Tests of constituent-quark generation methods which maintain both the nucleon center of mass and the desired radial distribution in Monte Carlo Glauber models

Several methods of generating three constituent quarks in a nucleon are evaluated which explicitly maintain the nucleon's center of mass and desired radial distribution and can be used within Monte Carlo Glauber frameworks. The geometric models provided by each method are used to generate distributions over the number of constituent quark participants $({N}_{\mathrm{qp}})$ in $p+p,\phantom{\rule{0.16em}{0ex}}d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions. The results are compared with each other and to a previous result of ${N}_{\mathrm{qp}}$ calculations, without this explicit constraint, used in measurements of $\sqrt{{s}_{{}_{NN}}}=200$ GeV $p+p,\phantom{\rule{0.16em}{0ex}}d+\mathrm{Au}$, and $\mathrm{Au}+\mathrm{Au}$ collisions at the BNL Relativistic Heavy Ion Collider.