Implement shading with Coons and tensor-product patch meshes

Of the seven shading methods described in the PDF specification, type 6 (Coons patch meshes) and type 7 (Tensor-product patch meshes) haven't been implemented. I have done type 1, 4 and 5, but I don't know the math for type 6 and 7. My math days are decades away.

Knowledge prerequisites:

• java, although you don't have to be a java ace, just feel confortable
• math: you should know what "cubic Bézier curves", "Degenerate Bézier curves", "bilinear interpolation", "tensor-product", "affine transform matrix" and "Bernstein polynomials" are, or be able to learn it
• maven (basic)
• svn (basic)
• an IDE like Netbeans or Eclipse or IntelliJ (basic)
• ideally, you are either a math student who likes to program, or a computer science student who is specializing in graphics.

A first look at PDFBOX: try the command utility here:
https://pdfbox.apache.org/commandline/#pdfToImage
and use your favorite PDF, or the PDFs mentioned in PDFBOX-615, these have the shading types that are already implemented.

Some simple source code to convert to images:

String filename = "blah.pdf";
PDDocument document = PDDocument.loadNonSeq(new File(filename), null);
List<PDPage> pdPages = document.getDocumentCatalog().getAllPages();
int page = 0;
for (PDPage pdPage : pdPages)
{
++page;
BufferedImage bim = RenderUtil.convertToImage(pdPage, BufferedImage.TYPE_BYTE_BINARY, 300);
ImageIO.write(bim, "png", new File(filename+page+".png"));
}
document.close();

You are not starting from scratch. The implementation of type 4 and 5 shows you how to read parameters from the PDF and set the graphics. You don't have to learn the complete PDF spec, only 15 pages related to the two shading types, and 6 pages about shading in general. The PDF specification is here:
http://www.adobe.com/devnet/pdf/pdf_reference.html

The tricky parts are:

• decide whether a point(x,y) is inside or outside a patch
• decide the color of a point within the patch

To get an idea about the code, look at the classes GouraudTriangle, GouraudShadingContext, Type4ShadingContext and Vertex here
https://svn.apache.org/viewvc/pdfbox/trunk/pdfbox/src/main/java/org/apache/pdfbox/pdmodel/graphics/shading/
or download the whole project from the repository.
https://pdfbox.apache.org/downloads.html#scm
If you want to see the existing code in the debugger with a Gouraud shading, try this file:
http://asymptote.sourceforge.net/gallery/Gouraud.pdf

Testing:
I have attached several example PDFs. To see which one has which shading, open them with an editor like NOTEPAD++, and search for "/ShadingType" (without the quotes). If your images are rendering like the example PDFs, then you were successful.

Optional:
Review and optimize the complete shading package for speed; implement cubic spline interpolation for type 0 (sampled) functions (that one is really low-low priority, see details by looking up "cubic spline interpolation" in the PDF spec, which tells that it is disregarded in printing, and I don't have a test PDF).

Mentor: Tilman Hausherr (European timezone, languages: german, english, french)