mirror of
https://github.com/ppy/osu.git
synced 2024-09-22 10:47:25 +08:00
353 lines
13 KiB
C#
353 lines
13 KiB
C#
// 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) })
|
|
};
|
|
|
|
#region CircularArcProperties
|
|
|
|
//TODO: Get this from osu!framework instead
|
|
public readonly struct CircularArcProperties
|
|
{
|
|
public readonly bool IsValid;
|
|
public readonly double ThetaStart;
|
|
public readonly double ThetaRange;
|
|
public readonly double Direction;
|
|
public readonly float Radius;
|
|
public readonly Vector2 Centre;
|
|
|
|
public double ThetaEnd => ThetaStart + ThetaRange * Direction;
|
|
|
|
public CircularArcProperties(double thetaStart, double thetaRange, double direction, float radius, Vector2 centre)
|
|
{
|
|
IsValid = true;
|
|
ThetaStart = thetaStart;
|
|
ThetaRange = thetaRange;
|
|
Direction = direction;
|
|
Radius = radius;
|
|
Centre = centre;
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Computes various properties that can be used to approximate the circular arc.
|
|
/// </summary>
|
|
/// <param name="controlPoints">Three distinct points on the arc.</param>
|
|
private static CircularArcProperties circularArcProperties(ReadOnlySpan<Vector2> controlPoints)
|
|
{
|
|
Vector2 a = controlPoints[0];
|
|
Vector2 b = controlPoints[1];
|
|
Vector2 c = controlPoints[2];
|
|
|
|
// If we have a degenerate triangle where a side-length is almost zero, then give up and fallback to a more numerically stable method.
|
|
if (Precision.AlmostEquals(0, (b.Y - a.Y) * (c.X - a.X) - (b.X - a.X) * (c.Y - a.Y)))
|
|
return default; // Implicitly sets `IsValid` to false
|
|
|
|
// See: https://en.wikipedia.org/wiki/Circumscribed_circle#Cartesian_coordinates_2
|
|
float d = 2 * (a.X * (b - c).Y + b.X * (c - a).Y + c.X * (a - b).Y);
|
|
float aSq = a.LengthSquared;
|
|
float bSq = b.LengthSquared;
|
|
float cSq = c.LengthSquared;
|
|
|
|
Vector2 centre = new Vector2(
|
|
aSq * (b - c).Y + bSq * (c - a).Y + cSq * (a - b).Y,
|
|
aSq * (c - b).X + bSq * (a - c).X + cSq * (b - a).X) / d;
|
|
|
|
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;
|
|
}
|
|
|
|
return new CircularArcProperties(thetaStart, thetaRange, dir, r, centre);
|
|
}
|
|
|
|
#endregion
|
|
|
|
public static IEnumerable<Vector2> ConvertToLegacyBezier(IList<PathControlPoint> controlPoints, Vector2 position)
|
|
{
|
|
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;
|
|
}
|
|
|
|
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)
|
|
{
|
|
var pr = circularArcProperties(controlPoints);
|
|
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;
|
|
}
|
|
}
|
|
}
|