A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier-Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed.
Interlocking puzzles are very challenging geometric problems with the fascinating property that once we solve one by putting together the puzzle pieces, the puzzle pieces interlock with one another, preventing the assembly from falling apart. Though interlocking puzzles have been known for hundreds of years, very little is known about the governing mechanics. Thus, designing new interlocking geometries is basically accomplished with extensive manual effort or expensive exhaustive search with computers.In this paper, we revisit the notion of interlocking in greater depth, and devise a formal method of the interlocking mechanics. From this, we can develop a constructive approach for devising new interlocking geometries that directly guarantees the validity of the interlocking instead of exhaustively testing it. In particular, we focus on an interesting subclass of interlocking puzzles that are recursive in the sense that the assembly of puzzle pieces can remain an interlocking puzzle also after sequential removal of pieces; there is only one specific sequence of assembling, or disassembling, such a puzzle. Our proposed method can allow efficient generation of recursive interlocking geometries of various complexities, and by further realizing it with LEGO bricks, we can enable the hand-built creation of custom puzzle games.
Commercial 3D scene acquisition systems such as the Microsoft Kinect sensor can reduce the cost barrier of realizing mid-air interaction. However, since it can only sense hand position but not hand orientation robustly, current mid-air interaction methods for 3D virtual object manipulation often require contextual and mode switching to perform translation, rotation, and scaling, thus preventing natural continuous gestural interactions. A novel handle bar metaphor is proposed as an effective visual control metaphor between the user's hand gestures and the corresponding virtual object manipulation operations. It mimics a familiar situation of handling objects that are skewered with a bimanual handle bar. The use of relative 3D motion of the two hands to design the mid-air interaction allows us to provide precise controllability despite the Kinect sensor's low image resolution. A comprehensive repertoire of 3D manipulation operations is proposed to manipulate single objects, perform fast constrained rotation, and pack/align multiple objects along a line. Three user studies were devised to demonstrate the efficacy and intuitiveness of the proposed interaction techniques on different virtual manipulation scenarios.
Figure 1: A large reciprocal frame (RF) AbstractA reciprocal frame (RF) is a self-supported three-dimensional structure made up of three or more sloping rods, which form a closed circuit, namely an RF-unit. Large RF-structures built as complex grillages of one or a few similar RF-units have an intrinsic beauty derived from their inherent self-similar and highly symmetric patterns. Designing RF-structures that span over large domains is an intricate and complex task. In this paper, we present an interactive computational tool for designing RF-structures over a 3D guiding surface, focusing on the aesthetic aspect of the design.There are three key contributions in this work. First, we draw an analogy between RF-structures and plane tiling with regular polygons, and develop a computational scheme to generate coherent RF-tessellations from simple grammar rules. Second, we employ a conformal mapping to lift the 2D tessellation over a 3D guiding surface, allowing a real-time preview and efficient exploration of wide ranges of RF design parameters. Third, we devise an optimization method to guarantee the collinearity of contact joints along each rod, while preserving the geometric properties of the RF-structure. Our tool not only supports the design of wide variety of RF pattern classes and their variations, but also allows preview and refinement through interactive controls.
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