Linqiao Zhang

A spectral-particle hybrid method for rendering falling snow

Falling snow has the visual property that it is simultaneously a set of discrete moving particles as well as a dynamic texture. To capture the dynamic texture properties of falling snow using particle systems can, however, require so many particles that it severely impacts rendering rates. Here we address this limitation by rendering the texture properties directly. We use a standard particle system to generate a relatively sparse set of falling snow flakes, and we then composite in a dynamic texture to fill in between the particles. The texture is generated using a novel image-based spectral synthesis method. The spectrum of the falling snow texture is defined by a dispersion relation in the image plane, derived from linear perspective. The dispersion relation relates image speed, image size, and particle depth. In the frequency domain, it relates the wavelength and speed of moving 2D image sinusoids. The parameters of this spectral snow can be varied both across the image and over time. This provides the flexibility to match the direction and speed parameters of the spectral snow to those of the falling particles. Camera motion can also be matched. Our method produces visually pleasing results at interactive rendering rates. We demonstrate our approach by adding snow effects to static and dynamic scenes. An extension for creating rain effects is also presented.

On the Size of the 3D Visibility Skeleton: Experimental Results

The 3D visibility skeleton is a data structure used to encode global visibility information about a set of objects. Previous theoretical results have shown that for kconvex polytopes with nedges in total, the worst case size complexity of this data structure is i¾?(n2k2) [Bronnimann et al. 07]; whereas for kuniformly distributed unit spheres, the expected size is i¾?(k) [Devillers et al. 03]. In this paper, we study the size of the visibility skeleton experimentally. Our results indicate that the size of the 3D visibility skeleton, in our setting, is

On the degree of standard geometric predicates for line transversals in 3D

C\,k\sqrt{n\,k}

ON THE EXPECTED SIZE OF THE 2D VISIBILITY COMPLEX

, where Cvaries with the scene density but remains small. This is the first experimentally determined asymptotic estimate of the size of the 3D visibility skeleton for reasonably large nand expressed in terms of both nand k. We suggest theoretical explanations for the experimental results we obtained. Our experiments also indicate that the running time of our implementation is O(n3/2klogk), while its worst-case running time complexity is O(n2k2logk).

Towards an implementation of the 3D visibility skeleton

In this paper we study various geometric predicates for determining the existence of and categorizing the configurations of lines in 3D that are transversal to lines or segments. We compute the degrees of standard procedures of evaluating these predicates. The degrees of some of these procedures are surprisingly high (up to 168), which may explain why computing line transversals with finite-precision floating-point arithmetic is prone to error. Our results suggest the need to explore alternatives to the standard methods of computing these quantities.

On the computation of 3D visibility skeletons

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the asymptotic expected number of free bitangents (which correspond to 0-faces of the visibility complex) among unit discs (or polygons of bounded aspect ratio and similar size) is linear and exhibit bounds in terms of the density of the objects. We also make an experimental assessment of the size of the visibility complex for disjoint random unit discs. We provide experimental estimates of the onset of the linear behavior and of the asymptotic slope and y-intercept of the number of free bitangents in terms of the density of discs. Finally, we analyze the quality of our estimates in terms of the density of discs.

A SUCCINCT 3D VISIBILITY SKELETON

In this note we describe the contents of a video illustrating analgorithm for computing the 3D visibility skeleton ofa set of disjoint convex polytopes. The video can be foundat http://www.cs.mcgill.ca/~lzhang15/video/ with file name socg07visidemo.mov.

Predicates for Line Transversals in 3D

The 3D visibility skeleton is a data structure that encodes the global visibility information of a set of 3D objects. While it is useful in answering global visibility queries, its large size often limits its practical use. In this paper, we address this issue by proposing a subset of the visibility skeleton, which is empirically about 25% to 50% of the whole set.We show that the rest of the data structure can be recovered from the subset as needed, partially or completely. The running time complexity, which we analyze in terms of output size, is efficient. We also prove that the subset is minimal in the sense that the complexity bound ceases to hold if the subset is restricted further.

Rendering Falling Snow Using an Inverse Fourier Transform

The 3D visibility skeleton is a data structure that encodes the global visibility information of a set of 3D objects. While it is useful in answering global visibility queries, its large size often limits its practical use. In this paper, we address this issue by proposing a subset of the visibility skeleton, which is empirically about 25% to 50% of the whole set. We show that the rest of the data structure can be recovered from the subset as needed, partially or completely. The running time complexity, which we analyze in terms of output size, is efficient. We also prove that the subset is minimal in the sense that the complexity bound ceases to hold if the subset is restricted further.