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Abstract This paper presents an experimental study on a novel mechanical surface treatment process, namely piezo vibration striking treatment (PVST), which is realized by a piezo stack vibration device installed on a computer numerical control (CNC) machine. Unlike other striking-based surface treatments, PVST employs non-resonant mode piezo vibration to induce controllable tool strikes on the workpiece surface. In this study, an experimental setup of PVST is implemented. Four types of experiments, i.e., tool-surface approaching, single-spot striking, one-dimensional (1D) scan striking, and 2D scan striking, are conducted to investigate the relationships among the striking force, tool vibration displacement, and surface deformation in PVST. The study shows that PVST can induce strikes with consistent intensity in each cycle of tool vibration. Both the striking intensity and striking location can be well controlled. Such process capability is particularly demonstrated by the resulting texture and roughness of the treated surfaces. Moreover, two linear force relationships have been found in PVST. The first linear relationship is between the striking force and the reduction in vibration amplitude during striking. The second one is between the striking force and the permanent indentation depth created by the strike. These linear force relationships offer the opportunity to realize real-timemore »monitoring and force-based feedback control of PVST. This study is the first step toward developing PVST as a more efficient deformation-based surface modification process.« less

This paper proposes a new way of designing and fabricating conformal flexible electronics on free-form surfaces, which can generate woven flexible electronics designs conforming to free-form 3D shapes with 2D printed electronic circuits. Utilizing our recently proposed foliation-based 3D weaving techniques, we can reap unprecedented advantages in conventional 2D electronic printing. The method is based on the foliation theory in differential geometry, which divides a surface into parallel leaves. Given a surface with circuit design, we first calculate a graph-value harmonic map and then create two sets of harmonic foliations perpendicular to each other. As the circuits are processed as the texture on the surface, they are separated and attached to each leaf. The warp and weft threads are then created and manually woven to reconstruct the surface and reconnect the circuits. Notably, The circuits are printed in 2D, which uniquely differentiates the proposed method from others. Compared with costly conformal 3D electronic printing methods requiring 5-axis CNC machines, our method is more reliable, more efficient, and economical. Moreover, the Harmonic foliation theory assures smoothness and orthogonality between every pair of woven yarns, which guarantees the precision of the flexible electronics woven on the surface. The proposed method provides anmore »alternative solution to the design and physical realization of surface electronic textiles for various applications, including wearable electronics, sheet metal craft, architectural designs, and smart woven-composite parts with conformal sensors in the automotive and aerospace industry. The performance of the proposed method is depicted using two examples.« less

Shape analysis has been playing an important role in early diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's diseases (AD). However, obtaining effective shape representations remains challenging. This paper proposes to use the Alexandrov polyhedra as surface-based shape signatures for cortical morphometry analysis. Given a closed genus-0 surface, its Alexandrov polyhedron is a convex representation that encodes its intrinsic geometry information. We propose to compute the polyhedra via a novel spherical optimal transport (OT) computation. In our experiments, we observe that the Alexandrov polyhedra of cortical surfaces between pathology-confirmed AD and cognitively unimpaired individuals are significantly different. Moreover, we propose a visualization method by comparing local geometry differences across cortical surfaces. We show that the proposed method is effective in pinpointing regional cortical structural changes impacted by AD.

Surface registration plays a fundamental role in shape analysis and geometric processing. Generally, there are three criteria in evaluating a surface mapping result: diffeomorphism, small distortion, and feature alignment. To fulfill these requirements, this work proposes a novel model of the space of point landmark constrained diffeomorphisms. Based on Teichm¨uller theory, this mapping space is generated by the Beltrami coefficients, which are infinitesimally Teichm¨uller equivalent to 0. These Beltrami coefficients are the solutions to a linear equation group. By using this theoretic model, optimal registrations can be achieved by iterative optimization with linear constraints in the diffeomorphism space, such as harmonic maps and Teichm¨uller maps, which minimize different types of distortion. The theoretical model is rigorous and has practical value. Our experimental results demonstrate the efficiency and efficacy of the proposed method.