Create joint generating code for multi-segment lines and refactor code for end caps.

Quik/QuikGeometry.cs

@@ -1,4 +1,5 @@
 using System;
+using Quik.VertexGenerator;
 
 namespace Quik
 {
@@ -10,9 +11,15 @@ namespace Quik
         public float X;
         public float Y;
 
-        public float Length() => MathF.Sqrt(X * X + Y * Y);
+        public float Magnitude => MathF.Sqrt(X * X + Y * Y);
 
-        public QuikVec2 Normalize() => this * (1.0f / this.Length());
+        public QuikVec2(float x, float y)
+        {
+            X = x;
+            Y = y;
+        }
+
+        public QuikVec2 Normalize() => this * (1.0f / Magnitude);
 
         public float Atan2() => MathF.Atan2(Y, X);
         public static QuikVec2 operator +(QuikVec2 a, QuikVec2 b)
@@ -52,6 +59,32 @@ namespace Quik
         }
 
         public static QuikVec2 operator *(QuikVec2 a, float b) => b * a;
+
+        public static bool operator ==(QuikVec2 a, QuikVec2 b) => a.X == b.X && a.Y == b.Y;
+
+        public static bool operator !=(QuikVec2 a, QuikVec2 b) => a.X != b.X || a.Y != b.Y;
+
+        public override bool Equals(object obj)
+        {
+            if (obj is QuikVec2)
+            {
+                return (QuikVec2) obj == this;
+            }
+            else
+            {
+                return false;
+            }
+        }
+
+        public override int GetHashCode()
+        {
+            return 63671 * X.GetHashCode() ^ 81083 * Y.GetHashCode();
+        }
+
+        public static float Dot(QuikVec2 a, QuikVec2 b)
+        {
+            return a.X * b.X + a.Y * b.Y;
+        }
     }
 
     /// <summary>
@@ -162,6 +195,20 @@ namespace Quik
         /// End point.
         /// </summary>
         public QuikVec2 End;
+
+        public QuikLine(QuikVec2 start, QuikVec2 end)
+        {
+            Start = start;
+            End = end;
+        }
+
+        public QuikLine(float startX, float startY, float endX, float endY)
+        {
+            Start.X = startX;
+            Start.Y = startY;
+            End.X = endX;
+            End.Y = endY;
+        }
     }
 
     /// <summary>

Quik/VertexGenerator/QuikVertexGenerator.cs

@@ -190,6 +190,322 @@ namespace Quik.VertexGenerator
             return null;
         }
 
+        /// <summary>
+        /// Generates a basic line segment.
+        /// </summary>
+        /// <param name="baseVertex">The vertex base to modify when generating vertices.</param>
+        /// <param name="line">The line segment.</param>
+        /// <param name="width">The width of the line.</param>
+        /// <param name="lineStartIndex">Start index of the generated line.</param>
+        /// <param name="normal">The line normal.</param>
+        private void GenerateLineSegment(
+            QuikVertex baseVertex,
+            QuikLine line,
+            float width,
+            out short lineStartIndex,
+            out QuikVec2 normal)
+        {
+            QuikVec2 tangent = (line.End - line.Start).Normalize();
+            normal = new QuikVec2() {X = -tangent.Y, Y = tangent.X};
+            lineStartIndex = (short)_vertexBufferPointer;
+
+            QuikVertex startA = baseVertex, startB = baseVertex;
+            QuikVertex endA = baseVertex, endB = baseVertex;
+
+            startA.Position = line.Start + width / 2 * normal;
+            startB.Position = line.Start - width / 2 * normal;
+            endA.Position = line.End + width / 2 * normal;
+            endB.Position = line.End - width / 2 * normal;
+
+            // Add the major line vertices.
+            AddVertex(startA, startB, endA, endB);
+            
+            // Add the line indices.
+            AddElement(
+                (short) (lineStartIndex + 1),
+                (short) (lineStartIndex + 2),
+                (short) (lineStartIndex + 0),
+                (short) (lineStartIndex + 1),
+                (short) (lineStartIndex + 3),
+                (short) (lineStartIndex + 2)
+            );
+        }
+        
+        /// <summary>
+        /// Gets the rounding resolution for a line segment.
+        /// </summary>
+        /// <param name="width">The width of the line.</param>
+        /// <param name="arc">The angle of the cap or joint arc.</param>
+        /// <returns>The rounding resolution.</returns>
+        private int GetRoundingResolution(float width, float arc)
+        {
+            int endCapResolution = (int) Math.Ceiling(arc * width * CurveGranularity);
+            return endCapResolution;
+        }
+        
+        /// <summary>
+        /// Generate a round start cap on a line.
+        /// </summary>
+        /// <param name="baseVertex">The base vertex to modify for generation.</param>
+        /// <param name="start">The start point.</param>
+        /// <param name="normal">The line normal.</param>
+        /// <param name="width">The width of line to generate.</param>
+        /// <param name="resolution">End cap resolution.</param>
+        /// <param name="lineStartPositiveIndex">The positive vertex index of the line start.</param>
+        /// <param name="lineStartNegativeIndex">The negative vertex index of the line start.</param>
+        public void GenerateStartCap(
+            QuikVertex baseVertex,
+            QuikVec2 start,
+            QuikVec2 normal,
+            float width,
+            int resolution,
+            short lineStartPositiveIndex,
+            short lineStartNegativeIndex
+        )
+        {
+            QuikVertex circlePoint = baseVertex;
+            short lastIndex = lineStartPositiveIndex;
+            for (int i = 0; i < resolution; i++)
+            {
+                float angle = (float) (i + 1) / (resolution + 1) * MathF.PI;
+                float cosT = MathF.Cos(angle);
+                float sinT = MathF.Sin(angle);
+
+                QuikVec2 displacement = new QuikVec2()
+                {
+                    X = normal.X * cosT - normal.Y * sinT,
+                    Y = normal.X * sinT + normal.Y * cosT
+                } * (width / 2);
+
+                circlePoint.Position = start + displacement;
+
+                short segmentIndex = (short)_vertexBufferPointer;
+
+                AddVertex(circlePoint);
+                AddElement(
+                    lineStartNegativeIndex,
+                    lastIndex,
+                    segmentIndex);
+
+                lastIndex = segmentIndex;
+            }
+        }
+
+        /// <summary>
+        /// Generate a round line end cap.
+        /// </summary>
+        /// <param name="baseVertex">Base vertex to modify for generation.</param>
+        /// <param name="end">The line end.</param>
+        /// <param name="normal">The line normal.</param>
+        /// <param name="width">The line width.</param>
+        /// <param name="resolution">Cap generation resolution.</param>
+        /// <param name="lineEndPositiveIndex">Vertex index of the positive line end.</param>
+        /// <param name="lineEndNegativeIndex">Vertex index of the negative line end.</param>
+        public void GenerateEndCap(
+            QuikVertex baseVertex,
+            QuikVec2 end,
+            QuikVec2 normal,
+            float width,
+            int resolution,
+            short lineEndPositiveIndex,
+            short lineEndNegativeIndex
+        )
+        {
+            QuikVertex circlePoint = baseVertex;
+            short lastIndex = lineEndPositiveIndex;
+            for (int i = 0; i < resolution; i++)
+            {
+                float angle = -(float) (i + 1) / (resolution + 1) * MathF.PI;
+                float cosT = MathF.Cos(angle);
+                float sinT = MathF.Sin(angle);
+
+                QuikVec2 displacement = new QuikVec2()
+                {
+                    X = normal.X * cosT - normal.Y * sinT,
+                    Y = normal.X * sinT + normal.Y * cosT
+                } * (width / 2);
+
+                circlePoint.Position = end + displacement;
+
+                AddVertex(circlePoint);
+                AddElement(
+                    lineEndNegativeIndex,
+                    lastIndex,
+                    (short) (_vertexBufferPointer - 1));
+
+                lastIndex = (short) (_vertexBufferPointer - 1);
+            }
+        }
+        
+        /// <summary>
+        /// Generate a joint on the line negative edge.
+        /// </summary>
+        /// <param name="baseVertex">Base vertex to modify for generation.</param>
+        /// <param name="focus">The focus of the joint.</param>
+        /// <param name="width">With of the lines.</param>
+        /// <param name="prevNegativeLineIndex">Index of the negative end vertex.</param>
+        /// <param name="nextNegativeLineIndex">Index of the negative start vertex.</param>
+        /// <param name="resolution">Joint resolution.</param>
+        /// <param name="arc">Arc length of the joint.</param>
+        /// <param name="prevNormal">Normal of the previous line.</param>
+        private void GenerateNegativeJoint(
+            QuikVertex baseVertex,
+            QuikVec2 focus,
+            float width,
+            short prevNegativeLineIndex,
+            short nextNegativeLineIndex,
+            int resolution,
+            float arc,
+            QuikVec2 prevNormal)
+        {
+            QuikVertex focusVertex = baseVertex;
+            short focusIndex = (short) _vertexBufferPointer;
+            short lastIndex = prevNegativeLineIndex;
+
+            focusVertex.Position = focus;
+            AddVertex(focusVertex);
+
+            for (int i = 0; i < resolution; i++)
+            {
+                float angle = (float) (i + 1) / (resolution + 1) * arc;
+                float cosT = MathF.Cos(angle);
+                float sinT = MathF.Sin(angle);
+
+                QuikVec2 displacement = new QuikVec2()
+                {
+                    X = -prevNormal.X * cosT + prevNormal.Y * sinT,
+                    Y = -prevNormal.X * sinT - prevNormal.Y * cosT
+                } * (width / 2);
+
+                QuikVertex segmentVertex = focusVertex;
+                segmentVertex.Position += displacement;
+
+                short segmentIndex = (short) _vertexBufferPointer;
+                AddVertex(segmentVertex);
+
+                AddElement(lastIndex, segmentIndex, focusIndex);
+                
+                lastIndex = segmentIndex;
+            }
+
+            // Add final triangle.
+            AddElement(lastIndex, nextNegativeLineIndex, focusIndex);
+        }
+
+        /// <summary>
+        /// Generate a joint on the line negative edge.
+        /// </summary>
+        /// <param name="baseVertex">Base vertex to modify for generation.</param>
+        /// <param name="focus">The focus of the joint.</param>
+        /// <param name="width">With of the lines.</param>
+        /// <param name="prevPositiveLineIndex">Index of the positive end vertex.</param>
+        /// <param name="nextPositiveLineIndex">Index of the positive start vertex.</param>
+        /// <param name="resolution">Joint resolution.</param>
+        /// <param name="arc">Arc length of the joint.</param>
+        /// <param name="nextNormal">Normal of the next line.</param>
+        private void GeneratePositiveJoint(
+            QuikVertex baseVertex,
+            QuikVec2 focus,
+            float width,
+            short prevPositiveLineIndex,
+            short nextPositiveLineIndex,
+            int resolution,
+            float arc,
+            QuikVec2 nextNormal)
+        {
+            QuikVertex focusVertex = baseVertex;
+            short focusIndex = (short) _vertexBufferPointer;
+            short lastIndex = nextPositiveLineIndex;
+
+            focusVertex.Position = focus;
+            AddVertex(focusVertex);
+
+            for (int i = 0; i < resolution; i++)
+            {
+                float angle = (float) (i + 1) / (resolution + 1) * arc;
+                float cosT = MathF.Cos(angle);
+                float sinT = MathF.Sin(angle);
+
+                QuikVec2 displacement = new QuikVec2()
+                {
+                    X = nextNormal.X * cosT - nextNormal.Y * sinT,
+                    Y = nextNormal.X * sinT + nextNormal.Y * cosT
+                } * (width / 2);
+
+                QuikVertex segmentVertex = focusVertex;
+                segmentVertex.Position += displacement;
+
+                short segmentIndex = (short) _vertexBufferPointer;
+                AddVertex(segmentVertex);
+
+                AddElement(lastIndex, segmentIndex, focusIndex);
+
+                lastIndex = segmentIndex;
+            }
+
+            // Add final triangle.
+            AddElement(lastIndex, prevPositiveLineIndex, focusIndex);
+        }
+
+        /// <summary>
+        /// Generate a joint.
+        /// </summary>
+        /// <param name="baseVertex">Base vertex to modify.</param>
+        /// <param name="focus">Focus of the joint.</param>
+        /// <param name="prevTangent">Tangent of the previous line segment.</param>
+        /// <param name="nextTangent">Tangent of the next line segment.</param>
+        /// <param name="width">Width of the lines.</param>
+        /// <param name="prevPositiveEndIndex">Vertex index of the positive end.</param>
+        /// <param name="prevNegativeEndIndex">Vertex index of the negative end.</param>
+        /// <param name="nextPositiveStartIndex">Vertex index of the positive start.</param>
+        /// <param name="nextNegativeStartIndex">Vertex index of the negative start.</param>
+        public void GenerateJoint(
+            QuikVertex baseVertex,
+            QuikVec2 focus,
+            QuikVec2 prevTangent,
+            QuikVec2 nextTangent,
+            float width,
+            short prevPositiveEndIndex,
+            short prevNegativeEndIndex,
+            short nextPositiveStartIndex,
+            short nextNegativeStartIndex
+        )
+        {
+            QuikVec2 prevNormal,  nextNormal;
+            QuikVec2 averageTangent;
+
+            prevNormal = new QuikVec2() { X = -prevTangent.Y, Y = prevTangent.X };
+            nextNormal = new QuikVec2() { X = -nextTangent.Y, Y = nextTangent.X };
+
+            averageTangent = 0.5f * (prevTangent + nextTangent);
+
+            // Figure out which side needs the joint.
+            QuikVec2 positiveEdge = ((focus + nextNormal) - (focus + prevNormal)).Normalize();
+            QuikVec2 negativeEdge = ((focus - nextNormal) - (focus - prevNormal)).Normalize();
+
+            float positiveDot, negativeDot;
+            positiveDot = QuikVec2.Dot(averageTangent, positiveEdge);
+            negativeDot = QuikVec2.Dot(averageTangent, negativeEdge);
+
+            float arc = MathF.Acos(QuikVec2.Dot(prevNormal, nextNormal));
+            int resolution = GetRoundingResolution(width, arc);
+
+            if (positiveDot < negativeDot)
+            {
+                // Negative edge rounding.
+                GenerateNegativeJoint(baseVertex, focus, width, prevNegativeEndIndex, nextNegativeStartIndex, resolution, arc, prevNormal);
+            }
+            else if (negativeDot < positiveDot)
+            {
+                // Positive edge rounding.
+                GeneratePositiveJoint(baseVertex, focus, width, prevPositiveEndIndex, nextPositiveStartIndex, resolution, arc, nextNormal);
+            }
+            else
+            {
+                // There is no need to generate anything because the lines are the same???
+            }
+        }
+
         /// <summary>
         /// Renders a line.
         /// </summary>
@@ -199,97 +515,85 @@ namespace Quik.VertexGenerator
         {
             // Skip over stipple patterns for now.
             QuikStrokeStyle style = line.Style ?? Context.DefaultStroke;
-            int endCapResolution;                               // Resolution of the end cap.
-            short startOffset = (short) _vertexBufferPointer;   // Starting index pointer.
-            QuikVec2 tangent;
-            QuikVec2 normal;
-
-            tangent = (line.Line.End - line.Line.Start).Normalize();
-            normal = new QuikVec2() {X = -tangent.Y, Y = tangent.X};
-
             QuikVertex baseVertex = new QuikVertex() { Color = style.Color };
-            QuikVertex startA = baseVertex, startB = baseVertex;
-            QuikVertex endA = baseVertex, endB = baseVertex;
             
-            startA.Position = line.Line.Start + style.Width / 2 * normal;
+            GenerateLineSegment(baseVertex, line.Line, style.Width, out short startOffset, out QuikVec2 normal);
-            startB.Position = line.Line.Start - style.Width / 2 * normal;
-            endA.Position = line.Line.End + style.Width / 2 * normal;
-            endB.Position = line.Line.End - style.Width / 2 * normal;
-
-            // Add the major line vertices.
-            AddVertex(startA, startB, endA, endB);
-            
-            // Add the line indices.
-            AddElement(
-                (short) (startOffset + 1),
-                (short) (startOffset + 2),
-                (short) (startOffset + 0),
-                (short) (startOffset + 1),
-                (short) (startOffset + 3),
-                (short) (startOffset + 2)
-                );
 
             // Now calculate the end caps.
-            endCapResolution = (int)Math.Ceiling(MathF.PI * style.Width * CurveGranularity);
+            int endCapResolution = GetRoundingResolution(style.Width, MathF.PI);
 
             // Construct start cap.
-            QuikVertex circlePoint = baseVertex;
+            GenerateStartCap(baseVertex, line.Line.Start, normal, style.Width, endCapResolution, startOffset, (short)
-            short lastIndex = startOffset;
+                (startOffset + 1));
-            for (int i = 0; i < endCapResolution; i++)
-            {
-                float angle = (float) (i + 1) / (endCapResolution + 1) * MathF.PI;
-                float cosT = MathF.Cos(angle);
-                float sinT = MathF.Sin(angle);
-
-                QuikVec2 displacement = new QuikVec2()
-                {
-                    X = normal.X * cosT - normal.Y * sinT,
-                    Y = normal.X * sinT + normal.Y * cosT
-                } * (style.Width / 2);
-
-                circlePoint.Position = line.Line.Start + displacement; 
-                
-                AddVertex(circlePoint);
-                AddElement(
-                    (short)(startOffset + 1),
-                    lastIndex,
-                    (short)(_vertexBufferPointer - 1));
-
-                lastIndex = (short) (_vertexBufferPointer - 1);
-            }
             
             // Construct end cap.
-            lastIndex = (short)(startOffset + 2);
+            GenerateEndCap(baseVertex, line.Line.End, normal, style.Width, endCapResolution, (short) (startOffset + 2),(short)
-            for (int i = 0; i < endCapResolution; i++)
+                (startOffset + 3));
-            {
-                float angle = -(float) (i + 1) / (endCapResolution + 1) * MathF.PI;
-                float cosT = MathF.Cos(angle);
-                float sinT = MathF.Sin(angle);
-
-                QuikVec2 displacement = new QuikVec2()
-                {
-                    X = normal.X * cosT - normal.Y * sinT,
-                    Y = normal.X * sinT + normal.Y * cosT
-                } * (style.Width / 2);
-
-                circlePoint.Position = line.Line.End + displacement; 
-                
-                AddVertex(circlePoint);
-                AddElement(
-                    (short)(startOffset + 3),
-                    lastIndex,
-                    (short)(_vertexBufferPointer - 1));
-
-                lastIndex = (short) (_vertexBufferPointer - 1);
-            }
 
             call.Offset = (short) (startOffset * 2);
             call.Count = (short) (_elementBufferPointer - startOffset);
         }
 
+        /// <summary>
+        /// Render lines.
+        /// </summary>
+        /// <param name="call">The draw call to generate.</param>
+        /// <param name="lines">The lines command.</param>
         private void RenderLine(ref QuikDrawCall call, QuikCommandLines lines)
         {
+            // Skip over stipple patterns for now.
+            QuikStrokeStyle style = lines.Style ?? Context.DefaultStroke;
+            QuikVertex baseVertex = new QuikVertex() { Color = style.Color };
+            bool isStart;
+            bool isEnd;
+            short startOffset = (short)_elementBufferPointer;
+            short lastStartIndex = 0;
+            short lineStartIndex;
+            QuikVec2 normal;
+            int resolution = GetRoundingResolution(style.Width, MathF.PI);
 
+            for (int i = 0; i < lines.Lines.Length; i++)
+            {
+                QuikLine line = lines.Lines[i];
+
+                isStart = i == 0 || line.Start != lines.Lines[i - 1].End;
+                isEnd = i == lines.Lines.Length - 1 || line.End != lines.Lines[i + 1].Start;
+                
+                GenerateLineSegment(baseVertex, line, style.Width, out lineStartIndex, out normal);
+
+                if (isStart)
+                {
+                    GenerateStartCap(baseVertex, line.Start, normal, style.Width, resolution, lineStartIndex,
+                        (short)(lineStartIndex + 1));
+                }
+                else
+                {
+                    QuikLine prev = lines.Lines[i - 1];
+                    QuikVec2 prevTangent = (prev.End - prev.Start).Normalize();
+                    QuikVec2 nextTangent = (line.End - line.Start).Normalize();
+
+                    GenerateJoint(
+                        baseVertex, 
+                        line.Start,
+                        prevTangent,
+                        nextTangent,
+                        style.Width,
+                        (short) (lastStartIndex + 2),
+                        (short) (lastStartIndex + 3),
+                        lineStartIndex,
+                        (short)(lineStartIndex + 1));
+                }
+                
+                if (isEnd)
+                {
+                    GenerateEndCap(baseVertex, line.End, normal, style.Width, resolution, (short)(lineStartIndex + 2), (short)(lineStartIndex + 3));
+                }
+
+                lastStartIndex = lineStartIndex;
+            }
+
+            call.Offset = (short) (startOffset * 2);
+            call.Count = (short) (_elementBufferPointer - startOffset);
         }
     }
 

QuikTestApplication/Program.cs

@@ -127,27 +127,34 @@ void main()
                 
                 Matrix4 matrix = Matrix4.CreateOrthographicOffCenter(
                     0,
-                    window.Size.X,
+                    (float)window.Size.X / 2,
                     0,
-                    window.Size.Y,
+                    (float)window.Size.Y / 2,
                     1, 
                     -1);
                 GL.UniformMatrix4(loc, false, ref matrix);
 
+                context.DefaultStroke.Color = new QuikColor(40, 128, 60, 255);
+                
                 context.Draw.Line(
-                    new QuikLine()
+                    // >
-                    {
+                    new QuikLine(10,10, 20, 20),
-                        Start = new QuikVec2()
+                    new QuikLine(20, 20, 10, 30),
-                        {
+                    
-                            X = 20,
+                    // s
-                            Y = 40
+                    new QuikLine(28, 10, 38, 10),
-                        },
+                    new QuikLine(38, 10, 38, 20),
-                        End = new QuikVec2()
+                    new QuikLine(38, 20, 28, 20),
-                        {
+                    new QuikLine(28, 20, 28, 30),
-                            X=100,
+                    new QuikLine(28, 30, 38, 30),
-                            Y=100
+                    
-                        }
+                    // e
-                    });
+                    new QuikLine(64, 20, 74, 20),
+                    new QuikLine(74, 20, 74, 30),
+                    new QuikLine(74, 30, 64, 30),
+                    new QuikLine(64, 30, 64, 10),
+                    new QuikLine(64, 10, 74, 10)
+                    );
 
                 QuikCommand command;
                 while (context.Draw.Commands.TryDequeue(out command))