We present an interactive system that lets a user move and deform a two-dimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The system then computes the positions of the remaining free vertices by minimizing the distortion of each triangle. While physically based simulation or iterative refinement can also be used for this purpose, they tend to be slow. We present a two-step closed-form algorithm that achieves real-time interaction. The first step finds an appropriate rotation for each triangle and the second step adjusts its scale. The key idea is to use quadratic error metrics so that each minimization problem becomes a system of linear equations. After solving the simultaneous equations at the beginning of interaction, we can quickly find the positions of free vertices during interactive manipulation. Our approach successfully conveys a sense of rigidity of the shape, which is difficult in space-warp approaches. With a multiple-point input device, even beginners can easily move, rotate, and deform shapes at will.
We present an interactive system that lets a user move and deform a two-dimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The system then computes the positions of the remaining free vertices by minimizing the distortion of each triangle. While physically based simulation or iterative refinement can also be used for this purpose, they tend to be slow. We present a two-step closed-form algorithm that achieves real-time interaction. The first step finds an appropriate rotation for each triangle and the second step adjusts its scale. The key idea is to use quadratic error metrics so that each minimization problem becomes a system of linear equations. After solving the simultaneous equations at the beginning of interaction, we can quickly find the positions of free vertices during interactive manipulation. Our approach successfully conveys a sense of rigidity of the shape, which is difficult in space-warp approaches. With a multiple-point input device, even beginners can easily move, rotate, and deform shapes at will.
Applications supporting navigation in large networks are used every days by millions of people. They include road map navigators, ight route visualization systems, and network visualization systems using node-link diagrams. These applications currently provide generic interaction methods for navigation: pan-and-zoom and sometimes bird's eye views.This article explores the idea of exploiting the connection information provided by the network to help navigate these large spaces. We visually augment two traditional navigation methods, and develop two special-purpose techniques. The first new technique, called "Link Sliding", provides guided panning when continuously dragging along a visible link. The second technique, called "Bring & Go", brings adjacent nodes nearby when pointing to a node. We compare the performance of these techniques in both an adjacency exploration task and a node revisiting task. This comparison illustrates the various advantages of content-aware network navigation techniques. A significant speed advantage is found for the Bring & Go technique over other methods.
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