This paper describes a new method for contouring a signed grid whose edges are tagged by Hermite data (i.e; exact intersection points and normals). This method avoids the need to explicitly identify and process "features" as required in previous Hermite contouring methods. Using a new, numerically stable representation for quadratic error functions, we develop an octree-based method for simplifying contours produced by this method. We next extend our contouring method to these simpli£ed octrees. This new method imposes no constraints on the octree (such as being a restricted octree) and requires no "crack patching". We conclude with a simple tion.

Crucial transitions in cancer-including tumor initiation, local expansion, metastasis, and therapeutic resistance-involve complex interactions between cells within the dynamic tumor ecosystem. Transformative single-cell genomics technologies and spatial multiplex in situ methods now provide an opportunity to interrogate this complexity at unprecedented resolution. The Human Tumor Atlas Network (HTAN), part of the National Cancer Institute (NCI) Cancer Moonshot Initiative, will establish a clinical, experimental, computational, and organizational framework to generate informative and accessible three-dimensional atlases of cancer transitions for a diverse set of tumor types. This effort complements both ongoing efforts to map healthy organs and previous largescale cancer genomics approaches focused on bulk sequencing at a single point in time. Generating single-cell, multiparametric, longitudinal atlases and integrating them with clinical outcomes should help identify novel predictive biomarkers and features as well as therapeutically relevant cell types, cell states, and cellular interactions across transitions. The resulting tumor atlases should have a profound impact on our understanding of cancer biology and have the potential to improve cancer detection, prevention, and therapeutic discovery for better precision-medicine treatments of cancer patients and those at risk for cancer.Cancer forms and progresses through a series of critical transitions-from pre-malignant to malignant states, from locally contained to metastatic disease, and from treatment-responsive to treatment-resistant tumors (Figure 1). Although specifics differ across tumor types and patients, all transitions involve complex dynamic interactions between diverse pre-malignant, malignant, and non-malignant cells (e.g., stroma cells and immune cells), often organized in specific patterns within the tumor

a) (b) (c) (d) Figure 1: Original horse model with enclosing triangle control mesh shown in black (a). Several deformations generated using our 3D mean value coordinates applied to a modified control mesh (b,c,d). AbstractConstructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics.Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed polygons, mean value coordinates have been proven to be an excellent method for constructing such an interpolant. In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh P, we show that these coordinates are continuous everywhere and smooth on the interior of P. The coordinates are linear on the triangles of P and can reproduce linear functions on the interior of P. To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.

An increasing number of structural studies of large macromolecular complexes, both in X-ray crystallography and cryo-electron microscopy, have resulted in intermediate-resolution (5-10 A) density maps. Despite being limited in resolution, significant structural and functional information may be extractable from these maps. To aid in the analysis and annotation of these complexes, we have developed SSEhunter, a tool for the quantitative detection of alpha helices and beta sheets. Based on density skeletonization, local geometry calculations, and a template-based search, SSEhunter has been tested and validated on a variety of simulated and authentic subnanometer-resolution density maps. The result is a robust, user-friendly approach that allows users to quickly visualize, assess, and annotate intermediate-resolution density maps. Beyond secondary structure element identification, the skeletonization algorithm in SSEhunter provides secondary structure topology, which is potentially useful in leading to structural models of individual molecular components directly from the density.

Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics. Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed polygons, mean value coordinates have been proven to be an excellent method for constructing such an interpolant. In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh P , we show that these coordinates are continuous everywhere and smooth on the interior of P . The coordinates are linear on the triangles of P and can reproduce linear functions on the interior of P . To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.

We present a robust method for repairing arbitrary polygon models. The method is guaranteed to produce a closed surface that partitions the space into disjoint internal and external volumes. Given any model represented as a polygon soup, we construct an inside/outside volume using an octree grid, and reconstruct the surface by contouring. Our novel algorithm can efficiently process large models containing millions of polygons and is capable of reproducing sharp features in the original geometry.

The ability to quickly and intuitively edit digital contents has become increasingly important in our everyday life. We propose a novel method for propagating a sparse set of user edits (e.g., changes in color, brightness, contrast, etc.) expressed as casual strokes to nearby regions in an image or video with similar appearances. Existing methods for edit propagation are typically based on optimization, whose computational cost can be prohibitive for large inputs. We re-formulate propagation as a function interpolation problem in a high-dimensional space, which we solve very efficiently using radial basis functions. While simple to implement, our method significantly improves the speed and space cost of existing methods, and provides instant feedback of propagation results even on large images and videos.

We present a robust method for repairing arbitrary polygon models. The method is guaranteed to produce a closed surface that partitions the space into disjoint internal and external volumes. Given any model represented as a polygon soup, we construct an inside/outside volume using an octree grid, and reconstruct the surface by contouring. Our novel algorithm can efficiently process large models containing millions of polygons and is capable of reproducing sharp features in the original geometry.