Optimization Modeling for Fitting Freeform Surfaces Based on Waterbomb Origami

The shape diversity and flexibility of waterbomb origami units enable them to adapt to various surfaces and realize the construction of complex models. To address the issues of vertex deviation from the target surface after optimization, leading to insufficient model approximation accuracy and large area differences among waterbomb units in the crease pattern which increase its irregularity, this paper proposes a freeform surface modeling method based on waterbomb origami. Under the constraints of developability and flat-foldability, a numerical approximation method based on multi-objective optimization is employed to fit the waterbomb mesh on the target surface more precisely. Equal-area waterbomb units are used to construct 3D models, reducing area differences and producing more regular crease patterns. Experimental results on various surfaces show that the maximum distance residuals significantly decrease after introducing distance constraints, and the maximum area residuals are all less than 1E−12. These results verify the effectiveness and feasibility of the proposed method, offering new insights and approaches for freeform surface modeling based on origami.