High-quality tree structures modelling using local convolution surface approximation

In this paper, we propose a local convolution surface approximation approach for quickly modelling tree structures with pleasing visual effect. Using our proposed local convolution surface approximation, we present a tree modelling scheme to create the structure of a tree with a single high-quality quad-only mesh. Through combining the strengths of the convolution surfaces, subdivision surfaces and GPU, our tree modelling approach achieves high efficiency and good mesh quality. With our method, we first extract the line skeletons of given tree models by contracting the meshes with the Laplace operator. Then we approximate the original tree mesh with a convolution surface based on the extracted skeletons. Next, we tessellate the tree trunks represented by convolution surfaces into quad-only subdivision surfaces with good edge flow along the skeletal directions. We implement the most time-consuming subdivision and convolution approximation on the GPU with CUDA, and demonstrate applications of our proposed approach in branch editing and tree composition

Convolutions on digital surfaces: on the way iterated convolutions behave and preliminary results about curvature estimation

In [FoureyMalgouyres09] the authors present a generalized convolution operator for functions defined on digital surfaces. We provide here some extra material related to this notion. Some about the relative isotropy of the way a convolution kernel (or mask) grows when the convolution operator is iterated. We also provide preliminary results about a way to estimate curvatures on a digital surface, using the same convolution operator

Faceted anomalous scaling in the epitaxial growth of semiconductor films

We apply the generic dynamical scaling theory (GDST) to the surfaces of CdTe polycrystalline films grown in glass substrates. The analysed data were obtained with a stylus profiler with an estimated resolution lateral resolution of $l_c=0.3 \mu$m. Both real two-point correlation function and power spectrum analyses were done. We found that the GDST applied to the surface power spectra foresees faceted morphology in contrast with the self-affine surface indicated by the local roughness exponent found via the height-height correlation function. This inconsistency is explained in terms of convolution effects resulting from the finite size of the probe tip used to scan the surfaces. High resolution AFM images corroborates the predictions of GDST.Comment: to appear in Europhysics Letter

On the strong convolution singularity property

We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type has simple spectrum. We use these methods to give examples of smooth flows on closed orientable surfaces of genus at least 2 with a weaker property: each of their maximal spectral types $\sigma$ is such that the Gaussian system induced by $\sigma$ has simple spectrum on the so-called 3rd chaos (i.e. $V_\sigma^{\odot 3}$ has simple spectrum).Comment: revised version, 53 page