The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the severe topological restrictions that NURBS impose. In order to move beyond these restrictions, we have recently introduced subdivision surfaces into our production environment. Subdivision surfaces are not new, but their use in high-end CG production has been limited.Here we describe a series of developments that were required in order for subdivision surfaces to meet the demands of high-end production. First, we devised a practical technique for constructing provably smooth variable-radius fillets and blends. Second, we developed methods for using subdivision surfaces in clothing simulation including a new algorithm for efficient collision detection. Third, we developed a method for constructing smooth scalar fields on subdivision surfaces, thereby enabling the use of a wider class of programmable shaders. These developments, which were used extensively in our recently completed short film Geri's game,ha v e become a highly valued feature of our production environment.

In this work, the aerodynamic performance of beetle wing in free-forward flight was explored by a three-dimensional computational fluid dynamics (CFDs) simulation with measured wing kinematics. It is shown from the CFD results that twist and camber variation, which represent the wing flexibility, are most important when determining the aerodynamic performance. Twisting wing significantly increased the mean lift and camber variation enhanced the mean thrust while the required power was lower than the case when neither was considered. Thus, in a comparison of the power economy among rigid, twisting and flexible models, the flexible model showed the best performance. When the positive effect of wing interaction was added to that of wing flexibility, we found that the elytron created enough lift to support its weight, and the total lift (48.4 mN) generated from the simulation exceeded the gravity force of the beetle (47.5 mN) during forward flight.

The Whitham equation is a nonlocal shallow water-wave model which combines the quadratic nonlinearity of the KdV equation with the linear dispersion of the full water wave problem. Whitham conjectured the existence of a highest, cusped, traveling-wave solution, and his conjecture was recently verified in the periodic case by Ehrnström and Wahlén. In the present paper we prove it for solitary waves. Like in the periodic case, the proof is based on global bifurcation theory but with several new challenges. In particular, the small-amplitude limit is singular and cannot be handled using regular bifurcation theory. Instead we use an approach based on a nonlocal version of the center manifold theorem. In the large-amplitude theory a new challenge is a possible loss of compactness, which we rule out using qualitative properties of the equation. The highest wave is found as a limit point of the global bifurcation curve.

We briefly summarized how to design and fabricate an insect-mimicking flapping-wing system and demonstrate how to implement inherent pitching stability for stable vertical takeoff. The effect of relative locations of the Center of Gravity (CG) and the mean Aerodynamic Center (AC) on vertical flight was theoretically examined through static force balance consideration. We conducted a series of vertical takeoff tests in which the location of the mean AC was determined using an unsteady Blade Element Theory (BET) previously developed by the authors. Sequential images were captured during the takeoff tests using a high-speed camera. The results demonstrated that inherent pitching stability for vertical takeoff can be achieved by controlling the relative position between the CG and the mean AC of the flapping system.

Detailed 3-Dimensional (3D) wing kinematics was experimentally presented in free flight of a beetle, Trypoxylus dichotomus, which has a pair of elytra (forewings) and flexible hind wings. The kinematic parameters such as the wing tip trajectory, angle of attack and camber deformation were obtained from a 3D reconstruction technique that involves the use of two synchronized high-speed cameras to digitize various points marked on the wings. Our data showed outstanding characteristics of deformation and flexibility of the beetle's hind wing compared with other measured insects, especially in the chordwise and spanwise directions during flapping motion. The hind wing produced 16% maximum positive camber deformation during the downstroke. It also experienced twisted shape showing large variation of the angle of attack from the root to the tip during the upstroke.