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.

Local illumination models try to describe the interaction between light and objects in the scene based on only few parameters representing some geometric and material properties at a given point on a surface. In this paper we present our research in local illumination models for the purpose of approximating light transport and shadow-masking effects in the local neighborhood of the surface point under evaluation. We assume that the amount of curvature at a surface point to some extent represents geometric properties in the surrounding neighborhood of this point. From this we define an empirical illumination model for diffuse reflecting materials which controls the amount of locally scattered light from the neighborhood as well as subsurface light transport based on some curvature metric.

The main idea presented herein is to use a multiscale texture synthesis approach in order to both colourize and upscale greyscale textures. Such textures can be vintage photos to be used in archaeological or urban 3D visualizations and obviously the colour needs to be reconstructed some way. Due to limited quality, walls etc in such 3D visualizations will appear either pixelized or blurry when the viewer approaches them on a close distance. The latter if some kind of interpolation technique is being used to reduce the pixelization. The low resolution greyscale texture and a high resolution coloured texture is used for the colourization and upscaling, which will produce a colour version of the greyscale texture with 4 times higher resolution in each upscale step. The novel idea is to use multiscale texture synthesis in HSV space for the first upscale in order to create a RGB colour image for subsequent upscaling, using either ordinary RGB multiscale texture synthesis or continue using HSV multiscale texture synthesis. These two main approaches will be compared and discussed.