Siqi Wang
Courant Institute of Mathematical Sciences, New York University

Bézier Spline Simplification Using Locally Integrated Error
New York University & Adobe Research, advised by Alec Jacobson, Daniele Panozzo and Denis Zorin

Inspired by surface mesh simplification methods, we present a technique for reducing the number of Bézier curves in a vector graphics while maintaining high fidelity. We propose a curve-to-curve distance metric to repeatedly conduct local segment removal operations. By construction, we identify all possible lossless removal operations ensuring the smallest possible zero-error representation of a given design. Subsequent lossy operations are computed via local Gauss-Newton optimization and processed in a priority queue. We tested our method on the OpenClipArts dataset of 20,000 real-world vector graphics images and show significant improvements over representative previous methods. The generality of our method allows us to show results for curves with varying thickness and for vector graphics animations.

Appearance-Preserving Tactile Optimization
New York University, advised by Denis Zorin

Textures are encountered often on various common objects and surfaces. Many textures combine visual and tactile aspects, each serving important purposes; most obviously, a texture alters the object's appearance or tactile feeling as well as serving for visual or tactile identification and improving usability. The tactile feel and visual appearance of objects are often linked, but they may interact in unpredictable ways. Advances in high-resolution 3D printing enable highly flexible control of geometry to permit manipulation of both visual appearance and tactile properties. In this paper, we propose an optimization method to independently control the tactile properties and visual appearance of a texture. Our optimization is enabled by neural network-based models, and allows the creation of textures with a desired tactile feeling while preserving a desired visual appearance at a relatively low computational cost, for use in a variety of applications.

An Adaptive Staggered-Tilted Grid for Incompressible Flow Simulation
Dartmouth College & SJTU, advised by Bo Zhu and Xubo Yang

Enabling adaptivity on a uniform Cartesian grid is challenging due to its highly structured grid cells and axis-aligned grid lines. In this paper, we propose a new grid structure -- the adaptive staggered-tilted (AST) grid -- to conduct adaptive fluid simulations on a regular discretization. The key mechanics underpinning our new grid structure is to allow the emergence of a new set of tilted grid cells from the nodal positions on a background uniform grid. The original axis-aligned cells, in conjunction with the populated axis-tilted cells, jointly function as the geometric primitives to enable adaptivity on a regular spatial discretization. By controlling the states of the tilted cells both temporally and spatially, we can dynamically evolve the adaptive discretizations on an Eulerian domain. Our grid structure preserves almost all the computational merits of a uniform Cartesian grid, including the cache-coherent data layout, the easiness for parallelization, and the existence of high-performance numerical solvers. Further, our grid structure can be integrated into other adaptive grid structures, such as an Octree or a sparsely populated grid, to accommodate the T-junction-free hierarchy. We demonstrate the efficacy of our AST grid by showing examples of large-scale incompressible flow simulation in domains with irregular boundaries.

Reconstructing Human Joint Motion with Computational Fabrics
Dartmouth College, advised by Xia Zhou

This work studies the use of everyday fabrics as a flexible and soft sensing medium to monitor joint angular motion accurately and reliably. Specifically we focus on the primary use of conductive stretchable fabrics to sense the skin deformation during joint motion and infer the joint rotational angle. We tackle challenges of fabric sensing originated by the inherent properties of elastic materials by leveraging two types of sensing fabric and characterizing their properties based on models in material science. We apply models from bio-mechanics to infer joint angles and propose the use of dual strain sensing to enhance sensing robustness against user diversity and fabric position offsets. We fabricate prototypes using off-the-shelf fabrics and micro-controller. Experiments with ten participants show 9.69° mean angular error in tracking joint angle and its sensing robustness across users and activities.