Surface Cutting and Flattening to Target Shapes

We introduce a novel framework for surface cutting and flattening, aiming to align the boundary of planar parameterization with a target shape. Diverging from traditional methods focused on minimizing distortion, we intend to also achieve shape similarity between the parameterized mesh and a specific planar target, which is important in some applications of art design and texture mapping. However, with existing methods commonly limited to ellipsoidal surfaces, it still remains a challenge to solve this problem on general surfaces. Our framework models the general case as a joint optimization of cuts and parameterization, guided by a novel metric assessing shape similarity. To circumvent the common issue of local minima, we introduce an extra global seam updating strategy which is guided by the target shape. Experimental results show that our framework not only aligns with previous approaches on ellipsoidal surfaces but also achieves satisfactory results on more complex ones.