User:Phoenix/GSoc2013/Proposal

Project title

NURBS Intersection & Evaluation

Brief summary

Last summer I tried to do something on NURBS surface-surface intersection for BRL-CAD, but due to the limitation of time I cannot completely finish this project. I have implemented a routine to compute the intersection curves of two NURBS surfaces, and in general cases it works well, but some improvement are still needed. And the remaining part was done in a rush, with lots of features still missing. So in this summer, I would like to continue to work on this project, finishing the remaining parts, and finally offer a routine to convert CSG combination objects to evaluated NURBS objects. The work includes but is not limited to: (1) improve the current SSI routine to deal with special cases; (2) split the surfaces with the intersection curves we get in (1); (3) combine the new trimmed faces to get a new evaluated model. If there's still some time remaining, I will tried some other interesting topics, like NURBS editing in mged/archer, or anything that have great priority in BRL-CAD.

Detailed description

Introduction

NURBS surface-surface intersection is still a high-priority project in BRL-CAD. NURBS is a dominant geometric representation format in CADs, so we need to have enough support for it in BRL-CAD. Currently most objects in BRL-CAD are modeled in CSG, when converted to NURBS representations, the primitives are first converted to NURBS primitives, which BRL-CAD supports, but the next step is missing - evaluate the boolean operations on NURBS primitives, and then get a evaluated NURBS combination as the original CSG combination object. Currently BRL-CAD only gives ``CSG tree + unevaluated NURBS primitives", so we need NURBS intersections and evaluations.

Below is my detailed proposal for this summer's project. In the first part, I'd like to mention the current status of this part left out last summer. Then I list my plan on how to implement the remaining parts, dividing into three parts. In addition, something I want to do if I have additional time will be listed. At last, I'd like to show you the schedule and what I have already done this year about this project.

The current status of NURBS intersections & evaluations

Last year I spent about a month on NURBS intersections after I almost finished the Implicit to NURBS conversion project. I implemented a surface-surface intersection routine, using the sub-division method referred in a paper [1]. Now it can give us the intersection curves of two NURBS surfaces in both 3D spaces and 2D uv spaces. If the two inputs are in good condition, the result is quite reasonable (For detailed information, please see my last year's development log, there will be some convincing figures). But when the two surfaces have some coincides, the routine may have problems, because it first calculates the intersection of surfaces' bounding boxes, and then use polylines to approximate the curves, however, in this case, we should get a surface, not some curves. And for some strange shaped surfaces, the accuracy of the output may be not ideal. (max_dis can be inputted manually to get a better result, but it's a burden for users)

And I also tried to calculate boolean operations on NURBS. I just focus on the union of two spheres, which is a well-conditioning problem, and tried to get a evaluated model which can pass the IsValid check offered by openNURBS, but failed. So this part only have many lines of code written, but doesn't have enough functionality, and lots of work ahead should be done.

Calculating surface-surface intersection curves

The function calculating NURBS surface-surface intersection curves is in /src/libbrep/opennurbs_ext.cpp:

int surface_surface_intersection(const ON_Surface* surfA, const ON_Surface* surfB, ON_SimpleArray<ON_NurbsCurve*> &intersect3d, ON_SimpleArray<ON_NurbsCurve*> &intersect_uv2d, ON_SimpleArray<ON_NurbsCurve*> &intersect_st2d, double max_dis, double)

Some improvements are still needed:

1) If we detect there are many intersection points that seems to form a surface, not just curves, that it seems that these may exist an intersection 'surface'. But finding out this is quite confusing, because that may be some cases where two surfaces have many intersection curves that are very close to each other, but they don't have anywhere coincide. (The paper [2] considers such degenerate overlap issues in Part 4.3 Robustness issues)

2) There should be some detection related to the two surfaces when merging polylines (the 3rd step of SSI), not just using the max_dis parameter. In some cases, there may be two segments that should be in one intersection curve have bigger distance than two segments that exists in two nearby intersection curves, but we tend to merge the latter two segments instead of the former, without that detection.

3）Detecting loops. Note: only loops in the 2D uv space is of interest, those in 3D space is just for displaying, not very useful in the later evaluation process. A loop in the 3D space may not be a loop in the 2D space.

4) We should test more cases and find more problems in the intersection routine, and fix them to get better performance. For example, two surfaces have many parts that intersects, resulting in many strange-shaped intersection curves.

5) Some code re-factoring is needed, and comments should be added to make the code more readable.

Split the surfaces and generate new trimmed sub-surfaces using intersection curves

The code in the function split_trimmed_face in src/librt/primitives/brep/brep.cpp currently works on this, but it's just a scratched draft worked out last summer. (I think there should be an independent file containing the NURBS evaluating code)

The paper [2] gives us a good direction on how to do this. We get intersection curves in 2D uv spaces in the first part, and a NURBS surface in a 2D uv space is much simpler than in the 3D space. Trimming curves are also 2D curves. As the paper suggests, we can use the non-intersecting chains to partitioning a simple polygon (just like what we need to do in the 2D space: the intersection curves are polylines, and the outer loop of a surface will always be a polygon). There has been some drafted code already in BRL-CAD, but they don't work well. Further study of this algorithm and better implementation are needed this summer.

Note that inner loops should be considered, as is not mentioned in the paper.

And curve-curve intersection is needed in this part when we need the intersection of intersection curves and trimming curves, but it's not difficult because they are all polylines. Actually, the paper suggests a fast routine using Seidel's algorithm for fast polygon triangulation to calculate this, as intersection curves are always close curves in spaces.

And I have a small question here: as far as I'm concerned, in this step, we just use trimming curves to define the border of a new partitioned face (the trimming curves will play a role in the final ON_Brep object), but the ON_Surface as well as ON_BrepFace is still the original one, is that enough to describe the result of splitting?

Computation of the new solid model

Currently nothing have been done on this. It's the last step - performing inside/outside tests to determine whether a trimmed surface should appear in the final evaluated model or not. But inside/outside tests are time-consuming (described later), and the paper [2] suggests using connectivity graphs, which can reduce the number of inside/outside tests to only two per operation.

A connectivity graph is an undirected graph describing the neighborhood information between the patches constituting the solid, representing the topology of the solid model. Each patch of a solid is associated with a vertex, and an edge exists in the graph iff the relative patches are neighboring patches. And when we compute the new model, we construct a new connectivity graph whose vertices are connected components of the old graph and there is an edge between two components if they lie on either side of the intersection curve. From the construction it is clear that if one vertex lies inside the other solid all its neighbors lie outside and vice versa. Therefore performing exactly one inside/outside test is sufficient to determine the containment classification of each component.

As for how to perform inside/outside tests - we use curve-surface intersection - computing the number of intersections of a semi-infinite ray emanating from a point with the solid, and if the number is odd, the point is inside the solid, otherwise it's outside.

Operations include: union, difference, intersection.

Finally we generate the ON_Brep object. Lots of elements should be added - edges, curves, trims, etc. and the ON_Brep::IsValid() will check. Read the code in IsValid() functions will help us know what a valid ON_Brep shbuld look like. The code in add_elements() in /src/librt/primitives/brep/brep.cpp has some basic routine but is far from complete.

Tests

First, some basic tests - e.g. two spheres have some part intersecting, an arb8 and a sph, etc.

If the evaluation on basic primitives is satisfiable, more complicate tests should be performed. Finally, we should test on the /share/db/*.g files, and tried to convert the big models (m35, havoc) into evaluated NURBS models.

Besides, the brep command in MGED should be extended, to support evaluations of NURBS objects (Don't forget the manual page). Maybe this command can also be migrated into archer. The conversion script (conversion.sh) should also be modified to generate evaluated NURBS.

Other ideas

If I finish my project beyond my schedule (just like last year), I will tried other projects, such as the NURBS related ones: NURBS Editing support, Vector Drawing from NURBS, etc. I'm quite familiar with NURBS after some projects, so I think I would be a good candidate for them. If BRL-CAD have other high-priority project, I would also like to have a try.

Links

[1] Adarsh Krishnamurthy, Rahul Khardekar, Sara McMains, Kirk Haller, and Gershon Elber. 2008. Performing efficient NURBS modeling operations on the GPU. In Proceedings of the 2008 ACM symposium on Solid and physical modeling (SPM '08). ACM, New York, NY, USA, 257-268. DOI=10.1145/1364901.1364937 http://doi.acm.org/10.1145/1364901.1364937

[2] S. Krishnan, A. Narkhede, and D. Manocha. BOOLE: A System to Compute Boolean Combinations of Sculptured Solids. Technical Report TR95-008. Department of Computer Science, University of North Carolina, 1995. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.88

Deliverables

• NURBS surface-surface intersection routines
• NURBS evaluation support
• CSG model to evaluated NURBS conversion