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