Ⅰ. INTRODUCTION In this note the weak semidifferentiability and the weak semiderivative of mappings\ are introduced and applied to the study of the problems concerning the set of all positive solutions of the
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 purpos...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.展开更多
文摘Ⅰ. INTRODUCTION In this note the weak semidifferentiability and the weak semiderivative of mappings\ are introduced and applied to the study of the problems concerning the set of all positive solutions of the
文摘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.
