20.500.12556/DiRROS-30714 New approach for constructing edge B-spline-like basis functions for $C^1$ and $C^2$ splines over triangulations Splines over triangulations provide a flexible and efficient way to approximate bivariate functions defined over domains, partitioned by triangles. One of the important challenges is the construction of locally supported non-negative basis functions that form a partition of unity, i.e., B-spline-like basis functions. Due to smoothness conditions that depend on the geometry of the triangulation, spline basis functions are typically divided into three groups: triangle, vertex, and edge functions. While the construction of triangle and vertex basis splines is well developed, the computation of non-negative edge basis splines of general degree that form a partition of unity has so far been addressed only for $C^1$ continuous splines, using a completely algebraic approach, with no explicit geometric interpretation ([7]). In this paper a novel approach is presented that extends the control-triangle-based idea known for vertex basis splines and can be geometrically explained and generalized to splines of a higher order of smoothness. The construction is developed on pairs of adjacent triangles forming a strictly convex quadrilateral. Since each smoothness order requires a separate analysis, a detailed study is provided for the $C^1$ and $C^2$ continuous splines of degrees $d \ge 2$ and $d \ge 4$, respectively. Numerical examples are provided to confirm the effectiveness and applicability of the derived construction. Bernstein-Bézier form ▫$C^r$▫ splines over triangulations B-spline-like basis control triangles subdivision true false true Angleški jezik Ni določen Neznano 2026-07-01 12:07:19 2026-07-01 12:07:19 2026-07-02 03:59:42 0000-00-00 00:00:00 2027 0 0 22 str. article 117914 Vol. 489 Jan. 2027 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2027-01-01 519.6 0377-0427 10.1016/j.cam.2026.117914 283120643 1-s2.0-S037704272600556X-main.pdf 1-s2.0-S037704272600556X-main.pdf 1 258BB6075CE01E3ECC0FBF53E8D2A586 ae9a5f955b87f3d59b7e4609d29e60e2fe6f4d541f4e2438b70da4a96649324e e39f71c8-7534-11f1-b0d9-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=46863 https://www.sciencedirect.com/science/article/pii/S037704272600556X 1 a62574b3-7534-11f1-b0d9-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=46862 Inštitut za matematiko, fiziko in mehaniko 0 0 0