The estimation of fractional abundances under physical constraints is a fundamental problem in hyperspectral data processing. In this paper, we propose to adapt Kaczmarz's cyclic projections to solve this problem. The main contribution of this work is two-fold: On the one hand, we show that the non-negativity and the sum-to-one constraints can be easily imposed in Kaczmarz's cyclic projections, and on the second hand, we illustrate that these constraints are advantageous in the convergence behavior of the algorithm. To this end, we derive theoretical results on the convergence performance, both in the noiseless case and in the case of noisy data. Experimental results show the relevance of the proposed method.