Recently, cross-modal effects in which perceptions interact with each other have been drawing attention. In the case of the cross-modal effect between vision and taste, the effect of the angularity of shapes on taste has been widely studied. However, there has been little research on the other features of shapes. Also, previous studies have shown that the emotional valence arisen from visual perception causes the cross-modal effect. Therefore, this study focuses on the complexity of shapes, which is said to influence emotional valence, as a visual stimulus and aims to confirm the cross-modal effect induced by its sensation. First, by using particle swarm optimization algorithm, closed curve shapes were generated based on curvature entropy, a quantitative index of the complexity of shapes. Second, cup holders, which had these closed curve shapes on their sides, were created by using a 3D printer. Third, by comparing the tastes of orange juice in these cup holders, the effect of the complexity of shapes on the perception of sweetness was confirmed. Finally, we propose index of Angularity derived from curvature, which has been suggested to be relevant in previous studies, and additionally test for cross-modal effects on this index. The results suggest that the complexity of shapes controlled by curvature entropy and the Angularity of shapes controlled by index of Angularity derived from curvature weaken the perception of sweetness. This finding can be used for reducing sugar intake in bottle packaging.