java - Drawing Curvy Lines Through PDFBox

Question

Using PDFBox, I have created a line chart to plot some data, and it looks much like any general line chart you will see through a google search. It also looks identical to the line chart I've attached to this question. The way the line chart drawing algorithm works is that it looks at the current point, and then the next one, and a line is drawn if a valid point is found there.

My problem is that a client does not like how sharply the lines connect with each other. Instead, they want the joins between the lines to happen in more of a curved fashion. Attached is an image of a rough idea of what the client wants. Note that although the lines look very curvy, the client specifically cares about the line joins themselves being curvy, and not sharp like in a standard line chart.

So far, I have tried using Bézier curves, but I can't seem to find the right values to make it scale right for all the different magnitudes between the points. I first tried changing the line cap and line join styles, but this did not produce the desired "cuvyness" between the line joins. I have also contemplated using paths to achieve this result, but I haven't managed to figure out how to proceed.

Is there something that I'm missing that could make it easier to draw these lines? If not, can anyone help me figure out the right Bézier values/paths to achieve these curves? Thanks in advance for any suggestions/code examples.

Due to an NDA, I cannot give a code example that shows how the chart is drawn and plotted (this would give up our algorithm entirely). All that I can say is that I created an internal representation for how the data should be plotted in the chart, and this system is very roughly translated in the provided image. I can say that the function that plots the data exclusively uses the PDPageContentStream classes's lineTo and strokeTo functions, after an initial moveTo to the position of the starting point based on our internal coordinate representation.

A rough idea of the curves the client wants.

Answer 1

---A quick "solution" is to use round line joins instead of miter joins (the default) --- it seems that I missed this.

The charts in your sample probably use curve interpolation and this question and answers might help you: How does polyline simplification in Adobe Illustrator work?

The code below shows how to transform a list of lines into Bezier connected lines (it's C# but it can be converted to Java with minimal changes):

/// <summary>
/// Draws the Bezier connected lines on the page.
/// </summary>
/// <param name="page">Page where to draw the lines.</param>
/// <param name="points">List of points representing the connected lines.</param>
/// <param name="pen">Pen to draw the final path.</param>
/// <param name="smoothFactor">Smooth factor for computing the Bezier curve</param>
/// <param name="font"></param>
private static void DrawBezierConnectedLines(PDFPage page, PDFPoint[] points, PDFPen pen, double smoothFactor, PDFFont font)
{

    PDFPath path = new PDFPath();
    path.StartSubpath(points[0].X, points[0].Y);

    for (int i = 0; i < points.Length - 2; i++)
    {
        PDFPoint[] pts = ComputeBezierConnectedLines(points[i], points[i + 1], points[i + 2], smoothFactor, i == 0, i == points.Length - 3);
        switch (pts.Length)
        {
            case 2: // Intermediate/last section - straight lines
                path.AddLineTo(pts[0].X, pts[0].Y);
                path.AddLineTo(pts[1].X, pts[1].Y);
                break;
            case 3: // First section - straight lines
                path.AddLineTo(pts[0].X, pts[0].Y);
                path.AddLineTo(pts[1].X, pts[1].Y);
                path.AddLineTo(pts[2].X, pts[2].Y);
                break;
            case 4: // Intermediate/last section
                path.AddLineTo(pts[0].X, pts[0].Y);
                path.AddBezierTo(pts[1].X, pts[1].Y, pts[1].X, pts[1].Y, pts[2].X, pts[2].Y);
                path.AddLineTo(pts[3].X, pts[3].Y);
                break;
            case 5: // First section
                path.AddLineTo(pts[0].X, pts[0].Y);
                path.AddLineTo(pts[1].X, pts[1].Y);
                path.AddBezierTo(pts[2].X, pts[2].Y, pts[2].X, pts[2].Y, pts[3].X, pts[3].Y);
                path.AddLineTo(pts[4].X, pts[4].Y);
                break;
        }
    }

    page.Canvas.DrawPath(pen, path);

    page.Canvas.DrawString($"Smooth factor = {smoothFactor}", font, new PDFBrush(), points[points.Length - 1].X, points[0].Y);
}

/// <summary>
/// Given a sequence of 3 consecutive points representing 2 connected lines the method computes the points required to display the new lines and the connecting curve.
/// </summary>
/// <param name="pt1">First point</param>
/// <param name="pt2">Second point</param>
/// <param name="pt3">Third point</param>
/// <param name="smoothFactor">Smooth factor for computing the Bezier curve</param>
/// <param name="isFirstSection">True if the points are the first 3 in the list of points</param>
/// <param name="isLastSection">True if the 3 points are last 3 in the list of points.</param>
/// <returns>A list of points representing the new lines and the connecting curve.</returns>
/// <remarks>The method returns 5 points if this is the first section, points that represent the first line, connecting curve and last line.
/// If this is not the first section the method returns 4 points representing the connecting curve and the last line.</remarks>
private static PDFPoint[] ComputeBezierConnectedLines(PDFPoint pt1, PDFPoint pt2, PDFPoint pt3, double smoothFactor, bool isFirstSection, bool isLastSection)
{
    PDFPoint[] outputPoints = null;

    if (smoothFactor > 0.5)
    {
        smoothFactor = 0.5; // Half line maximum
    }
    if (((pt1.X == pt2.X) && (pt2.X == pt3.X)) || // Vertical lines
        ((pt1.Y == pt2.Y) && (pt2.Y == pt3.Y)) || // Horizontal lines
        (smoothFactor == 0))
    {
        if (!isFirstSection)
        {
            pt1 = ComputeIntermediatePoint(pt1, pt2, smoothFactor, false);
        }
        if (!isLastSection)
        {
            pt3 = ComputeIntermediatePoint(pt2, pt3, smoothFactor, true);
        }
        if (isFirstSection)
        {
            outputPoints = new PDFPoint[] { pt1, pt2, pt3 };
        }
        else
        {
            outputPoints = new PDFPoint[] { pt2, pt3 };
        }
    }
    else
    {
        PDFPoint startPoint = new PDFPoint(pt1);
        if (!isFirstSection)
        {
            startPoint = ComputeIntermediatePoint(pt1, pt2, smoothFactor, false);
        }
        PDFPoint firstIntermediaryPoint = ComputeIntermediatePoint(pt1, pt2, smoothFactor, true);
        PDFPoint secondIntermediaryPoint = new PDFPoint(pt2);
        PDFPoint thirdIntermediaryPoint = ComputeIntermediatePoint(pt2, pt3, smoothFactor, false);
        PDFPoint endPoint = new PDFPoint(pt3);
        if (!isLastSection)
        {
            endPoint = ComputeIntermediatePoint(pt2, pt3, smoothFactor, true);
        }

        if (isFirstSection)
        {
            outputPoints = new PDFPoint[] { startPoint, firstIntermediaryPoint, secondIntermediaryPoint, thirdIntermediaryPoint, endPoint };
        }
        else
        {
            outputPoints = new PDFPoint[] { firstIntermediaryPoint, secondIntermediaryPoint, thirdIntermediaryPoint, endPoint };
        }
    }

    return outputPoints;
}

/// <summary>
/// Given the line from pt1 to pt2 the method computes an intermediary point on the line.
/// </summary>
/// <param name="pt1">Start point</param>
/// <param name="pt2">End point</param>
/// <param name="smoothFactor">Smooth factor specifying how from from the line end the intermediary point is located.</param>
/// <param name="isEndLocation">True if the intermediary point should be computed relative to end point, 
/// false if the intermediary point should be computed relative to start point.</param>
/// <returns>A point on the line defined by pt1->pt2</returns>
private static PDFPoint ComputeIntermediatePoint(PDFPoint pt1, PDFPoint pt2, double smoothFactor, bool isEndLocation)
{
    if (isEndLocation)
    {
        smoothFactor = 1 - smoothFactor;
    }

    PDFPoint intermediate = new PDFPoint();
    if (pt1.X == pt2.X)
    {
        intermediate.X = pt1.X;
        intermediate.Y = pt1.Y + (pt2.Y - pt1.Y) * smoothFactor;
    }
    else
    {
        intermediate.X = pt1.X + (pt2.X - pt1.X) * smoothFactor;
        intermediate.Y = (intermediate.X * (pt2.Y - pt1.Y) + (pt2.X * pt1.Y - pt1.X * pt2.Y)) / (pt2.X - pt1.X);
    }

    return intermediate;
}

For this set of points:

PDFPoint[] points = new PDFPoint[] {
    new PDFPoint(50, 150), new PDFPoint(100, 200), new PDFPoint(150, 50), new PDFPoint(200, 150), new PDFPoint(250, 50) };
DrawBezierConnectedLines(page, points, pen, 0, helvetica);

this the result:

The corresponding PDF file can be downloaded here: https://github.com/o2solutions/pdf4net/blob/master/GettingStarted/BezierConnectedLines/BezierConnectedLines.pdf