Dashboard/Dashboard/Geometry.cs

using OpenTK.Mathematics;
using System;
using System.Diagnostics;

namespace Dashboard
{
    /// <summary>
    /// A bezier curve segment.
    /// </summary>
    [DebuggerDisplay("{Start} -- {ControlA} -- {ControlB} -- {End}")]
    public struct QBezier
    {
        /// <summary>
        /// Segment start point.
        /// </summary>
        public Vector2 Start;
        
        /// <summary>
        /// Start point control point.
        /// </summary>
        public Vector2 ControlA;
        
        /// <summary>
        /// End point control point.
        /// </summary>
        public Vector2 ControlB;
        
        /// <summary>
        /// Segment end point.
        /// </summary>
        public Vector2 End;

        /// <summary>
        /// An approximation of the arc length of the bezier curve, for calculating rasterization resolution.
        /// </summary>
        public float RasterizationArc => 
            0.5f * (End - Start).Length + 
            0.5f * ((ControlA - Start).Length + (ControlB - ControlA).Length + (End - ControlB).Length);

        public QBezier(Vector2 start, Vector2 controlA, Vector2 controlB, Vector2 end)
        {
            Start = start;
            ControlA = controlA;
            ControlB = controlB;
            End = end;
        }

        public QBezier(
            float startX,
            float startY,
            float controlAx,
            float controlAy,
            float controlBx,
            float controlBy,
            float endX,
            float endY)
        : this(
            new Vector2(startX, startY),
            new Vector2(controlAx, controlAy),
            new Vector2(controlBx, controlBy),
            new Vector2(endX, endY))
        {
        }

        /// <summary>
        /// Get a point in the curve segment.
        /// </summary>
        /// <param name="t">Control parameter (between 0 and 1)</param>
        /// <returns>The point on the curve.</returns>
        public Vector2 GetBezierPoint(float t)
        {
            float T = 1 - t;
            return
                T * T * T * Start +
                3 * T * T * t * ControlA +
                3 * T * t * t * ControlB +
                t * t * t * End;
        }

        /// <summary>
        /// Get the tangent on the curve.
        /// </summary>
        /// <param name="t">Control parameter (between 0 and 1)</param>
        /// <returns>The tangent curve.</returns>
        public Vector2 GetBezierTangent(float t)
        {
            float T = 1 - t;
            return
                (
                    3 * T * T * (ControlA - Start) +
                    6 * T * t * (ControlB - ControlA) +
                    3 * t * t * (End - ControlB)
                ).Normalized();
        }

        internal Vector2 GetBezierNormal(float t)
        {
            Vector2 tangent = GetBezierTangent(t);
            return new Vector2(-tangent.Y, tangent.X);
        }
    }

    /// <summary>
    /// A line segment.
    /// </summary>
    [DebuggerDisplay("{Start} -- {End}")]
    public struct QLine
    {
        /// <summary>
        /// Start point.
        /// </summary>
        public Vector2 Start;
        
        /// <summary>
        /// End point.
        /// </summary>
        public Vector2 End;

        public QLine(Vector2 start, Vector2 end)
        {
            Start = start;
            End = end;
        }

        public QLine(float startX, float startY, float endX, float endY)
        {
            Start.X = startX;
            Start.Y = startY;
            End.X = endX;
            End.Y = endY;
        }

        public Vector2 Normal()
        {
            Vector2 tangent = Tangent();
            return new Vector2(-tangent.Y, tangent.X);
        }
        public Vector2 Tangent()
        {
            return (End - Start).Normalized();
        }
    }

    /// <summary>
    /// A rectangle.
    /// </summary>
    [DebuggerDisplay("({Left}, {Top}, {Right}, {Bottom})")]
    public struct QRectangle
    {
        /// <summary>
        /// Position maximum point.
        /// </summary>
        public Vector2 Max;
        
        /// <summary>
        /// Position minimum point.
        /// </summary>
        public Vector2 Min;

        public float Left
        {
            get => Min.X;
            set => Min.X = value;
        }

        public float Right
        {
            get => Max.X;
            set => Max.X = value;
        }

        public float Top
        {
            get => Min.Y;
            set => Min.Y = value;
        }

        public float Bottom
        {
            get => Max.Y;
            set => Max.Y = value;
        }

        public Vector2 Size
        {
            get => Max - Min;
            set => Max = Min + value;
        }

        public QRectangle(Vector2 max, Vector2 min)
        {
            Max = max;
            Min = min;
        }

        public QRectangle(float r, float b, float l, float t)
        {
            Max = new Vector2(r, b);
            Min = new Vector2(l, t);
        }

        public bool Contains(Vector2 point)
        {
            return
                point.X > Left   && point.X < Right &&
                point.Y > Bottom && point.Y < Top;
        }

        internal void Translate(in Vector2 offset)
        {
            Min += offset;
            Max += offset;
        }

        public static QRectangle Intersect(in QRectangle a, in QRectangle b) =>
            new QRectangle(
                Math.Max(a.Right, b.Right),
                Math.Max(a.Bottom, b.Bottom)
,
                Math.Min(a.Left, b.Left),
                Math.Min(a.Top, b.Top));
    }

    /// <summary>
    /// An ellipse.
    /// </summary>
    /// <remarks>It is undefined to have an ellipse with non-orthogonal axes.</remarks>
    [DebuggerDisplay("{Center} ellipse {AxisA}; {AxisB}")]
    public struct QEllipse
    {
        /// <summary>
        /// Ellipse center point.
        /// </summary>
        public Vector2 Center;
        
        /// <summary>
        /// First ellipse axis.
        /// </summary>
        public Vector2 AxisA;
        
        /// <summary>
        /// Second ellipse axis.
        /// </summary>
        public Vector2 AxisB;
    }

    /// <summary>
    /// A triangle.
    /// </summary>
    [DebuggerDisplay("{A} -- {B} -- {C}")]
    public struct QTriangle
    {
        /// <summary>
        /// First vertex.
        /// </summary>
        public Vector2 A;
        
        /// <summary>
        /// Second vertex.
        /// </summary>
        public Vector2 B;
        
        /// <summary>
        /// Third vertex.
        /// </summary>
        public Vector2 C;
    }
}