摘要
In this paper we propose an optimization frame- work for interior carving of 3D fabricated shapes. Interior carving is an important technique widely used in industrial and artistic designs to achieve functional purposes by hollow- ing interior shapes in objects. We formulate such functional purpose as the objective function of an optimization prob- lem whose solution indicates the optimal interior shape. In contrast to previous volumetric methods, we directly repre- sent the boundary of the interior shape as a triangular mesh. We use Eulerian semiderivative to relate the time derivative of the object function to a virtual velocity field and iteratively evolve the interior shape guided by the velocity field with sur- face tracking. In each iteration, we compute the velocity field guaranteeing the decrease of objective function by solving a linear programming problem. We demonstrate this general framework in a novel application of designing objects float- hag in fluid and two previously investigated applications, and print various optimized objects to verify its effectiveness.
In this paper we propose an optimization frame- work for interior carving of 3D fabricated shapes. Interior carving is an important technique widely used in industrial and artistic designs to achieve functional purposes by hollow- ing interior shapes in objects. We formulate such functional purpose as the objective function of an optimization prob- lem whose solution indicates the optimal interior shape. In contrast to previous volumetric methods, we directly repre- sent the boundary of the interior shape as a triangular mesh. We use Eulerian semiderivative to relate the time derivative of the object function to a virtual velocity field and iteratively evolve the interior shape guided by the velocity field with sur- face tracking. In each iteration, we compute the velocity field guaranteeing the decrease of objective function by solving a linear programming problem. We demonstrate this general framework in a novel application of designing objects float- hag in fluid and two previously investigated applications, and print various optimized objects to verify its effectiveness.
