In conjoint analysis, interaction effects characterize how preference for the level of one product attribute is dependent on the level of another attribute. When interaction effects are negligible, a main effects fractional factorial experimental design can be used to reduce data requirements and survey cost. This is particularly important when the presence of many parameters or levels makes full factorial designs intractable. However, if interaction effects are relevant, main effects design can create biased estimates and lead to erroneous conclusions. This work investigates consumer preference interactions in the nontraditional context of visual choice-based conjoint analysis, where the conjoint attributes are parameters that define a product's shape. Although many conjoint studies assume interaction effects to be negligible, they may play a larger role for shape parameters. The role of interaction effects is explored in two visual conjoint case studies. The results suggest that interactions can be either negligible or dominant in visual conjoint, depending on consumer preferences. Generally, we suggest using randomized designs to avoid any bias resulting from the presence of interaction effects.