Recently, I'm working on something about polynomial splines over hierarchical T-meshes, which is basically a rectangular grid that allows T-junctions. I want to do some numerical experiments but I don't know how to represent T-meshes and splines over it in a computer. I'm going to study about PHT-splines and Hermite splines over T-meshes.

So my problem is: Which data structure should I use for them? Thank you~

I've tried to search for it on google. But all I found are about mathematical analysis of them and none is about the data structure.

Note: For details of T-meshes and PHT splines you can refer to this article
[pdf] Polynomial splines over hierarchical T-meshes

  • $\begingroup$ To my (untrained) eye, this looks more like a question for programmers, in which case it may fare better on StackOverflow. $\endgroup$ – Loop Space Aug 8 '11 at 11:37
  • $\begingroup$ Looks like that to my trained eye also. $\endgroup$ – Igor Rivin Aug 8 '11 at 12:57
  • $\begingroup$ @Andrew @Igor: Uh.. Well, it does be a program problem. But I think mathematicians in this area may be more familiar with T-meshes and PHT-splines. These mathematical conceptions is not so easy to be explained in a few words, if I asked it on StackOverflow... And I believe mathematicians who have worked with such splines will know the answer. $\endgroup$ – Roun Aug 8 '11 at 13:19
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    $\begingroup$ The problem is that typical programmers would have even less of a clue about this topic than mathematicians. $\endgroup$ – Victor Liu Aug 9 '11 at 2:59
  • $\begingroup$ I also need any code in c++ or matlab to implement how to generate this PHT spline in hierarchical t-meshes. If anyone can help me then it will be really great for me. Thanks... $\endgroup$ – user2855326 Nov 18 '13 at 13:24

PHT-Splines are hierarchical, and therefore recursive in nature. I use a kd-tree structure for my surfaces. This facilitates a fast lookup when querying on (x,y) or (u,v).

There are a number of ways you can manage the storage. I actually store the full set of Bezier control points for my bicubic patches in each leaf. It's not the most space efficient, but it is fairly convenient for evaluation.


There is literature on how to represent T-meshes. For example, the paper below acknowledges that the flexibility of T-meshes make them difficult to represent in a data structure. So they

"recommend using the extended T-mesh instead of the original one. We will show that, the extended T-mesh can be represented by a obj-like format file, and converted into a simple face-edge-vertex data structure easily."

"Extended T-mesh and Data Structure for the Easy Computation of T-spline." Hongwei Lin, Ye Cai, Shuming Gao. Journal of Information & Computational Science 9: 3 (2012) 583–593. (Journal link)

  • $\begingroup$ Thanks for your reply. I want to implement polynomial spline over hierarchical t-meshes for isogeometric analysis and for this reason I need any sample code or data structure or algorithm for implementing polynomial spline over hierarchical t-meshes. If you can help me then please kindly let me know. Thanks for your suggestion. $\endgroup$ – user42942 Nov 18 '13 at 14:55

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