Efficient evaluation of triangular B-splines

Evaluation routines are essential for any application that uses triangular B-splines. This paper describes an algorithm to efficiently evaluate triangular B-splines. The novelty of the algorithm is its generality: there is no restriction on the degree of the B-spline or on the dimension of the domain. Constructing an evaluation graph allows us to reuse partial results and hence, to decrease computation time. Computation time gets reduced even more by making choices in unfolding the recurrence relation of simplex splines such that the evaluation graph becomes smaller. The complexity of the algorithm is measured by the number of leaves of the graph.