One problem in the field of computational geometry is the triangulation of convex layers. The rotating caliper algorithm is an alternative to the constrained Delaunay triangulation method. We present an improved triangulation algorithm, which gives a mesh quality close to that of the Constrained Delaunay but substantially faster. Each layer will be connected to the neighboring layer by edges and from the two vertices constituting an edge the proposed algorithm will select the shortest diagonal to its next neighbors in the polygonal chain on the other side, i.e. from the outer layer to the inner layer or vice versa. We discuss quality issues regarding the rotating caliper method and some improvements to it, as well as how a Constrained Delaunay can be efficiently implemented for convex layers.

3D reconstruction from visual hulls is a well established technique for camera based reconstruction of 3D objects in computer graphics. We propose in this paper to employ visual hull techniques to quantify the volume of diffusely defined gaseous structures. In our evaluation, visual quality of the 3D reconstructions is secondary. Instead, using synthetic ground truth data, we determine the number of independent silhouette images needed to achieve a stable volume estimate. We also estimate the influence of different segmentation results of the silhouette images on final volume estimates. Our results show that comparably few camera views yield to convergent volume estimates. For the type of 3D data studied, visual hull reconstructions overestimate actual volumes with about 50%. This proportion seems to be consistent for different data sets tested and may serve for re-calibration of volume estimation of gaseous structures.