Two dominant coordination constraints have been identified during isofrequency conditions in previous work: the egocentric constraint, i.e., simultaneous activation of homologous muscle groups, and the allocentric constraint, i.e., moving the segments in the same direction in extrinsic space. To verify their generalization, bimanual drawing movements were performed in different planes of motion (transverse, frontal, sagittal, frontal-transverse) according to the in-phase and anti-phase mode along the X- and Y-axes. Convergent findings were obtained across the transverse, frontal, and frontal-transverse planes. The in-phase mode along both axes was performed most accurately/consistently, whereas the anti-phase mode resulted in a deterioration of the coordination pattern and this effect was most pronounced when the latter mode was introduced with respect to both dimensions. For sagittal plane motions, the in-phase mode was again superior but the second most optimal configuration was the anti-phase mode along both axes. This finding was hypothesized to result from the familiarity with the pattern since it resembles cycling behavior. It illustrates how cognitive mapping is superimposed onto the dynamics of interlimb coordination. Overall, these results support the presence of both the egocentric and allocentric constraint during bimanual movement production.