In this paper we propose a method for the interactive detailed cutting of deformable thin sheets. Our method builds on the ability of frame-based simulation to solve for dynamics using very few control frames while embedding highly detailed geometry - here an adaptive mesh that accurately represents the cut boundaries. Our solution relies on a non-manifold grid to compute shape functions that faithfully adapt to the topological changes occurring while cutting. New frames are dynamically inserted to describe new regions. We provide incremental mechanisms for updating simulation data, enabling us to achieve interactive rates. We illustrate our method with examples inspired by the traditional Kirigami artform.

This work presents Sketch2Scene , a framework that automatically turns a freehand sketch drawing inferring multiple scene objects to semantically valid, well arranged scenes of 3D models. Unlike the existing works on sketch-based search and composition of 3D models, which typically process individual sketched objects one by one, our technique performs co-retrieval and co-placement of 3D relevant models by jointly processing the sketched objects. This is enabled by summarizing functional and spatial relationships among models in a large collection of 3D scenes as structural groups . Our technique greatly reduces the amount of user intervention needed for sketch-based modeling of 3D scenes and fits well into the traditional production pipeline involving concept design followed by 3D modeling. A pilot study indicates that it is promising to use our technique as an alternative but more efficient tool of standard 3D modeling for 3D scene construction.

We present a novel anisotropic Spherical Gaussian (ASG) function, built upon the Bingham distribution [Bingham 1974], which is much more effective and efficient in representing anisotropic spherical functions than Spherical Gaussians (SGs). In addition to retaining many desired properties of SGs, ASGs are also rotationally invariant and capable of representing all-frequency signals. To further strengthen the properties of ASGs, we have derived approximate closed-form solutions for their integral, product and convolution operators, whose errors are nearly negligible, as validated by quantitative analysis. Supported by all these operators, ASGs can be adapted in existing SG-based applications to enhance their scalability in handling anisotropic effects. To demonstrate the accuracy and efficiency of ASGs in practice, we have applied ASGs in two important SG-based rendering applications and the experimental results clearly reveal the merits of ASGs.