My code to subject "Önálló laboratórium 2" at masters. I used the framework implemented by Peter Salvi: https://github.com/salvipeter/sample-framework/tree/757a0b1af2f4a17fb536777664c68145f386b65e.
- With key K you can change whether you want surface-keeping insertion or not (the latter is the default).
- With key E you can change whether you want insertions at any given point of an edge (this is the default) or at the half of the edge.
According to the publication T-Splines and T-NURCCs by Sederberg et al. 2003 two rules of T-mesh have to be checked in order to validate the correctness of the topology.
Rule 1: The sum of knot intervals on opposing edges of any face must be equal.
Rule 2: If a T-junction on one edge of a face can be connected to a T-junction on an opposing edge of the face (thereby splitting the face into two faces) without violating Rule 1, that edge must be included in the T-mesh.
I based my implementation on T-spline simplification and local refinement by Sederberg et al. 2004 partly, too. I implemented the control net drawing in such a way, that the T-mesh topology created this way is never going to fail the rule written in this publication:
Knot vectors si (4) and ti (5) for the blending function of Pi are determined as follows. (si2; ti2) are the knot coordinates of Pi. Consider a ray in parameter space R(a) = (si2 +a; ti2). Then si3 and si4 are the s coordinates of the first two s-edges intersected by the ray (not including the initial (si2; ti2)). By s-edge, we mean a vertical line segment of constant s. The other knots in si and ti are found in like manner.
I bind two consecutive points in a row or column if the fourth element of the knot vector of the first point in order is the knot value of the point itself = the third element of its knot vector (for rows and columns accordingly). This way Rule 2 is always going to apply to my implementation.
(Although Rule 2 doesn't explicitly say whether a T-junction should be connected with opposing single point on edge, according to page 12-13 of this presentation it should, so my implementation is correct in the aspect of Rule 2)
Rule 1 is also always going to apply to my implementation thanks to the fact that I'm representing my topologies in sparse matrices. In my topologies two points can only be connected if they are in the same row or same column. This way Rule 1 always applies, because the endpoints of any two opposing edges have same knot coordinate (the other coordinate than the one which is the same with the other endpoint of their according edge) as the opposing endpoint of the other edge.
TODO consider faces that are not rectangle