float aSq = (b - c).LengthSquared;
float bSq = (a - c).LengthSquared;
float cSq = (a - b).LengthSquared;
// If we have a degenerate triangle where a side-length is almost zero, then give up and fall
// back to a more numerically stable method.
if (Precision.AlmostEquals(aSq, 0) || Precision.AlmostEquals(bSq, 0) || Precision.AlmostEquals(cSq, 0))
return new List<Vector2>();
float s = aSq * (bSq + cSq - aSq);
float t = bSq * (aSq + cSq - bSq);
float u = cSq * (aSq + bSq - cSq);
float sum = s + t + u;
// If we have a degenerate triangle with an almost-zero size, then give up and fall
// back to a more numerically stable method.
if (Precision.AlmostEquals(sum, 0))
return new List<Vector2>();
Vector2 centre = (s * a + t * b + u * c) / sum;
Vector2 dA = a - centre;
Vector2 dC = c - centre;
float r = dA.Length;
double thetaStart = Math.Atan2(dA.Y, dA.X);
double thetaEnd = Math.Atan2(dC.Y, dC.X);
while (thetaEnd < thetaStart)
thetaEnd += 2 * Math.PI;
double dir = 1;
double thetaRange = thetaEnd - thetaStart;
// Decide in which direction to draw the circle, depending on which side of
// AC B lies.
Vector2 orthoAtoC = c - a;
orthoAtoC = new Vector2(orthoAtoC.Y, -orthoAtoC.X);
if (Vector2.Dot(orthoAtoC, b - a) < 0)
{
dir = -dir;
thetaRange = 2 * Math.PI - thetaRange;
}
// We select the amount of points for the approximation by requiring the discrete curvature
// to be smaller than the provided tolerance. The exact angle required to meet the tolerance
// is: 2 * Math.Acos(1 - TOLERANCE / r)
// The special case is required for extremely short sliders where the radius is smaller than
// the tolerance. This is a pathological rather than a realistic case.
int amountPoints = 2 * r <= tolerance ? 2 : Math.Max(2, (int)Math.Ceiling(thetaRange / (2 * Math.Acos(1 - tolerance / r))));
List<Vector2> output = new List<Vector2>(amountPoints);
for (int i = 0; i < amountPoints; ++i)
{
double fract = (double)i / (amountPoints - 1);
double theta = thetaStart + dir * fract * thetaRange;
Vector2 o = new Vector2((float)Math.Cos(theta), (float)Math.Sin(theta)) * r;
output.Add(centre + o);
}
return output;
}
}
}

19
osu.Game/Rulesets/Objects/IApproximator.cs
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@ -1,19 +0,0 @@
// Copyright (c) 2007-2018 ppy Pty Ltd <contact@ppy.sh>.
// Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
using System;
using System.Collections.Generic;
using OpenTK;
namespace osu.Game.Rulesets.Objects
{
public interface IApproximator
{
/// <summary>
/// Approximates a path by interpolating a sequence of control points.
/// </summary>
/// <param name="controlPoints">The control points of the path.</param>
/// <returns>A set of points that lie on the path.</returns>
List<Vector2> Approximate(ReadOnlySpan<Vector2> controlPoints);
}
}

22
osu.Game/Rulesets/Objects/LinearApproximator.cs
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@ -1,22 +0,0 @@
// Copyright (c) 2007-2018 ppy Pty Ltd <contact@ppy.sh>.
// Licensed under the MIT Licence - https://raw.githubusercontent.com/ppy/osu/master/LICENCE
using System;
using System.Collections.Generic;
using OpenTK;
namespace osu.Game.Rulesets.Objects
{
public readonly struct LinearApproximator : IApproximator
{
public List<Vector2> Approximate(ReadOnlySpan<Vector2> controlPoints)
{
var result = new List<Vector2>(controlPoints.Length);
foreach (var c in controlPoints)
result.Add(c);
return result;
}
}
}

8
osu.Game/Rulesets/Objects/SliderPath.cs
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@ -28,14 +28,14 @@ namespace osu.Game.Rulesets.Objects
switch (PathType)
{
case PathType.Linear:
return new LinearApproximator().Approximate(subControlPoints);
return PathApproximator.ApproximateLinear(subControlPoints);
case PathType.PerfectCurve:
//we can only use CircularArc iff we have exactly three control points and no dissection.
if (ControlPoints.Length != 3 || subControlPoints.Length != 3)
break;
// Here we have exactly 3 control points. Attempt to fit a circular arc.
List<Vector2> subpath = new CircularArcApproximator().Approximate(subControlPoints);
List<Vector2> subpath = PathApproximator.ApproximateCircularArc(subControlPoints);
// If for some reason a circular arc could not be fit to the 3 given points, fall back to a numerically stable bezier approximation.
if (subpath.Count == 0)
@ -43,10 +43,10 @@ namespace osu.Game.Rulesets.Objects
return subpath;
case PathType.Catmull:
return new CatmullApproximator().Approximate(subControlPoints);
return PathApproximator.ApproximateCatmull(subControlPoints);
}
return new BezierApproximator().Approximate(subControlPoints);
return PathApproximator.ApproximateBezier(subControlPoints);
}
private void calculatePath()

2
osu.Game/osu.Game.csproj
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@ -18,7 +18,7 @@
<PackageReference Include="Microsoft.EntityFrameworkCore.Sqlite" Version="2.1.4" />
<PackageReference Include="Microsoft.EntityFrameworkCore.Sqlite.Core" Version="2.1.4" />
<PackageReference Include="Newtonsoft.Json" Version="11.0.2" />
<PackageReference Include="ppy.osu.Framework" Version="2018.1030.0" />
<PackageReference Include="ppy.osu.Framework" Version="2018.1102.0" />
<PackageReference Include="SharpCompress" Version="0.22.0" />
<PackageReference Include="NUnit" Version="3.11.0" />
<PackageReference Include="SharpRaven" Version="2.4.0" />