Implicit to NURBS conversion
At present, BRL-CAD has implemented lots of geometric primitives in an implicit form, but when it comes to interactive shaded displays and conversion to other formats, the disadvantages of implicit primitives come out. So we need a conversion to NURBS bundary representations. Lots of primitives have already been implemented as NURBS, but some are not robust and some still need to be improved. Besides, some are still missing. This summer, if I'm accepted, I'm going to accomplish the goal of converting all (if needed) implicit primitives to NURBS, including fixing the bugs and correcting the errors existing now, and adding new conversions that have not been implemented yet. Finally, I'd like to build a converter that can walk a CSG tree and convert the implicit primitives in the tree altogether to their NURBS form. The original implementation in BRL-CAD is a good starting point, and I will take the current routines of BRL-CAD.
Although I have read a few books on Computer Graphics before, I'm not very familiar with NURBS/BREP before I started preparing for the application. These days I have read a lot of materials relevant and read the codes of BRL-CAD, so now I have a deeper understand of what I'm going to do in this project, and some patches (See below) related to this project have been made. As I'm making these patches, I get much more familiar with what I should do and the techniques (mathematics knowledge, algorithms, APIs, etc.) I should use in this project.
Below is my detailed proposal for the project. In the first part I'd like to show what BRL-CAD has already done in the implicit to NURBS conversion. Then I will tell you detailed things I'm going to do in my summer. At last, I'd like to show you the schedule and what I have already done about this project.
The conversions of implicit primitives to NURBS in BRL-CAD can be seen in functions rt_*_brep() in src/librt/primitives/, and the conversion of each primitive is done in a separate function. The executable file csgbrep.exe can call most of them to produce NURBS represtations of many primitives together for a test.
This work is significantly dependent on the OpenNURBS library as its basic NURBS support. The data structures to describe NURBS is based on OpenNURBS, and OpenNURBS provides many useful algorithms for our work. But OpenNURBS is not perfect, with lots of useful and important functionality missing, so we still need lots of work to implement the functionality by hand.
Although lots of work has been done in BRL-CAD already, some bugs still exist and some work is still located at the mathematical orgin. It may not work well if the parameters are changed in some occasions. And some primitives are still not included. The robustness need to be improved and the missing ones should be added.
The document /share/brlcad/7.21.0/doc/brep.txt describes the current routine of brep primitives in BRL-CAD.
As there has been a lot of work done in BRL-CAD already in this field, so I should continue the work following the current routines and try my best to make it better.
First of all, I'd like to fix the problems remained in the current version. Some are listed above, and more are going to be discovered and added to the list (like extrude, revolve, etc.). Besides, I should provide the conversion of primitives at locations other than the origin. As for this, I should deduce the transformation matrices that are needed to transform the BREP at the origin back to the 3-space location where the CSG implicit is, including scaling (most already done in BRL-CAD), rotating, shearing and translating. Matrix transformations are applied to the control points of the NURBS surfaces to make the changes. These days I have done some work on this (sph, ell, ehy, hyp) and the results seem quiet good, but I think it will be more challenging later, as the primitives gets more complicated. The codes in other primitives that already work well can be referred to when I need help. In a word, to determine and apply the transmation matrices for non-origin CSG primitives is an important part of this project. My background in linear algebra might offer me great help, I hope.:)
During my coding, I should always keep in mind writing maintainable, portable and complete code. To keep a good habit of coding is really important. I will write clear documents in the meantime, and discuss my opinions with the development team. After the conversion of one primitive, I will improve its documents immediately, so that the work is complete.
To test the result of conversions, I am going to replace the implicit primitives in the CSG tree with the NURBS representation, raytrace the whole model to see whether it is changed. Once I found some mistakes in my conversion like overflows, I should modify my code immediately.
But the current routine for testing the conversion is to use csgbrep.exe, which is quite inconvenient. So I'd like to write a converter that is easy to use. It can convert arbitrary implicit primitives to breps, as long as the conversion function has been implemented. I have already add an option to the brep command in my MGED to do this. The command followed by an object's name (a CSG implicit primitive) calls the related rt_*_brep() function and writes the brep primitive generated to the current database, and then I can draw it onto the screen. In such way the test becomes an much easier and convenient job. This should be done early in the project, because it benefits the following developing a lot. My present work is still incomplete, but it can work already.
After I finish doing something on the implemented conversions, I'd like to add more new conversions from implicit primitives to NURBS. For example, the conversions of implicit primitives like ars, half, part, grip, superell, metaball and so on are still missing now. Study the current code as examples may be of great help. Implementation of conversions of different primitives still have lots of things in common, like creating a curve and rotate or extrude it, creating surfaces, etc. And the comments in librt/primitives can tell me the concrete algorithms I should use to deal with that kind of primitives. Math books as well as materials online or in the library can offer me theoretical assistance. By the way, I should really learn more about the classes and functions in OpenNURBS, which provides basic support for our NURBS representation, with abundant APIs provided. I need to get full use of the library of OpenNURBS to implement my own methods, like bezier curves, surfaces, etc. As well as the others, the new implemented conversions should not be only for primitives located at the origin, and I should try my best to make the result as robust as possible. So as well as writing new code, the test is also very important, as I have mentioned above.
Finally, after finish all the rt_*_brep() functions for all primitives that would be included in a model, I am going to write a conversion function which walks the CSG tree and converts the implicit primitives in it to NURBS. The tree structure is duplicated, but the implicit primitives are replaced by the brep primitives. The conversion function may be available in a command in MGED, using an object or the whole model as its parameter. As there is already a command named "brep" in MGED, I'd like to follow it and add new options to it. The MGED command can be like this:
brep obj [brepname]
brep -t root [suffix] // -t means it deals with a tree
The former converts an implicit primitive to brep, and the latter can convert primitives in a CSG tree together. brepname and suffix are optional. When brepname is not specified, the name of the generated brep would be objname_brep (or objname.brep like what csgbrep.exe does). When the suffix is not specified, the names of the generated breps would be originalname_brep (or .brep). Of course, the specific details should not be decided now, and lots of discussion are needed when I develop this feature.
The deliverables and detailed schedule of my summer is as below.
I will have lots of free time during my summer vacation, so time is not a problem. I can work about 8 hours a day and 7 days a week. I'll have the final exams during June 11 to June 18, which takes about a week.
I have made patches related to the project I'm applying. The original revision(48890) of functions rt_ell_brep(), rt_ehy_brep() and rt_hyp_brep() cannot deal with objects centered at a non-origin point. I add rotation, translation and shearing matrices and apply them to do the transformation. They work quiet well in my tests. I hope it's a good start point for my work. This patch can be seen on https://sourceforge.net/tracker/?func=detail&aid=3513288&group_id=105292&atid=640804 .
I also add an option to the 'brep' command in MGED which can call functions rt_*_brep() to convert an implicit primitive to brep. So I can test the conversion function in MGED, which is a much more convenient way then csgbrep. I also share it as a patch on https://sourceforge.net/tracker/?func=detail&aid=3515194&group_id=105292&atid=640804 .
I'm really interested in computer graphics, and BRL-CAD is an excellent open-source CAD software. I think working for BRL-CAD is an interesting and meaningful experience, and I can learn much from it.
I'm good at mathematics, and this project needs lots of math knowledge. I'm also good at programming in C++. And I have made some patches on the functions I'm going to deal with in this project, which makes me confident that I can do a good job in this project.
I think I will get lots of practice if I participate in this project, and I hope to continue work for BRL-CAD, because once I start I cannot stop myself. I am really interested in working for BRL-CAD, and I found open source is such an interesting place.