Merge pull request #206 from SixLabors/sw/path-drawer

Add drawing centric path building api.

Author: JimBobSquarePants

src/ImageSharp.Drawing/Processing/Processors/Text/DrawTextProcessor{TPixel}.cs

@@ -259,7 +259,7 @@ public void BeginText(FontRectangle bounds)
 
             public void CubicBezierTo(Vector2 secondControlPoint, Vector2 thirdControlPoint, Vector2 point)
             {
-                this.builder.AddBezier(this.currentPoint, secondControlPoint, thirdControlPoint, point);
+                this.builder.AddCubicBezier(this.currentPoint, secondControlPoint, thirdControlPoint, point);
                 this.currentPoint = point;
             }
 
@@ -418,7 +418,7 @@ public void MoveTo(Vector2 point)
 
             public void QuadraticBezierTo(Vector2 secondControlPoint, Vector2 point)
             {
-                this.builder.AddBezier(this.currentPoint, secondControlPoint, point);
+                this.builder.AddQuadraticBezier(this.currentPoint, secondControlPoint, point);
                 this.currentPoint = point;
             }
 

src/ImageSharp.Drawing/Shapes/ArcLineSegment.cs

@@ -0,0 +1,316 @@
+// Copyright (c) Six Labors.
+// Licensed under the Apache License, Version 2.0.
+
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Runtime.CompilerServices;
+
+namespace SixLabors.ImageSharp.Drawing
+{
+    /// <summary>
+    /// Represents a line segment that contains radii and angles that will be rendered as a elliptical arc.
+    /// </summary>
+    public class ArcLineSegment : ILineSegment
+    {
+        private const float ZeroTolerance = 1e-05F;
+        private readonly PointF[] linePoints;
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="ArcLineSegment"/> class.
+        /// </summary>
+        /// <param name="from">The absolute coordinates of the current point on the path.</param>
+        /// <param name="to">The absolute coordinates of the final point of the arc.</param>
+        /// <param name="radius">The radii of the ellipse (also known as its semi-major and semi-minor axes).</param>
+        /// <param name="rotation">The angle, in degrees, from the x-axis of the current coordinate system to the x-axis of the ellipse.</param>
+        /// <param name="largeArc">
+        /// The large arc flag, and is <see langword="false"/> if an arc spanning less than or equal to 180 degrees
+        /// is chosen, or <see langword="true"/> if an arc spanning greater than 180 degrees is chosen.
+        /// </param>
+        /// <param name="sweep">
+        /// The sweep flag, and is <see langword="false"/> if the line joining center to arc sweeps through decreasing
+        /// angles, or <see langword="true"/> if it sweeps through increasing angles.
+        /// </param>
+        public ArcLineSegment(PointF from, PointF to, SizeF radius, float rotation, bool largeArc, bool sweep)
+        {
+            rotation = GeometryUtilities.DegreeToRadian(rotation);
+            bool circle = largeArc && ((Vector2)to - (Vector2)from).LengthSquared() < ZeroTolerance && radius.Width > 0 && radius.Height > 0;
+            this.linePoints = EllipticArcFromEndParams(from, to, radius, rotation, largeArc, sweep, circle);
+            this.EndPoint = this.linePoints[this.linePoints.Length - 1];
+        }
+
+        /// <summary>
+        /// Initializes a new instance of the <see cref="ArcLineSegment"/> class.
+        /// </summary>
+        /// <param name="center">The coordinates of the center of the ellipse.</param>
+        /// <param name="radius">The radii of the ellipse (also known as its semi-major and semi-minor axes).</param>
+        /// <param name="rotation">The angle, in degrees, from the x-axis of the current coordinate system to the x-axis of the ellipse.</param>
+        /// <param name="startAngle">
+        /// The start angle of the elliptical arc prior to the stretch and rotate operations.
+        /// (0 is at the 3 o'clock position of the arc's circle).
+        /// </param>
+        /// <param name="sweepAngle">The angle between <paramref name="startAngle"/> and the end of the arc.</param>
+        public ArcLineSegment(PointF center, SizeF radius, float rotation, float startAngle, float sweepAngle)
+        {
+            rotation = GeometryUtilities.DegreeToRadian(rotation);
+            startAngle = GeometryUtilities.DegreeToRadian(Clamp(startAngle, -360F, 360F));
+            sweepAngle = GeometryUtilities.DegreeToRadian(Clamp(sweepAngle, -360F, 360F));
+
+            Vector2 from = EllipticArcPoint(center, radius, rotation, startAngle);
+            Vector2 to = EllipticArcPoint(center, radius, rotation, startAngle + sweepAngle);
+
+            bool largeArc = Math.Abs(sweepAngle) > MathF.PI;
+            bool sweep = sweepAngle > 0;
+            bool circle = largeArc && (to - from).LengthSquared() < ZeroTolerance && radius.Width > 0 && radius.Height > 0;
+
+            this.linePoints = EllipticArcFromEndParams(from, to, radius, rotation, largeArc, sweep, circle);
+            this.EndPoint = this.linePoints[this.linePoints.Length - 1];
+        }
+
+        private ArcLineSegment(PointF[] linePoints)
+        {
+            this.linePoints = linePoints;
+            this.EndPoint = this.linePoints[this.linePoints.Length - 1];
+        }
+
+        /// <inheritdoc/>
+        public PointF EndPoint { get; }
+
+        /// <inheritdoc/>
+        public ReadOnlyMemory<PointF> Flatten() => this.linePoints;
+
+        /// <summary>
+        /// Transforms the current <see cref="ArcLineSegment"/> using specified matrix.
+        /// </summary>
+        /// <param name="matrix">The transformation matrix.</param>
+        /// <returns>An <see cref="ArcLineSegment"/> with the matrix applied to it.</returns>
+        public ILineSegment Transform(Matrix3x2 matrix)
+        {
+            if (matrix.IsIdentity)
+            {
+                return this;
+            }
+
+            var transformedPoints = new PointF[this.linePoints.Length];
+            for (int i = 0; i < this.linePoints.Length; i++)
+            {
+                transformedPoints[i] = PointF.Transform(this.linePoints[i], matrix);
+            }
+
+            return new ArcLineSegment(transformedPoints);
+        }
+
+        /// <inheritdoc/>
+        ILineSegment ILineSegment.Transform(Matrix3x2 matrix) => this.Transform(matrix);
+
+        private static PointF[] EllipticArcFromEndParams(PointF from, PointF to, SizeF radius, float rotation, bool largeArc, bool sweep, bool circle)
+        {
+            {
+                var absRadius = Vector2.Abs(radius);
+
+                if (circle)
+                {
+                    // It's a circle. SVG arcs cannot handle this so let's hack together our own angles.
+                    // This appears to match the behavior of Web CanvasRenderingContext2D.arc().
+                    // https://developer.mozilla.org/en-US/docs/Web/API/CanvasRenderingContext2D/arc
+                    Vector2 center = (Vector2)from - new Vector2(absRadius.X, 0);
+                    return EllipticArcToBezierCurve(from, center, absRadius, rotation, 0, 2 * MathF.PI);
+                }
+                else
+                {
+                    if (EllipticArcOutOfRange(from, to, radius))
+                    {
+                        return new[] { from, to };
+                    }
+
+                    float xRotation = rotation;
+                    EndpointToCenterArcParams(from, to, ref absRadius, xRotation, largeArc, sweep, out Vector2 center, out Vector2 angles);
+
+                    return EllipticArcToBezierCurve(from, center, absRadius, xRotation, angles.X, angles.Y);
+                }
+            }
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static bool EllipticArcOutOfRange(Vector2 from, Vector2 to, Vector2 radius)
+        {
+            // F.6.2 Out-of-range parameters
+            radius = Vector2.Abs(radius);
+            float len = (to - from).LengthSquared();
+            if (len < ZeroTolerance)
+            {
+                return true;
+            }
+
+            if (radius.X < ZeroTolerance || radius.Y < ZeroTolerance)
+            {
+                return true;
+            }
+
+            return false;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static Vector2 EllipticArcDerivative(Vector2 r, float xAngle, float t)
+            => new(
+                (-r.X * MathF.Cos(xAngle) * MathF.Sin(t)) - (r.Y * MathF.Sin(xAngle) * MathF.Cos(t)),
+                (-r.X * MathF.Sin(xAngle) * MathF.Sin(t)) + (r.Y * MathF.Cos(xAngle) * MathF.Cos(t)));
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static Vector2 EllipticArcPoint(Vector2 c, Vector2 r, float xAngle, float t)
+            => new(
+                c.X + (r.X * MathF.Cos(xAngle) * MathF.Cos(t)) - (r.Y * MathF.Sin(xAngle) * MathF.Sin(t)),
+                c.Y + (r.X * MathF.Sin(xAngle) * MathF.Cos(t)) + (r.Y * MathF.Cos(xAngle) * MathF.Sin(t)));
+
+        private static PointF[] EllipticArcToBezierCurve(Vector2 from, Vector2 center, Vector2 radius, float xAngle, float startAngle, float sweepAngle)
+        {
+            List<PointF> points = new();
+
+            float s = startAngle;
+            float e = s + sweepAngle;
+            bool neg = e < s;
+            float sign = neg ? -1 : 1;
+            float remain = Math.Abs(e - s);
+
+            Vector2 prev = EllipticArcPoint(center, radius, xAngle, s);
+
+            while (remain > ZeroTolerance)
+            {
+                float step = (float)Math.Min(remain, Math.PI / 4);
+                float signStep = step * sign;
+
+                Vector2 p1 = prev;
+                Vector2 p2 = EllipticArcPoint(center, radius, xAngle, s + signStep);
+
+                float alphaT = (float)Math.Tan(signStep / 2);
+                float alpha = (float)(Math.Sin(signStep) * (Math.Sqrt(4 + (3 * alphaT * alphaT)) - 1) / 3);
+                Vector2 q1 = p1 + (alpha * EllipticArcDerivative(radius, xAngle, s));
+                Vector2 q2 = p2 - (alpha * EllipticArcDerivative(radius, xAngle, s + signStep));
+
+                ReadOnlySpan<PointF> bezierPoints = new CubicBezierLineSegment(from, q1, q2, p2).Flatten().Span;
+                for (int i = 0; i < bezierPoints.Length; i++)
+                {
+                    points.Add(bezierPoints[i]);
+                }
+
+                from = p2;
+
+                s += signStep;
+                remain -= step;
+                prev = p2;
+            }
+
+            return points.ToArray();
+        }
+
+        private static void EndpointToCenterArcParams(
+            Vector2 p1,
+            Vector2 p2,
+            ref Vector2 r,
+            float xRotation,
+            bool flagA,
+            bool flagS,
+            out Vector2 center,
+            out Vector2 angles)
+        {
+            double rX = Math.Abs(r.X);
+            double rY = Math.Abs(r.Y);
+
+            // (F.6.5.1)
+            double dx2 = (p1.X - p2.X) / 2.0;
+            double dy2 = (p1.Y - p2.Y) / 2.0;
+            double x1p = (Math.Cos(xRotation) * dx2) + (Math.Sin(xRotation) * dy2);
+            double y1p = (-Math.Sin(xRotation) * dx2) + (Math.Cos(xRotation) * dy2);
+
+            // (F.6.5.2)
+            double rxs = rX * rX;
+            double rys = rY * rY;
+            double x1ps = x1p * x1p;
+            double y1ps = y1p * y1p;
+
+            // check if the radius is too small `pq < 0`, when `dq > rxs * rys` (see below)
+            // cr is the ratio (dq : rxs * rys)
+            double cr = (x1ps / rxs) + (y1ps / rys);
+            if (cr > 1)
+            {
+                // scale up rX,rY equally so cr == 1
+                double s = Math.Sqrt(cr);
+                rX = s * rX;
+                rY = s * rY;
+                rxs = rX * rX;
+                rys = rY * rY;
+            }
+
+            double dq = (rxs * y1ps) + (rys * x1ps);
+            double pq = ((rxs * rys) - dq) / dq;
+            double q = Math.Sqrt(Math.Max(0, pq)); // Use Max to account for float precision
+            if (flagA == flagS)
+            {
+                q = -q;
+            }
+
+            double cxp = q * rX * y1p / rY;
+            double cyp = -q * rY * x1p / rX;
+
+            // (F.6.5.3)
+            double cx = (Math.Cos(xRotation) * cxp) - (Math.Sin(xRotation) * cyp) + ((p1.X + p2.X) / 2);
+            double cy = (Math.Sin(xRotation) * cxp) + (Math.Cos(xRotation) * cyp) + ((p1.Y + p2.Y) / 2);
+
+            // (F.6.5.5)
+            double theta = SvgAngle(1, 0, (x1p - cxp) / rX, (y1p - cyp) / rY);
+
+            // (F.6.5.6)
+            double delta = SvgAngle((x1p - cxp) / rX, (y1p - cyp) / rY, (-x1p - cxp) / rX, (-y1p - cyp) / rY);
+            delta %= Math.PI * 2;
+
+            if (!flagS && delta > 0)
+            {
+                delta -= 2 * Math.PI;
+            }
+
+            if (flagS && delta < 0)
+            {
+                delta += 2 * Math.PI;
+            }
+
+            r = new Vector2((float)rX, (float)rY);
+            center = new Vector2((float)cx, (float)cy);
+            angles = new Vector2((float)theta, (float)delta);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static float Clamp(float val, float min, float max)
+        {
+            if (val < min)
+            {
+                return min;
+            }
+            else if (val > max)
+            {
+                return max;
+            }
+            else
+            {
+                return val;
+            }
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static float SvgAngle(double ux, double uy, double vx, double vy)
+        {
+            var u = new Vector2((float)ux, (float)uy);
+            var v = new Vector2((float)vx, (float)vy);
+
+            // (F.6.5.4)
+            float dot = Vector2.Dot(u, v);
+            float len = u.Length() * v.Length();
+            float ang = (float)Math.Acos(Clamp(dot / len, -1, 1)); // floating point precision, slightly over values appear
+            if (((u.X * v.Y) - (u.Y * v.X)) < 0)
+            {
+                ang = -ang;
+            }
+
+            return ang;
+        }
+    }
+}

src/ImageSharp.Drawing/Shapes/CubicBezierLineSegment.cs

@@ -60,29 +60,13 @@ public CubicBezierLineSegment(PointF start, PointF controlPoint1, PointF control
         /// <summary>
         /// Gets the control points.
         /// </summary>
-        /// <value>
-        /// The control points.
-        /// </value>
         public IReadOnlyList<PointF> ControlPoints => this.controlPoints;
 
-        /// <summary>
-        /// Gets the end point.
-        /// </summary>
-        /// <value>
-        /// The end point.
-        /// </value>
+        /// <inheritdoc/>
         public PointF EndPoint { get; }
 
-        /// <summary>
-        /// Returns the current <see cref="ILineSegment" /> a simple linear path.
-        /// </summary>
-        /// <returns>
-        /// Returns the current <see cref="ILineSegment" /> as simple linear path.
-        /// </returns>
-        public ReadOnlyMemory<PointF> Flatten()
-        {
-            return this.linePoints;
-        }
+        /// <inheritdoc/>
+        public ReadOnlyMemory<PointF> Flatten() => this.linePoints;
 
         /// <summary>
         /// Transforms the current LineSegment using specified matrix.
@@ -107,11 +91,7 @@ public CubicBezierLineSegment Transform(Matrix3x2 matrix)
             return new CubicBezierLineSegment(transformedPoints);
         }
 
-        /// <summary>
-        /// Transforms the current LineSegment using specified matrix.
-        /// </summary>
-        /// <param name="matrix">The matrix.</param>
-        /// <returns>A line segment with the matrix applied to it.</returns>
+        /// <inheritdoc/>
         ILineSegment ILineSegment.Transform(Matrix3x2 matrix) => this.Transform(matrix);
 
         private static PointF[] GetDrawingPoints(PointF[] controlPoints)