Asymmetric objects with uniform mass distribution can also become tops
Generally speaking, a top needs a completely symmetrical shape around its axis of rotation to be able to rotate stably for a long time. If an asymmetrical object with uniform mass distribution, such as a solid toy teapot, even if a handle-like shaft is installed on its rotating shaft to make it rotate, it will lose its balance in a very short time and stop rotating. This is because objects with uniform mass but asymmetrical shape cannot maintain a stable moment of inertia. Since the shape of the toy cannot be changed easily, the research team started with another method: by redistributing the mass distribution inside the toy. They use algorithms to analyze the rotation of the object and modify the internal mass distribution to achieve a stable moment of inertia. This method can make the object produce stable rotation without changing the shape of the toy. The team hollowed out the solid model after the analysis of the computer algorithm, and kept the center of mass as low as possible on the axis of rotation. At SIGGRAPH 2014 and above, the Disney research team described that 'the moment of inertia depends on the overall volume of the object, not the geometry of the surface of the object. We change the internal design and mass distribution of the object (to make the object rotate stably)'. They call it 'cage-based deformation' (cage-based deformation) to increase the space between objects to improve stability. In addition, they also use a technology they call 'dual-density optimization'. Through the filling of various density materials, the effect of stable rotation can be produced without changing the shape. Moritz Bcher, a postdoctoral fellow at the Disney Research Institute, said, “Our approach is very effective and has been applied to a variety of models. From the elephant toy character standing on tiptoes to keep balance, to the armadillo and the breakdancing armadillo. Various abstract shapes. It is very suitable for 3D printers to make toy spinning tops and yo-yos with unique shapes.'