A Family of Barycentric Coordinates for Co‐Dimension 1 Manifolds with Simplicial Facets

We construct a family of barycentric coordinates for 2D shapes including non‐convex shapes, shapes with boundaries, and skeletons. Furthermore, we extend these coordinates to 3D and arbitrary dimension. Our approach modifies the construction of the Floater‐Hormann‐Kós family of barycentric coordinates for 2D convex shapes. We show why such coordinates are restricted to convex shapes and show how to modify these coordinates to extend to discrete manifolds of co‐dimension 1 whose boundaries are composed of simplicial facets. Our coordinates are well‐defined everywhere (no poles) and easy to evaluate. While our construction is widely applicable to many domains, we show several examples related to image and mesh deformation.     

Singularity-Free Frame Fields for Line Drawing Vectorization

State-of-the-art methods for line drawing vectorization rely on generated frame fields for robust direction disambiguation, with each of the two axes aligning to different intersecting curve tangents around junctions. However, a common source of topological error for such methods are frame field singularities. To remedy this, we introduce the first frame field optimization framework guaranteed to produce singularity-free fields aligned to a line drawing. We first perform a convex solve for a roughly-aligned orthogonal frame field (cross field), and then comb away its internal singularities with an optimal transport–based matching. The resulting topology of the field is strictly maintained with the machinery of discrete trivial connections in a final, non-convex optimization that allows non-orthogonality of the field, improving smoothness and tangent alignment. Our frame fields can serve as a drop-in replacement for frame field optimizations used in previous work, improving the quality of the final vectorizations.     

Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization

The combinatorial dual of a hex mesh induces a collection of mutually intersecting surfaces (dual sheets). Inspired by Campen et al.'s work on quad meshing [CBK12, CK14], we propose to directly generate such dual sheets so that, as long as the volume is properly partitioned by the dual sheets, we are guaranteed to arrive at a valid all‐hex mesh topology. Since automatically generating dual sheets seems much harder than the 2D counterpart, we chose to leave the task to the user; our system is equipped with a few simple 3D modeling tools for interactively designing dual sheets. Dual sheets are represented as implicit surfaces in our approach, greatly simplifying many of the computational steps such as finding intersections and analyzing topology. We also propose a simple algorithm for primalizing the dual graph where each dual cell, often enclosing singular edges, gets mapped onto a reference polyhedron via harmonic parameterization. Preservation of sharp features is simply achieved by modifying the boundary conditions. We demonstrate the feasibility of our approach through various modeling examples.     

Fast Catmull‐Rom Spline Interpolation for High‐Quality Texture Sampling

It is well known that cubic texture filtering can be efficiently implemented on the GPU by using a method published by Sigg and Hadwiger [ SH05 ], which simplifies the evaluation to a linear combination of linear texture fetches. However, their method cannot be directly applied if the filter kernel takes also negative values like the popular Catmull‐Rom spline, for example. In this paper, we propose a modified algorithm that is able to handle also the negative weights. Therefore, using our method, the Catmull‐Rom spline interpolation can also be evaluated in one, two, and three dimensions by taking two, four, and eight linear texture fetches, respectively.     

Elastic Correspondence between Triangle Meshes

We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes.     

Controllable Dendritic Crystal Simulation Using Orientation Field

Real world dendritic growths show charming structures by their exquisite balance between the symmetry and randomness in the crystal formation. Other than the variety in the natural crystals, richer visual appearance of crystals can benefit from artificially controlling of the crystal growth on its growing directions and shapes. In this paper, by introducing one extra dimension of freedom, i.e. the orientation field, into the simulation, we propose an efficient algorithm for dendritic crystal simulation that is able to reproduce arbitrary symmetry patterns with different levels of asymmetry breaking effect on general grids or meshes, including spreading on curved surfaces and growth in 3D. Flexible artistic control is also enabled in a unified manner by exploiting and guiding the orientation field in the visual simulation. We show the effectiveness of our approach by various demonstrations of simulation results.     

Sensor‐aware Normal Estimation for Point Clouds from 3D Range Scans

Normal vectors are essential for many point cloud operations, including segmentation, reconstruction and rendering. The robust estimation of normal vectors from 3D range scans is a challenging task due to undersampling and noise, specially when combining points sampled from multiple sensor locations. Our error model assumes a Gaussian distribution of the range error with spatially‐varying variances that depend on sensor distance and reflected intensity, mimicking the features of Lidar equipment. In this paper we study the impact of measurement errors on the covariance matrices of point neighborhoods. We show that covariance matrices of the true surface points can be estimated from those of the acquired points plus sensor‐dependent directional terms. We derive a lower bound on the neighbourhood size to guarantee that estimated matrix coefficients will be within a predefined error with a prescribed probability. This bound is key for achieving an optimal trade‐off between smoothness and fine detail preservation. We also propose and compare different strategies for handling neighborhoods with samples coming from multiple materials and sensors. We show analytically that our method provides better normal estimates than competing approaches in noise conditions similar to those found in Lidar equipment.     

Local Editing of Procedural Models

Procedural modeling is used across many industries for rapid 3D content creation. However, professional procedural tools often lack artistic control, requiring manual edits on baked results, diminishing the advantages of a procedural modeling pipeline. Previous approaches to enable local artistic control require special annotations of the procedural system and manual exploration of potential edit locations. Therefore, we propose a novel approach to discover meaningful and non‐redundant good edit locations (GELs). We introduce a bottom‐up algorithm for finding GELs directly from the attributes in procedural models, without special annotations. To make attribute edits at GELs persistent, we analyze their local spatial context and construct a meta‐locator to uniquely specify their structure. Meta‐locators are calculated independently per attribute, making them robust against changes in the procedural system. Functions on meta‐locators enable intuitive and robust multi‐selections. Finally, we introduce an algorithm to transfer meta‐locators to a different procedural model. We show that our approach greatly simplifies the exploration of the local edit space, and we demonstrate its usefulness in a user study and multiple real‐world examples.     

PointProNets: Consolidation of Point Clouds with Convolutional Neural Networks

With the widespread use of 3D acquisition devices, there is an increasing need of consolidating captured noisy and sparse point cloud data for accurate representation of the underlying structures. There are numerous algorithms that rely on a variety of assumptions such as local smoothness to tackle this ill‐posed problem. However, such priors lead to loss of important features and geometric detail. Instead, we propose a novel data‐driven approach for point cloud consolidation via a convolutional neural network based technique. Our method takes a sparse and noisy point cloud as input, and produces a dense point cloud accurately representing the underlying surface by resolving ambiguities in geometry. The resulting point set can then be used to reconstruct accurate manifold surfaces and estimate surface properties. To achieve this, we propose a generative neural network architecture that can input and output point clouds, unlocking a powerful set of tools from the deep learning literature. We use this architecture to apply convolutional neural networks to local patches of geometry for high quality and efficient point cloud consolidation. This results in significantly more accurate surfaces, as we illustrate with a diversity of examples and comparisons to the state‐of‐the‐art.     

Distribution Update of Deformable Patches for Texture Synthesis on the Free Surface of Fluids

We propose an approach for temporally coherent patch‐based texture synthesis on the free surface of fluids. Our approach is applied as a post‐process, using the surface and velocity field from any fluid simulator. We apply the texture from the exemplar through multiple local mesh patches fitted to the surface and mapped to the exemplar. Our patches are constructed from the fluid free surface by taking a subsection of the free surface mesh. As such, they are initially very well adapted to the fluid's surface, and can later deform according to the free surface velocity field, allowing a greater ability to represent surface motion than rigid or 2D grid‐based patches. From one frame to the next, the patch centers and surrounding patch vertices are advected according to the velocity field. We seek to maintain a Poisson disk distribution of patches, and following advection, the Poisson disk criterion determines where to add new patches and which patches should e flagged for removal. The removal considers the local number of patches: in regions containing too many patches, we accelerate the temporal removal. This reduces the number of patches while still meeting the Poisson disk criterion. Reducing areas with too many patches speeds up the computation and avoids patch‐blending artifacts. The final step of our approach creates the overall texture in an atlas where each texel is computed from the patches using a contrast‐preserving blending function. Our tests show that the approach works well on free surfaces undergoing significant deformation and topological changes. Furthermore, we show that our approach provides good results for many fluid simulation scenarios, and with many texture exemplars. We also confirm that the optical flow from the resulting texture matches the fluid velocity field. Overall, our approach compares favorably against recent work in this area.