John C. Bowers

Parallel Poisson disk sampling with spectrum analysis on surfaces

The ability to place surface samples with Poisson disk distribution can benefit a variety of graphics applications. Such a distribution satisfies the blue noise property, i.e. lack of low frequency noise and structural bias in the Fourier power spectrum. While many techniques are available for sampling the plane, challenges remain for sampling arbitrary surfaces. In this paper, we present new methods for Poisson disk sampling with spectrum analysis on arbitrary manifold surfaces. Our first contribution is a parallel dart throwing algorithm that generates high-quality surface samples at interactive rates. It is flexible and can be extended to adaptive sampling given a user-specified radius field. Our second contribution is a new method for analyzing the spectral quality of surface samples. Using the spectral mesh basis derived from the discrete mesh Laplacian operator, we extend standard concepts in power spectrum analysis such as radial means and anisotropy to arbitrary manifold surfaces. This provides a way to directly evaluate the spectral distribution quality of surface samples without requiring mesh parameterization. Finally, we implement our Poisson disk sampling algorithm on the GPU, and demonstrate practical applications involving interactive sampling and texturing on arbitrary surfaces.

A ray tracing approach to diffusion curves

Diffusion curves [ OBW*08 ] provide a flexible tool to create smooth‐shaded images from curves defined with colors. The resulting image is typically computed by solving a Poisson equation that diffuses the curve colors to the interior of the image. In this paper we present a new method for solving diffusion curves by using ray tracing. Our approach is analogous to final gathering in global illumination, where the curves define source radiance whose visible contribution will be integrated at a shading pixel to produce a color using stochastic ray tracing. Compared to previous work, the main benefit of our method is that it provides artists with extended flexibility in achieving desired image effects. Specifically, we introduce generalized curve colors called shaders that allow for the seamless integration of diffusion curves with classic 2D graphics including vector graphics (e.g. gradient fills) and raster graphics (e.g. patterns and textures). We also introduce several extended curve attributes to customize the contribution of each curve. In addition, our method allows any pixel in the image to be independently evaluated, without having to solve the entire image globally (as required by a Poisson‐based approach). Finally, we present a GPU‐based implementation that generates solution images at interactive rates, enabling dynamic curve editing. Results show that our method can easily produce a variety of desirable image effects.

Shape of Elastic Strings in Euclidean Space

We construct a 1-parameter family of geodesic shape metrics on a space of closed parametric curves in Euclidean space of any dimension. The curves are modeled on homogeneous elastic strings whose elasticity properties are described in terms of their tension and rigidity coefficients. As we change the elasticity properties, we obtain the various elastic models. The metrics are invariant under reparametrizations of the curves and induce metrics on shape space. Analysis of the geometry of the space of elastic strings and path spaces of elastic curves enables us to develop a computational model and algorithms for the estimation of geodesics and geodesic distances based on energy minimization. We also investigate a curve registration procedure that is employed in the estimation of shape distances and can be used as a general method for matching the geometric features of a family of curves. Several examples of geodesics are given and experiments are carried out to demonstrate the discriminative quality of the elastic metrics.

Managing Reproducible Computational Experiments with Curated Proteins in KINARI-2

KINARI-2 is the second release of the web server KINARI-Web for rigidity and flexibility of biomolecules. Besides incorporating new web technologies and making substantially improved tools available to the user, KINARI-2 is designed to automatically ensure the reproducibility of its computational experiments. It is also designed to facilitate incorporating third-party software into computational pipelines and to simplify the process of large scale validation of its underlying model through comprehensive comparisons with other competing coarse-grained models. In this paper we describe the underlying architecture of the new system, as it pertains to experiment management and reproducibility.

Modeling Brain Anatomy with 3D Arrangements of Curves

We employ 3D arrangements of curves to represent and analyze biological shapes, in particular, the anatomy of the human brain. The arrangements of curves may vary from fairly sparse - such as a collection of sulcal lines that coarsely approximates the global shape of the brain - to very dense decompositions of the cortical surface into space curves. A space of shapes of such arrangements is constructed equipped with geodesic metrics that can be used in conjunction with curve registration techniques to quantify shape resemblance or dissimilarity, as well as to identify the regions where anatomical differences are most pronounced. The metric is applied to the panellation and labeling of configurations associated with the left and right hemispheres of the brain. Examples are also given of geodesic interpolations between decompositions into space curves of surfaces representing the entire left hemisphere of the brain.

Lang's Universal molecule algorithm

Robert Lang’s Universal Molecule algorithm, a landmark in modern computational origami, is the main component of his widely used TreeMaker program for origami design. It computes a crease pattern of a convex polygonal region, starting with a compatible metric tree. Although it has been informally described in several publications, neither the full power nor the inherent limitations of the method are well understood. In this paper we introduce a rigorous mathematical formalism to relate the input metric tree, the output crease pattern and the folded uniaxial origami base produced by the Universal Molecule algorithm. We characterize the family of tree-like 3D shapes that are foldable from the computed crease patterns and give a correctness proof of the algorithm.

Rigidity of Origami Universal Molecules

In a seminal paper from 1996 that marks the beginning of computational origami, R. Lang introduced TreeMaker, a method for designing origami crease patterns with an underlying metric tree structure. In this paper we address the foldability of paneled origamis produced by Lang’s Universal Molecule algorithm, a key component of TreeMaker.

Ma–Schlenker c-Octahedra in the 2-Sphere

We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in~\cite{Ma:2012hl} of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary constructions use only the inversive geometry of the

Geodesic Universal Molecules

2

A framework for tool path optimization in fused filament fabrication

-sphere.