osu/osu.Game/Rulesets/Objects/BezierConverter.cs

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// Copyright (c) ppy Pty Ltd <contact@ppy.sh>. Licensed under the MIT Licence.
// See the LICENCE file in the repository root for full licence text.
using System;
using System.Collections.Generic;
using System.Linq;
using osu.Framework.Utils;
using osu.Game.Rulesets.Objects.Types;
using osuTK;
namespace osu.Game.Rulesets.Objects
{
public static class BezierConverter
{
private struct CircleBezierPreset
{
public readonly double ArcLength;
public readonly Vector2d[] ControlPoints;
public CircleBezierPreset(double arcLength, Vector2d[] controlPoints)
{
ArcLength = arcLength;
ControlPoints = controlPoints;
}
}
// Extremely accurate a bezier anchor positions for approximating circles of several arc lengths
private static readonly CircleBezierPreset[] circle_presets =
{
new CircleBezierPreset(0.4993379862754501,
new[] { new Vector2d(1, 0), new Vector2d(1, 0.2549893626632736f), new Vector2d(0.8778997558480327f, 0.47884446188920726f) }),
new CircleBezierPreset(1.7579419829169447,
new[] { new Vector2d(1, 0), new Vector2d(1, 0.6263026f), new Vector2d(0.42931178f, 1.0990661f), new Vector2d(-0.18605515f, 0.9825393f) }),
new CircleBezierPreset(3.1385246920140215,
new[] { new Vector2d(1, 0), new Vector2d(1, 0.87084764f), new Vector2d(0.002304826f, 1.5033062f), new Vector2d(-0.9973236f, 0.8739115f), new Vector2d(-0.9999953f, 0.0030679568f) }),
new CircleBezierPreset(5.69720464620727,
new[] { new Vector2d(1, 0), new Vector2d(1, 1.4137783f), new Vector2d(-1.4305235f, 2.0779421f), new Vector2d(-2.3410065f, -0.94017583f), new Vector2d(0.05132711f, -1.7309346f), new Vector2d(0.8331702f, -0.5530167f) }),
new CircleBezierPreset(2 * Math.PI,
new[] { new Vector2d(1, 0), new Vector2d(1, 1.2447058f), new Vector2d(-0.8526471f, 2.118367f), new Vector2d(-2.6211002f, 7.854936e-06f), new Vector2d(-0.8526448f, -2.118357f), new Vector2d(1, -1.2447058f), new Vector2d(1, 0) })
};
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/// <summary>
/// Counts the number of segments in a slider path.
/// </summary>
/// <param name="controlPoints">The control points of the path.</param>
/// <returns>The number of segments in a slider path.</returns>
public static int CountSegments(IList<PathControlPoint> controlPoints) => controlPoints.Where((t, i) => t.Type != null && i < controlPoints.Count - 1).Count();
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/// <summary>
/// Converts a slider path to bezier control point positions compatible with the legacy osu! client.
/// </summary>
/// <param name="controlPoints">The control points of the path.</param>
/// <param name="position">The offset for the whole path.</param>
/// <returns>The list of legacy bezier control point positions.</returns>
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public static List<Vector2> ConvertToLegacyBezier(IList<PathControlPoint> controlPoints, Vector2 position)
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{
Vector2[] vertices = new Vector2[controlPoints.Count];
for (int i = 0; i < controlPoints.Count; i++)
vertices[i] = controlPoints[i].Position;
var result = new List<Vector2>();
int start = 0;
for (int i = 0; i < controlPoints.Count; i++)
{
if (controlPoints[i].Type == null && i < controlPoints.Count - 1)
continue;
// The current vertex ends the segment
var segmentVertices = vertices.AsSpan().Slice(start, i - start + 1);
var segmentType = controlPoints[start].Type ?? PathType.Linear;
switch (segmentType)
{
case PathType.Catmull:
result.AddRange(from segment in ConvertCatmullToBezierAnchors(segmentVertices) from v in segment select v + position);
break;
case PathType.Linear:
result.AddRange(from segment in ConvertLinearToBezierAnchors(segmentVertices) from v in segment select v + position);
break;
case PathType.PerfectCurve:
result.AddRange(ConvertCircleToBezierAnchors(segmentVertices).Select(v => v + position));
break;
default:
foreach (Vector2 v in segmentVertices)
{
result.Add(v + position);
}
break;
}
// Start the new segment at the current vertex
start = i;
}
return result;
}
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/// <summary>
/// Converts a path of control points to an identical path using only Bezier type control points.
/// </summary>
/// <param name="controlPoints">The control points of the path.</param>
/// <returns>The list of bezier control points.</returns>
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public static List<PathControlPoint> ConvertToModernBezier(IList<PathControlPoint> controlPoints)
{
Vector2[] vertices = new Vector2[controlPoints.Count];
for (int i = 0; i < controlPoints.Count; i++)
vertices[i] = controlPoints[i].Position;
var result = new List<PathControlPoint>();
int start = 0;
for (int i = 0; i < controlPoints.Count; i++)
{
if (controlPoints[i].Type == null && i < controlPoints.Count - 1)
continue;
// The current vertex ends the segment
var segmentVertices = vertices.AsSpan().Slice(start, i - start + 1);
var segmentType = controlPoints[start].Type ?? PathType.Linear;
switch (segmentType)
{
case PathType.Catmull:
foreach (var segment in ConvertCatmullToBezierAnchors(segmentVertices))
{
for (int j = 0; j < segment.Length - 1; j++)
{
result.Add(new PathControlPoint(segment[j], j == 0 ? PathType.Bezier : null));
}
}
break;
case PathType.Linear:
foreach (var segment in ConvertLinearToBezierAnchors(segmentVertices))
{
for (int j = 0; j < segment.Length - 1; j++)
{
result.Add(new PathControlPoint(segment[j], j == 0 ? PathType.Bezier : null));
}
}
break;
case PathType.PerfectCurve:
var circleResult = ConvertCircleToBezierAnchors(segmentVertices);
for (int j = 0; j < circleResult.Length - 1; j++)
{
result.Add(new PathControlPoint(circleResult[j], j == 0 ? PathType.Bezier : null));
}
break;
default:
for (int j = 0; j < segmentVertices.Length - 1; j++)
{
result.Add(new PathControlPoint(segmentVertices[j], j == 0 ? PathType.Bezier : null));
}
break;
}
// Start the new segment at the current vertex
start = i;
}
result.Add(new PathControlPoint(controlPoints[^1].Position));
return result;
}
/// <summary>
/// Converts perfect curve anchors to bezier anchors.
/// </summary>
/// <param name="controlPoints">The control point positions to convert.</param>
public static Vector2[] ConvertCircleToBezierAnchors(ReadOnlySpan<Vector2> controlPoints)
{
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if (controlPoints.Length != 3)
return controlPoints.ToArray();
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var pr = new CircularArcProperties(controlPoints);
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if (!pr.IsValid)
return controlPoints.ToArray();
CircleBezierPreset preset = circle_presets.Last();
foreach (CircleBezierPreset cbp in circle_presets)
{
if (cbp.ArcLength < pr.ThetaRange) continue;
preset = cbp;
break;
}
double arcLength = preset.ArcLength;
var arc = new Vector2d[preset.ControlPoints.Length];
preset.ControlPoints.CopyTo(arc, 0);
// Converge on arcLength of thetaRange
int n = arc.Length - 1;
double tf = pr.ThetaRange / arcLength;
while (Math.Abs(tf - 1) > 1E-7)
{
for (int j = 0; j < n; j++)
{
for (int i = n; i > j; i--)
{
arc[i] = arc[i] * tf + arc[i - 1] * (1 - tf);
}
}
arcLength = Math.Atan2(arc.Last()[1], arc.Last()[0]);
if (arcLength < 0)
{
arcLength += 2 * Math.PI;
}
tf = pr.ThetaRange / arcLength;
}
// Adjust rotation, radius, and position
var result = new Vector2[arc.Length];
for (int i = 0; i < arc.Length; i++)
{
result[i] = new Vector2(
(float)((Math.Cos(pr.ThetaStart) * arc[i].X + -Math.Sin(pr.ThetaStart) * pr.Direction * arc[i].Y) * pr.Radius + pr.Centre.X),
(float)((Math.Sin(pr.ThetaStart) * arc[i].X + Math.Cos(pr.ThetaStart) * pr.Direction * arc[i].Y) * pr.Radius + pr.Centre.Y));
}
return result;
}
/// <summary>
/// Converts catmull anchors to bezier anchors.
/// </summary>
/// <param name="controlPoints">The control point positions to convert.</param>
public static Vector2[][] ConvertCatmullToBezierAnchors(ReadOnlySpan<Vector2> controlPoints)
{
int iLen = controlPoints.Length;
var bezier = new Vector2[iLen - 1][];
for (int i = 0; i < iLen - 1; i++)
{
var v1 = i > 0 ? controlPoints[i - 1] : controlPoints[i];
var v2 = controlPoints[i];
var v3 = i < iLen - 1 ? controlPoints[i + 1] : v2 + v2 - v1;
var v4 = i < iLen - 2 ? controlPoints[i + 2] : v3 + v3 - v2;
bezier[i] = new[]
{
v2,
(-v1 + 6 * v2 + v3) / 6,
(-v4 + 6 * v3 + v2) / 6,
v3
};
}
return bezier;
}
/// <summary>
/// Converts linear anchors to bezier anchors.
/// </summary>
/// <param name="controlPoints">The control point positions to convert.</param>
public static Vector2[][] ConvertLinearToBezierAnchors(ReadOnlySpan<Vector2> controlPoints)
{
int iLen = controlPoints.Length;
var bezier = new Vector2[iLen - 1][];
for (int i = 0; i < iLen - 1; i++)
{
bezier[i] = new[]
{
controlPoints[i],
controlPoints[i + 1]
};
}
return bezier;
}
}
}