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.     

Polycube Shape Space

There are many methods proposed for generating polycube polyhedrons, but it lacks the study about the possibility of generating polycube polyhedrons. In this paper, we prove a theorem for characterizing the necessary condition for the skeleton graph of a polycube polyhedron, by which Steinitz's theorem for convex polyhedra and Eppstein's theorem for simple orthogonal polyhedra are generalized to polycube polyhedra of any genus and with non‐simply connected faces. Based on our theorem, we present a faster linear algorithm to determine the dimensions of the polycube shape space for a valid graph, for all its possible polycube polyhedrons. We also propose a quadratic optimization method to generate embedding polycube polyhedrons with interactive assistance. Finally, we provide a graph‐based framework for polycube mesh generation, quadrangulation, and all‐hex meshing to demonstrate the utility and applicability of our approach.     

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.     

Hierarchical Functional Maps between Subdivision Surfaces

We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multi‐resolution spectral basis functions that are open used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high‐resolution sculpting displacement maps and textures between subdivision models.     

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.     

Global Texture Mapping for Dynamic Objects

We propose a novel framework to generate a global texture atlas for a deforming geometry. Our approach distinguishes from prior arts in two aspects. First, instead of generating a texture map for each timestamp to color a dynamic scene, our framework reconstructs a global texture atlas that can be consistently mapped to a deforming object. Second, our approach is based on a single RGB‐D camera, without the need of a multiple‐camera setup surrounding a scene. In our framework, the input is a 3D template model with an RGB‐D image sequence, and geometric warping fields are found using a state‐of‐the‐art non‐rigid registration method [GXW*15] to align the template mesh to noisy and incomplete input depth images. With these warping fields, our multi‐scale approach for texture coordinate optimization generates a sharp and clear texture atlas that is consistent with multiple color observations over time. Our approach is accelerated by graphical hardware and provides a handy configuration to capture a dynamic geometry along with a clean texture atlas. We demonstrate our approach with practical scenarios, particularly human performance capture. We also show that our approach is resilient on misalignment issues caused by imperfect estimation of warping fields and inaccurate camera parameters.     

A CNN‐based Flow Correction Method for Fast Preview

Eulerian‐based smoke simulations are sensitive to the initial parameters and grid resolutions. Due to the numerical dissipation on different levels of the grid and the nonlinearity of the governing equations, the differences in simulation resolutions will result in different results. This makes it challenging for artists to preview the animation results based on low‐resolution simulations. In this paper, we propose a learning‐based flow correction method for fast previewing based on low‐resolution smoke simulations. The main components of our approach lie in a deep convolutional neural network, a grid‐layer feature vector and a special loss function. We provide a novel matching model to represent the relationship between low‐resolution and high‐resolution smoke simulations and correct the overall shape of a low‐resolution simulation to closely follow the shape of a high‐resolution down‐sampled version. We introduce the grid‐layer concept to effectively represent the 3D fluid shape, which can also reduce the input and output dimensions. We design a special loss function for the fluid divergence‐free constraint in the neural network training process. We have demonstrated the efficacy and the generality of our approach by simulating a diversity of animations deviating from the original training set. In addition, we have integrated our approach into an existing fluid simulation framework to showcase its wide applications.     

Distortion‐Free Displacement Mapping

Displacement mapping is routinely used to add geometric details in a fast and easy‐to‐control way, both in offline rendering as well as recently in interactive applications such as games. However, it went largely unnoticed (with the exception of McGuire and Whitson [MW08]) that, when applying displacement mapping to a surface with a low‐distortion parametrization, this parametrization is distorted as the geometry was changed by the displacement mapping. Typical resulting artifacts are “rubber band”‐like distortion patterns in areas of strong displacement change where a small isotropic area in texture space is mapped to a large anisotropic area in world space. We describe a fast, fully GPU‐based two‐step procedure to resolve this problem. First, a correction deformation is computed from the displacement map. Second, two variants to apply this correction when computing displacement mapping are proposed. The first variant is backward‐compatible and can resolve the artifact in any rendering pipeline without modifying it and without requiring additional computation at render time, but only works for bijective parametrizations. The second variant works for more general parametrizations, but requires to modify the rendering code and incurs a very small computational overhead.     

Fast and Robust QEF Minimization using Probabilistic Quadrics

Error quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad-hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting (“probabilistic quadrics”) where the optimal point minimizes the expected squared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system — 50× faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop-in replacement which we demonstrate with mesh smoothing via filtered quadrics and non-linear subdivision surfaces.     

Exact Constraint Satisfaction for Truly Seamless Parametrization

In the field of global surface parametrization a recent focus has been on so‐called seamless parametrization. This term refers to parametrization approaches which, while using an atlas of charts to enable the handling of surfaces of arbitrary topology, relate the parametrization across the cuts between charts via transition functions from special classes of transformations. This effectively makes the cuts invisible to applications which are invariant to these specific transformations in some sense. In actual implementations of these parametrization approaches, however, these restrictions are obeyed only approximately; errors stem from the tolerances of numerical solvers employed and, ultimately, from the limited accuracy of floating point arithmetic. In practice, robustness issues arise from these flaws in the seamlessness of a parametrization, no matter how small. We present a robust global algorithm that turns a given approximately seamless parametrization into an exactly seamless one ‐ that still is representable by standard floating point numbers. It supports common practically relevant additional constraints regarding boundary and feature curve alignment or isocurve connectivity, and ensures that these are likewise fulfilled exactly. This allows subsequent algorithms to operate robustly on the resulting truly seamless parametrization. We believe that the core of our method will furthermore be of benefit in a broader range of applications involving linearly constrained numerical optimization.     

Object Partitioning for Support‐Free 3D‐Printing

Fused deposition modeling based 3D‐printing is becoming increasingly popular due to it's low‐cost and simple operation and maintenance. While it produces rugged prints made from a wide range of materials, it suffers from an inherent printing limitation where it cannot produce overhanging surfaces of non‐trivial size. This limitation can be handled by constructing temporary support‐structures, however this solution involves additional material costs, longer print time, and often a fair amount of labor in removing it. In this paper we present a new method for partitioning general solid objects into a small number of parts that can be printed with no support. The partitioning is computed by applying a sequence of cutting‐planes that split the object recursively. Unlike existing algorithms, the planes are not chosen at random, rather they are derived from shape analysis routines that identify and resolve various commonly‐found geometric configurations. In addition, we guide this search by a revised set of conditions that both ensure the objects' printability as well as realistically model the printing capabilities of the printer at hand. Evaluation of the new method demonstrates its ability to efficiently obtain support‐free partitionings typically containing fewer parts compared to existing methods that rely on support‐structures.     

Repairing Inconsistent Curve Networks on Non‐parallel Cross‐sections

In this work we present the first algorithm for restoring consistency between curve networks on non‐parallel cross‐sections. Our method addresses a critical but overlooked challenge in the reconstruction process from cross‐sections that stems from the fact that cross‐sectional slices are often generated independently of one another, such as in interactive volume segmentation. As a result, the curve networks on two non‐parallel slices may disagree where the slices intersect, which makes these cross‐sections an invalid input for surfacing. We propose a method that takes as input an arbitrary number of non‐parallel slices, each partitioned into two or more labels by a curve network, and outputs a modified set of curve networks on these slices that are guaranteed to be consistent. We formulate the task of restoring consistency while preserving the shape of input curves as a constrained optimization problem, and we propose an effective solution framework. We demonstrate our method on a data‐set of complex multi‐labeled input cross‐sections. Our technique efficiently produces consistent curve networks even in the presence of large errors.     

Fast Corotated FEM using Operator Splitting

In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss‐Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements.     

Efficient Caustic Rendering with Lightweight Photon Mapping

Robust and efficient rendering of complex lighting effects, such as caustics, remains a challenging task. While algorithms like vertex connection and merging can render such effects robustly, their significant overhead over a simple path tracer is not always justified and – as we show in this paper ‐ also not necessary. In current rendering solutions, caustics often require the user to enable a specialized algorithm, usually a photon mapper, and hand‐tune its parameters. But even with carefully chosen parameters, photon mapping may still trace many photons that the path tracer could sample well enough, or, even worse, that are not visible at all. Our goal is robust, yet lightweight, caustics rendering. To that end, we propose a technique to identify and focus computation on the photon paths that offer significant variance reduction over samples from a path tracer. We apply this technique in a rendering solution combining path tracing and photon mapping. The photon emission is automatically guided towards regions where the photons are useful, i.e., provide substantial variance reduction for the currently rendered image. Our method achieves better photon densities with fewer light paths (and thus photons) than emission guiding approaches based on visual importance. In addition, we automatically determine an appropriate number of photons for a given scene, and the algorithm gracefully degenerates to pure path tracing for scenes that do not benefit from photon mapping.     

Practical Foldover‐Free Volumetric Mapping Construction

In this paper, we present a practically robust method for computing foldover‐free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non‐trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high‐quality foldover‐free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh‐based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.     

A Temporally Adaptive Material Point Method with Regional Time Stepping

Spatially and temporally adaptive algorithms can substantially improve the computational efficiency of many numerical schemes in computational mechanics and physics‐based animation. Recently, a crucial need for temporal adaptivity in the Material Point Method (MPM) is emerging due to the potentially substantial variation of material stiffness and velocities in multi‐material scenes. In this work, we propose a novel temporally adaptive symplectic Euler scheme for MPM with regional time stepping (RTS), where different time steps are used in different regions. We design a time stepping scheduler operating at the granularity of small blocks to maintain a natural consistency with the hybrid particle/grid nature of MPM. Our method utilizes the Sparse Paged Grid (SPGrid) data structure and simultaneously offers high efficiency and notable ease of implementation with a practical multi‐threaded particle‐grid transfer strategy. We demonstrate the efficacy of our asynchronous MPM method on various examples including elastic objects, granular media, and fluids.     

A Stationary SVBRDF Material Modeling Method Based on Discrete Microsurface

Microfacet theory is commonly used to build reflectance models for surfaces. While traditional microfacet‐based models assume that the distribution of a surface's microstructure is continuous, recent studies indicate that some surfaces with tiny, discrete and stochastic facets exhibit glittering visual effects, while some surfaces with structured features exhibit anisotropic specular reflection. Accordingly, this paper proposes an efficient and stationary method of surface material modeling to process both glittery and non‐glittery surfaces in a consistent way. Our method comprises two steps: in the preprocessing step, we take a fixed‐size sample normal map as input, then organize 4D microfacet trees in position and normal space for arbitrary‐sized surfaces; we also cluster microfacets into 4D K‐lobes via the adaptive k‐means method. In the rendering step, moreover, surface normals can be efficiently evaluated using pre‐clustered microfacets. Our method is able to efficiently render any structured, discrete and continuous micro‐surfaces using a precisely reconstructed surface NDF. Our method is both faster and uses less memory compared to the state‐of‐the‐art glittery surface modeling works.     

Generating 3D Faces using Multi‐column Graph Convolutional Networks

In this work, we introduce multi‐column graph convolutional networks (MGCNs), a deep generative model for 3D mesh surfaces that effectively learns a non‐linear facial representation. We perform spectral decomposition of meshes and apply convolutions directly in the frequency domain. Our network architecture involves multiple columns of graph convolutional networks (GCNs), namely large GCN (L‐GCN), medium GCN (M‐GCN) and small GCN (S‐GCN), with different filter sizes to extract features at different scales. L‐GCN is more useful to extract large‐scale features, whereas S‐GCN is effective for extracting subtle and fine‐grained features, and M‐GCN captures information in between. Therefore, to obtain a high‐quality representation, we propose a selective fusion method that adaptively integrates these three kinds of information. Spatially non‐local relationships are also exploited through a self‐attention mechanism to further improve the representation ability in the latent vector space. Through extensive experiments, we demonstrate the superiority of our end‐to‐end framework in improving the accuracy of 3D face reconstruction. Moreover, with the help of variational inference, our model has excellent generating ability.     

Fast Penetration Volume for Rigid Bodies

Handling collisions among a large number of bodies can be a performance bottleneck in video games and many other real‐time applications. We present a new framework for detecting and resolving collisions using the penetration volume as an interpenetration measure. Given two non‐convex polyhedral bodies, a new sampling paradigm locates their near‐contact configurations in advance, and stores associated contact information in a compact database. At runtime, we retrieve a given configuration's nearest neighbors. By taking advantage of the penetration volume's continuity, cheap geometric methods can use the neighbors to estimate contact information as well as a translational gradient. This results in an extremely fast, geometry‐independent, and trivially parallelizable computation, which constitutes the first global volume‐based collision resolution. When processing multiple collisions simultaneously on a 4‐core processor, the average running cost is as low as 5 μs. Furthermore, no additional proximity or contact‐regions queries are required. These results are orders of magnitude faster than previous penetration volume approaches.     

A Composite BRDF Model for Hazy Gloss

We introduce a bidirectional reflectance distribution function (BRDF) model for the rendering of materials that exhibit hazy reflections, whereby the specular reflections appear to be flanked by a surrounding halo. The focus of this work is on artistic control and ease of implementation for real‐time and off‐line rendering. We propose relying on a composite material based on a pair of arbitrary BRDF models; however, instead of controlling their physical parameters, we expose perceptual parameters inspired by visual experiments [ VBF17 ]. Our main contribution then consists in a mapping from perceptual to physical parameters that ensures the resulting composite BRDF is valid in terms of reciprocity, positivity and energy conservation. The immediate benefit of our approach is to provide direct artistic control over both the intensity and extent of the haze effect, which is not only necessary for editing purposes, but also essential to vary haziness spatially over an object surface. Our solution is also simple to implement as it requires no new importance sampling strategy and relies on existing BRDF models. Such a simplicity is key to approximating the method for the editing of hazy gloss in real‐time and for compositing.