The exact shape of intracranial aneurysms is critical in medical diagnosis and surgical planning. While voxel-based deep learning frameworks have been proposed for this segmentation task, their performance remains limited. In this study, we offer a two-step surface-based deep learning pipeline that achieves significantly better results. Our proposed model takes a surface model of an entire set of principal brain arteries containing aneurysms as input and returns aneurysm surfaces as output. A user first generates a surface model by manually specifying multiple thresholds for time-of-flight magnetic resonance angiography images. The system then samples small surface fragments from the entire set of brain arteries and classifies the surface fragments according to whether aneurysms are present using a point-based deep learning network (PointNet++). Finally, the system applies surface segmentation (SO-Net) to surface fragments containing aneurysms. We conduct a direct comparison of the segmentation performance of our proposed surface-based framework and an existing voxel-based method by counting voxels: our framework achieves a much higher Dice similarity ( $72\%$) than the prior approach ( $46\%$).

We introduce a new advection scheme for fluid animation. Our main contribution is the use of long-term temporal changes in pressure to extend the commonly used semi-Lagrangian scheme further back along the time axis. Our algorithm starts by tracing sample points along a trajectory following the velocity field backwards in time for many steps. During this backtracing process, the pressure gradient along the path is integrated to correct the velocity of the current time step. We show that our method effectively suppresses numerical diffusion, retains small-scale vorticity, and provides better long-term kinetic energy preservation.

Iris folding is an art-form consisting of layered strips of paper, forming a spiral pattern behind an aperture, which can be used to make cards and gift tags. This paper describes an interactive computational tool to assist in the design and construction of original iris folding patterns. The design of iris folding patterns is formulated as the calculation of a circumscribed polygonal sequence around a seed polygon. While it is possible to compute the positions of vertices analytically for a regular polygon, it is not straightforward to do so for irregular polygons. We give a numerical method for irregular polygons, which can be applied to arbitrary convex seed polygons. The user can quickly experiment with various patterns using the system prior to constructing the art-form.