/// <summary>
        /// Renders the specified axis.
        /// </summary>
        /// <param name="axis">The axis.</param>
        /// <param name="pass">The pass.</param>
        public override void Render(Axis axis, int pass)
        {
            base.Render(axis, pass);

            double totalShift = axis.AxisDistance + axis.PositionTierMinShift;
            double tierSize = axis.PositionTierSize - this.Plot.AxisTierDistance;

            // store properties locally for performance
            double plotAreaLeft = this.Plot.PlotArea.Left;
            double plotAreaRight = this.Plot.PlotArea.Right;
            double plotAreaTop = this.Plot.PlotArea.Top;
            double plotAreaBottom = this.Plot.PlotArea.Bottom;

            // Axis position (x or y screen coordinate)
            double axisPosition = 0;
            double titlePosition = 0;

            switch (axis.Position)
            {
                case AxisPosition.Left:
                    axisPosition = plotAreaLeft - totalShift;
                    titlePosition = axisPosition - tierSize;
                    break;
                case AxisPosition.Right:
                    axisPosition = plotAreaRight + totalShift;
                    titlePosition = axisPosition + tierSize;
                    break;
                case AxisPosition.Top:
                    axisPosition = plotAreaTop - totalShift;
                    titlePosition = axisPosition - tierSize;
                    break;
                case AxisPosition.Bottom:
                    axisPosition = plotAreaBottom + totalShift;
                    titlePosition = axisPosition + tierSize;
                    break;
            }

            if (axis.PositionAtZeroCrossing)
            {
                var perpendicularAxis = axis.IsHorizontal() ? this.Plot.DefaultYAxis : this.Plot.DefaultXAxis;
                axisPosition = perpendicularAxis.Transform(0);
            }

            if (pass == 0)
            {
                this.RenderMinorItems(axis, axisPosition);
            }

            if (pass == 1)
            {
                this.RenderMajorItems(axis, axisPosition, titlePosition);
                this.RenderAxisTitle(axis, titlePosition);
            }
        }
        /// <summary>
        /// Renders the minor items.
        /// </summary>
        /// <param name="axis">The axis.</param>
        /// <param name="axisPosition">The axis position.</param>
        protected virtual void RenderMinorItems(Axis axis, double axisPosition)
        {
            double eps = axis.ActualMinorStep * 1e-3;
            double actualMinimum = axis.ActualMinimum;
            double actualMaximum = axis.ActualMaximum;

            double plotAreaLeft = this.Plot.PlotArea.Left;
            double plotAreaRight = this.Plot.PlotArea.Right;
            double plotAreaTop = this.Plot.PlotArea.Top;
            double plotAreaBottom = this.Plot.PlotArea.Bottom;
            bool isHorizontal = axis.IsHorizontal();

            double a0;
            double a1;
            var minorSegments = new List<ScreenPoint>();
            var minorTickSegments = new List<ScreenPoint>();

            this.GetTickPositions(axis, axis.TickStyle, axis.MinorTickSize, axis.Position, out a0, out a1);

            foreach (double value in this.MinorTickValues)
            {
                if (value < actualMinimum - eps || value > actualMaximum + eps)
                {
                    continue;
                }

                if (this.MajorTickValues.Contains(value))
                {
                    continue;
                }

                if (axis.PositionAtZeroCrossing && Math.Abs(value) < eps)
                {
                    continue;
                }

                double transformedValue = axis.Transform(value);

                if (isHorizontal)
                {
                    SnapTo(plotAreaLeft, ref transformedValue);
                    SnapTo(plotAreaRight, ref transformedValue);
                }
                else
                {
                    SnapTo(plotAreaTop, ref transformedValue);
                    SnapTo(plotAreaBottom, ref transformedValue);
                }

                // Draw the minor grid line
                if (this.MinorPen != null)
                {
                    if (isHorizontal)
                    {
                        minorSegments.Add(new ScreenPoint(transformedValue, plotAreaTop));
                        minorSegments.Add(new ScreenPoint(transformedValue, plotAreaBottom));
                    }
                    else
                    {
                        if (transformedValue < plotAreaTop || transformedValue > plotAreaBottom)
                        {
                        }

                        minorSegments.Add(new ScreenPoint(plotAreaLeft, transformedValue));
                        minorSegments.Add(new ScreenPoint(plotAreaRight, transformedValue));
                    }
                }

                // Draw the minor tick
                if (axis.TickStyle != TickStyle.None && axis.MinorTickSize > 0)
                {
                    if (isHorizontal)
                    {
                        minorTickSegments.Add(new ScreenPoint(transformedValue, axisPosition + a0));
                        minorTickSegments.Add(new ScreenPoint(transformedValue, axisPosition + a1));
                    }
                    else
                    {
                        minorTickSegments.Add(new ScreenPoint(axisPosition + a0, transformedValue));
                        minorTickSegments.Add(new ScreenPoint(axisPosition + a1, transformedValue));
                    }
                }
            }

            // Draw all the line segments);
            if (this.MinorPen != null)
            {
                this.RenderContext.DrawLineSegments(minorSegments, this.MinorPen);
            }

            if (this.MinorTickPen != null)
            {
                this.RenderContext.DrawLineSegments(minorTickSegments, this.MinorTickPen);
            }
        }
        /// <summary>
        /// Renders the specified axis.
        /// </summary>
        /// <param name="axis">The axis.</param>
        /// <param name="pass">The pass.</param>
        public override void Render(Axis axis, int pass)
        {
            base.Render(axis, pass);

            bool drawAxisLine = true;
            double totalShift = axis.AxisDistance + axis.PositionTierMinShift;
            double tierSize = axis.PositionTierSize - this.Plot.AxisTierDistance;

            // store properties locally for performance
            double plotAreaLeft = this.Plot.PlotArea.Left;
            double plotAreaRight = this.Plot.PlotArea.Right;
            double plotAreaTop = this.Plot.PlotArea.Top;
            double plotAreaBottom = this.Plot.PlotArea.Bottom;

            // Axis position (x or y screen coordinate)
            double axisPosition = 0;
            double titlePosition = 0;

            switch (axis.Position)
            {
                case AxisPosition.Left:
                    axisPosition = plotAreaLeft - totalShift;
                    break;
                case AxisPosition.Right:
                    axisPosition = plotAreaRight + totalShift;
                    break;
                case AxisPosition.Top:
                    axisPosition = plotAreaTop - totalShift;
                    break;
                case AxisPosition.Bottom:
                    axisPosition = plotAreaBottom + totalShift;
                    break;
            }

            if (axis.PositionAtZeroCrossing)
            {
                var perpendicularAxis = axis.IsHorizontal() ? this.Plot.DefaultYAxis : this.Plot.DefaultXAxis;

                // the axis should be positioned at the origin of the perpendicular axis
                axisPosition = perpendicularAxis.Transform(0);

                var p0 = perpendicularAxis.Transform(perpendicularAxis.ActualMinimum);
                var p1 = perpendicularAxis.Transform(perpendicularAxis.ActualMaximum);

                // find the min/max positions
                var min = Math.Min(p0, p1);
                var max = Math.Max(p0, p1);

                // also consider the plot area
                var areaMin = axis.IsHorizontal() ? plotAreaTop : plotAreaLeft;
                var areaMax = axis.IsHorizontal() ? plotAreaBottom : plotAreaRight;
                min = Math.Max(min, areaMin);
                max = Math.Min(max, areaMax);

                if (axisPosition < min)
                {
                    axisPosition = min;

                    var borderThickness = axis.IsHorizontal()
                        ? this.Plot.PlotAreaBorderThickness.Top
                        : this.Plot.PlotAreaBorderThickness.Left;
                    if (borderThickness > 0 && this.Plot.PlotAreaBorderColor.IsVisible())
                    {
                        // there is already a line here...
                        drawAxisLine = false;
                    }
                }

                if (axisPosition > max)
                {
                    axisPosition = max;

                    var borderThickness = axis.IsHorizontal()
                        ? this.Plot.PlotAreaBorderThickness.Bottom
                        : this.Plot.PlotAreaBorderThickness.Right;
                    if (borderThickness > 0 && this.Plot.PlotAreaBorderColor.IsVisible())
                    {
                        // there is already a line here...
                        drawAxisLine = false;
                    }
                }
            }

            switch (axis.Position)
            {
                case AxisPosition.Left:
                    titlePosition = axisPosition - tierSize;
                    break;
                case AxisPosition.Right:
                    titlePosition = axisPosition + tierSize;
                    break;
                case AxisPosition.Top:
                    titlePosition = axisPosition - tierSize;
                    break;
                case AxisPosition.Bottom:
                    titlePosition = axisPosition + tierSize;
                    break;
            }

            if (pass == 0)
            {
                this.RenderMinorItems(axis, axisPosition);
            }

            if (pass == 1)
            {
                this.RenderMajorItems(axis, axisPosition, titlePosition, drawAxisLine);
                this.RenderAxisTitle(axis, titlePosition);
            }
        }
        /// <summary>
        /// Renders the major items.
        /// </summary>
        /// <param name="axis">The axis.</param>
        /// <param name="axisPosition">The axis position.</param>
        /// <param name="titlePosition">The title position.</param>
        /// <param name="drawAxisLine">Draw the axis line if set to <c>true</c>.</param>
        protected virtual void RenderMajorItems(Axis axis, double axisPosition, double titlePosition, bool drawAxisLine)
        {
            double eps = axis.ActualMinorStep * 1e-3;

            double actualMinimum = axis.ActualMinimum;
            double actualMaximum = axis.ActualMaximum;

            double plotAreaLeft = this.Plot.PlotArea.Left;
            double plotAreaRight = this.Plot.PlotArea.Right;
            double plotAreaTop = this.Plot.PlotArea.Top;
            double plotAreaBottom = this.Plot.PlotArea.Bottom;
            bool isHorizontal = axis.IsHorizontal();

            double a0;
            double a1;
            var majorSegments = new List<ScreenPoint>();
            var majorTickSegments = new List<ScreenPoint>();
            this.GetTickPositions(axis, axis.TickStyle, axis.MajorTickSize, axis.Position, out a0, out a1);

            foreach (double value in this.MajorTickValues)
            {
                if (value < actualMinimum - eps || value > actualMaximum + eps)
                {
                    continue;
                }

                if (axis.PositionAtZeroCrossing && Math.Abs(value) < eps)
                {
                    continue;
                }

                double transformedValue = axis.Transform(value);
                if (isHorizontal)
                {
                    SnapTo(plotAreaLeft, ref transformedValue);
                    SnapTo(plotAreaRight, ref transformedValue);
                }
                else
                {
                    SnapTo(plotAreaTop, ref transformedValue);
                    SnapTo(plotAreaBottom, ref transformedValue);
                }

                if (this.MajorPen != null)
                {
                    if (isHorizontal)
                    {
                        majorSegments.Add(new ScreenPoint(transformedValue, plotAreaTop));
                        majorSegments.Add(new ScreenPoint(transformedValue, plotAreaBottom));
                    }
                    else
                    {
                        majorSegments.Add(new ScreenPoint(plotAreaLeft, transformedValue));
                        majorSegments.Add(new ScreenPoint(plotAreaRight, transformedValue));
                    }
                }

                if (axis.TickStyle != TickStyle.None && axis.MajorTickSize > 0)
                {
                    if (isHorizontal)
                    {
                        majorTickSegments.Add(new ScreenPoint(transformedValue, axisPosition + a0));
                        majorTickSegments.Add(new ScreenPoint(transformedValue, axisPosition + a1));
                    }
                    else
                    {
                        majorTickSegments.Add(new ScreenPoint(axisPosition + a0, transformedValue));
                        majorTickSegments.Add(new ScreenPoint(axisPosition + a1, transformedValue));
                    }
                }
            }

            // Render the axis labels (numbers or category names)
            foreach (double value in this.MajorLabelValues)
            {
                if (value < actualMinimum - eps || value > actualMaximum + eps)
                {
                    continue;
                }

                if (axis.PositionAtZeroCrossing && Math.Abs(value) < eps)
                {
                    continue;
                }

                double transformedValue = axis.Transform(value);
                if (isHorizontal)
                {
                    SnapTo(plotAreaLeft, ref transformedValue);
                    SnapTo(plotAreaRight, ref transformedValue);
                }
                else
                {
                    SnapTo(plotAreaTop, ref transformedValue);
                    SnapTo(plotAreaBottom, ref transformedValue);
                }

                var pt = new ScreenPoint();
                var ha = HorizontalAlignment.Right;
                var va = VerticalAlignment.Middle;
                switch (axis.Position)
                {
                    case AxisPosition.Left:
                        pt = new ScreenPoint(axisPosition + a1 - axis.AxisTickToLabelDistance, transformedValue);
                        this.GetRotatedAlignments(
                            axis.Angle,
                            HorizontalAlignment.Right,
                            VerticalAlignment.Middle,
                            out ha,
                            out va);
                        break;
                    case AxisPosition.Right:
                        pt = new ScreenPoint(axisPosition + a1 + axis.AxisTickToLabelDistance, transformedValue);
                        this.GetRotatedAlignments(
                            axis.Angle,
                            HorizontalAlignment.Left,
                            VerticalAlignment.Middle,
                            out ha,
                            out va);
                        break;
                    case AxisPosition.Top:
                        pt = new ScreenPoint(transformedValue, axisPosition + a1 - axis.AxisTickToLabelDistance);
                        this.GetRotatedAlignments(
                            axis.Angle,
                            HorizontalAlignment.Center,
                            VerticalAlignment.Bottom,
                            out ha,
                            out va);
                        break;
                    case AxisPosition.Bottom:
                        pt = new ScreenPoint(transformedValue, axisPosition + a1 + axis.AxisTickToLabelDistance);
                        this.GetRotatedAlignments(
                            axis.Angle,
                            HorizontalAlignment.Center,
                            VerticalAlignment.Top,
                            out ha,
                            out va);
                        break;
                }

                string text = axis.FormatValue(value);
                this.RenderContext.DrawMathText(
                    pt,
                    text,
                    axis.ActualTextColor,
                    axis.ActualFont,
                    axis.ActualFontSize,
                    axis.ActualFontWeight,
                    axis.Angle,
                    ha,
                    va);
            }

            // Draw the zero crossing line
            if (axis.PositionAtZeroCrossing && this.ZeroPen != null && this.IsWithin(0, actualMinimum, actualMaximum))
            {
                double t0 = axis.Transform(0);
                if (isHorizontal)
                {
                    this.RenderContext.DrawLine(t0, plotAreaTop, t0, plotAreaBottom, this.ZeroPen);
                }
                else
                {
                    this.RenderContext.DrawLine(plotAreaLeft, t0, plotAreaRight, t0, this.ZeroPen);
                }
            }

            // Draw extra grid lines
            if (axis.ExtraGridlines != null && this.ExtraPen != null)
            {
                foreach (double value in axis.ExtraGridlines)
                {
                    if (!this.IsWithin(value, actualMinimum, actualMaximum))
                    {
                        continue;
                    }

                    double transformedValue = axis.Transform(value);
                    if (isHorizontal)
                    {
                        this.RenderContext.DrawLine(
                            transformedValue,
                            plotAreaTop,
                            transformedValue,
                            plotAreaBottom,
                            this.ExtraPen);
                    }
                    else
                    {
                        this.RenderContext.DrawLine(
                            plotAreaLeft,
                            transformedValue,
                            plotAreaRight,
                            transformedValue,
                            this.ExtraPen);
                    }
                }
            }

            if (drawAxisLine)
            {
                // Draw the axis line (across the tick marks)
                if (isHorizontal)
                {
                    this.RenderContext.DrawLine(
                        axis.Transform(actualMinimum),
                        axisPosition,
                        axis.Transform(actualMaximum),
                        axisPosition,
                        this.AxislinePen);
                }
                else
                {
                    this.RenderContext.DrawLine(
                        axisPosition,
                        axis.Transform(actualMinimum),
                        axisPosition,
                        axis.Transform(actualMaximum),
                        this.AxislinePen);
                }
            }

            if (this.MajorPen != null)
            {
                this.RenderContext.DrawLineSegments(majorSegments, this.MajorPen);
            }

            if (this.MajorTickPen != null)
            {
                this.RenderContext.DrawLineSegments(majorTickSegments, this.MajorTickPen);
            }
        }
        /// <summary>
        /// Renders the axis title.
        /// </summary>
        /// <param name="axis">The axis.</param>
        /// <param name="titlePosition">The title position.</param>
        protected virtual void RenderAxisTitle(Axis axis, double titlePosition)
        {
            if (string.IsNullOrEmpty(axis.ActualTitle))
            {
                return;
            }

            bool isHorizontal = axis.IsHorizontal();

            OxySize? maxSize = null;

            if (axis.ClipTitle)
            {
                // Calculate the title clipping dimensions
                double screenLength = isHorizontal
                                          ? Math.Abs(axis.ScreenMax.X - axis.ScreenMin.X)
                                          : Math.Abs(axis.ScreenMax.Y - axis.ScreenMin.Y);

                maxSize = new OxySize(screenLength * axis.TitleClippingLength, double.MaxValue);
            }

            double angle = -90;

            var halign = HorizontalAlignment.Center;
            var valign = VerticalAlignment.Top;

            var lpt = this.GetAxisTitlePositionAndAlignment(axis, titlePosition, ref angle, ref halign, ref valign);

            this.RenderContext.DrawMathText(
                lpt,
                axis.ActualTitle,
                axis.ActualTitleColor,
                axis.ActualTitleFont,
                axis.ActualTitleFontSize,
                axis.ActualTitleFontWeight,
                angle,
                halign,
                valign,
                maxSize);
        }
        /// <summary>
        /// Gets the axis title position, rotation and alignment.
        /// </summary>
        /// <param name="axis">The axis.</param>
        /// <param name="titlePosition">The title position.</param>
        /// <param name="angle">The angle.</param>
        /// <param name="halign">The horizontal alignment.</param>
        /// <param name="valign">The vertical alignment.</param>
        /// <returns>The <see cref="ScreenPoint" />.</returns>
        protected virtual ScreenPoint GetAxisTitlePositionAndAlignment(
            Axis axis,
            double titlePosition,
            ref double angle,
            ref HorizontalAlignment halign,
            ref VerticalAlignment valign)
        {
            double middle = axis.IsHorizontal()
                                ? Lerp(axis.ScreenMin.X, axis.ScreenMax.X, axis.TitlePosition)
                                : Lerp(axis.ScreenMax.Y, axis.ScreenMin.Y, axis.TitlePosition);

            if (axis.PositionAtZeroCrossing)
            {
                middle = Lerp(axis.Transform(axis.ActualMaximum), axis.Transform(axis.ActualMinimum), axis.TitlePosition);
            }

            switch (axis.Position)
            {
                case AxisPosition.Left:
                    return new ScreenPoint(titlePosition, middle);
                case AxisPosition.Right:
                    valign = VerticalAlignment.Bottom;
                    return new ScreenPoint(titlePosition, middle);
                case AxisPosition.Top:
                    halign = HorizontalAlignment.Center;
                    valign = VerticalAlignment.Top;
                    angle = 0;
                    return new ScreenPoint(middle, titlePosition);
                case AxisPosition.Bottom:
                    halign = HorizontalAlignment.Center;
                    valign = VerticalAlignment.Bottom;
                    angle = 0;
                    return new ScreenPoint(middle, titlePosition);
                default:
                    throw new ArgumentOutOfRangeException("axis");
            }
        }