In PDFBox, how to change the origin (0,0) point of a PDRectangle object?

You can change coordinate systems somewhat but most likely things won't get more elegant in the end.

To start with...

First of all let's clear up some misconception:

You assume

In PDFBox, PDRectangle objects' default origin (0,0) seems to be the lower-left corner of a page.

This is not true for all cases, merely often.

The area containing the displayed page area (on paper or on screen) usually is defined by the CropBox entry of the page in question:

CropBox rectangle (Optional; inheritable) A rectangle, expressed in default user space units, that shall define the visible region of default user space. When the page is displayed or printed, its contents shall be clipped (cropped) to this rectangle and then shall be imposed on the output medium in some implementation-defined manner.

... The positive x axis extends horizontally to the right and the positive y axis vertically upward, as in standard mathematical practice (subject to alteration by the Rotate entry in the page dictionary).

... In PostScript, the origin of default user space always corresponds to the lower-left corner of the output medium. While this convention is common in PDF documents as well, it is not required; the page dictionary’s CropBox entry can specify any rectangle of default user space to be made visible on the medium.

Thus, the origin (0,0) can literally be anywhere, it may be at the lower left, at the upper left, in the middle of the page or even far outside the displayed page area.

And by means of the Rotate entry, that area can even be rotated (by 90°, 180°, or 270°).

Putting the origin (as you seem to have observed) in the lower left merely is done by convention.

Furthermore you seem to think that the coordinate system is constant. This also is not the case, there are operations by which you can transform the user space coordinate system drastically, you can translate, rotate, mirror, skew, and/or scale it!

Thus, even if at the beginning the coordinate system is the usual one, origin in lower left, x-axis going right, y-axis going up, it may be changed to something weird some way into the page content description. Drawing your rectangle new PDRectangle(0, 0, 100, 100) there might produce some rhomboid form just right of the page center.

What you can do...

As you see coordinates in PDF user space are a very dynamic matter. what you can do to tame the situation, depends on the context you use your rectangle in.

Unfortunately you were quite vague in the description of what you do. Thus, this will be somewhat vague, too.

Coordinates in the page content

If you want to draw some rectangle on an existing page, you first of all need a page content stream to write to, i.e. a PDPageContentStream instance, and it should be prepared in a manner guaranteeing that the original user space coordinate system has not been disturbed. You get such an instance by using the constructor with three boolean arguments setting all them to true:

PDPageContentStream contentStream = new PDPageContentStream(doc, page, true, true, true);

Then you can apply a transformation to the coordinate system. You want the top left to be the origin and the y-value increasing downwards. If the crop box of the page tells you the top left has coordinates (xtl, ytl), therefore, you apply

contentStream.concatenate2CTM(new AffineTransform(1, 0, 0, -1, xtl, ytl));

and from here on you have a coordinate system you wanted, origin top left and y coordinates mirrored.

Be aware of one thing, though: If you are going to draw text, too, not only the text insertion point y coordinate is mirrored but also the text itself unless you counteract that by adding an also mirroring text matrix! If you want to add much text, therefore, this may not be as elegant as you want.

Coordinates for annotations

If you don't want to use the rectangle in the content stream but instead for adding annotations, you are not subject to the transformations mentioned above but you can not make use of it, either.

Thus, in this context you have to take the crop box as it is and transform your rectangle accordingly.

Why PDFBox text extraction coordinates are as they are

Essentially for putting lines of text together in the right order and sorting the lines correctly, you don't want such a weird situation but instead a simple stable coordinate system. Some PDFBox developers chose the top-left-origin, y-increasing-downwards variant for that, and so the TextPosition coordinates have been normalized to that scheme.

In my opinion a better choice would have been to use the default user space coordinates for easier re-use of the coordinates. You might, therefore, want to try working with textPosition.getTextMatrix().getTranslateX(), textPosition.getTextMatrix().getTranslateY() for a TextPosition textPosition

The following seems to be the best way to "adjust" the TextPosition coordinates:

x_adjusted =  x_original + page.findCropBox().getLowerLeftX();
y_adjusted = -y_original + page.findCropBox().getUpperRightY();

where page is the PDPage on which the TextPosition object is located