The simple mesh refinement algorithm of Groiss et al. (2023) generates T-
meshes admitting Reachable Minimally supported (RM) B-splines that possess the 
property of local linear independence and form a non-negative partition of 
unity. The construction was first presented for the bilinear case and has 
later been extended to $C^s$-smooth splines of degree $p=2s+1$. The present 
paper is devoted to algorithms and data structures for RMB-splines. We prove 
that the memory consumption of the data structures for representing a T-mesh 
and the associated RMB-splines is linear with respect to the mesh size, and we 
describe the details of the underlying refinement algorithm. Moreover, we 
introduce a novel evaluation algorithm for RMB-spline surfaces, which is based 
solely on repeated convex combinations of the control points, thereby 
generalizing de Boor's algorithm for tensor-product splines. Numerical 
experiments are included to demonstrate the advantageous behaviour of the 
proposed data structures and algorithms with respect to their efficiency. We 
observe that the total computational time (which includes also error 
estimation and spline projection) scales roughly linearly with the number of 
degrees of freedom for the meshes considered by us. Joint work with Maodong 
Pan.