Digital watermarking is widely used for copyright protection. Traditional 3D watermarking approaches or commercial software are typically designed to embed messages into 3D meshes, and later retrieve the messages directly from distorted/undistorted watermarked 3D meshes. However, in many cases, users only have access to rendered 2D images instead of 3D meshes. Unfortunately, retrieving messages from 2D renderings of 3D meshes is still challenging and underexplored. We introduce a novel end-to-end learning framework to solve this problem through: 1) an encoder to covertly embed messages in both mesh geometry and textures; 2) a differentiable renderer to render watermarked 3D objects from different camera angles and under varied lighting conditions; 3) a decoder to recover the messages from 2D rendered images. From our experiments, we show that our model can learn to embed information visually imperceptible to humans, and to retrieve the embedded information from 2D renderings that undergo 3D distortions. In addition, we demonstrate that our method can also work with other renderers, such as ray tracers and real-time renderers with and without fine-tuning.

Abstract In this work we detail a method that leverages the two color heads of recent low‐end fused deposition modeling (FDM) 3D printers to produce continuous tone imagery. The challenge behind producing such two‐tone imagery is how to finely interleave the two colors while minimizing the switching between print heads, making each color printed span as long and continuous as possible to avoid artifacts associated with printing short segments. The key insight behind our work is that by applying small geometric offsets, tone can be varied without the need to switch color print heads within a single layer. We can now effectively print (two‐tone) texture mapped models capturing both geometric and color information in our output 3D prints.

Abstract Procedural tree models have been popular in computer graphics for their ability to generate a variety of output trees from a set of input parameters and to simulate plant interaction with the environment for a realistic placement of trees in virtual scenes. However, defining such models and their parameters is a difficult task. We propose an inverse modelling approach for stochastic trees that takes polygonal tree models as input and estimates the parameters of a procedural model so that it produces trees similar to the input. Our framework is based on a novel parametric model for tree generation and uses Monte Carlo Markov Chains to find the optimal set of parameters. We demonstrate our approach on a variety of input models obtained from different sources, such as interactive modelling systems, reconstructed scans of real trees and developmental models.

Abstract We propose an optimization framework for 3D printing that seeks to save printing time and the support material required to print 3D shapes. Three‐dimensional printing technology is rapidly maturing and may revolutionize how we manufacture objects. The total cost of printing, however, is governed by numerous factors which include not only the price of the printer but also the amount of material and time to fabricate the shape. Our PackMerger framework converts the input 3D watertight mesh into a shell by hollowing its inner parts. The shell is then divided into segments. The location of splits is controlled based on several parameters, including the size of the connection areas or volume of each segment. The pieces are then tightly packed using optimization. The optimization attempts to minimize the amount of support material and the bounding box volume of the packed segments while keeping the number of segments minimal. The final packed configuration can be printed with substantial time and material savings, while also allowing printing of objects that would not fit into the printer volume. We have tested our system on three different printers and it shows a reduction of 5–30% of the printing time while simultaneously saving 15–65% of the support material. The optimization time was approximately 1 min. Once the segments are printed, they need to be assembled.

We present a dynamic tree modeling and representation technique that allows complex tree models to interact with their environment. Our method uses changes in the light distribution and proximity to solid obstacles and other trees as approximations of biologically motivated transformations on a skeletal representation of the tree's main branches and its procedurally generated foliage. Parts of the tree are transformed only when required, thus our approach is much faster than common algorithms such as Open L-Systems or space colonization methods. Input is a skeleton-based tree geometry that can be computed from common tree production systems or from reconstructed laser scanning models. Our approach enables content creators to directly interact with trees and to create visually convincing ecosystems interactively. We present different interaction types and evaluate our method by comparing our transformations to biologically based growth simulation techniques.

The use of 3D printing has rapidly expanded in the past couple of years. It is now possible to produce 3D-printed objects with exceptionally high fidelity and precision. However, although the quality of 3D printing has improved, both the time to print and the material costs have remained high. Moreover, there is no guarantee that a printed model is structurally sound. The printed product often does not survive cleaning, transportation, or handling, or it may even collapse under its own weight. We present a system that addresses this issue by providing automatic detection and correction of the problematic cases. The structural problems are detected by combining a lightweight structural analysis solver with 3D medial axis approximations. After areas with high structural stress are found, the model is corrected by combining three approaches: hollowing, thickening, and strut insertion. Both detection and correction steps are repeated until the problems have been eliminated. Our process is designed to create a model that is visually similar to the original model but possessing greater structural integrity.

Abstract Procedural methods present one of the most powerful techniques for authoring a vast variety of computer graphics models. However, their massive applicability is hindered by the lack of control and a low predictability of the results. In the classical procedural modeling pipeline, the user usually defines a set of rules, executes the procedural system, and by examining the results attempts to infer what should be changed in the system definition in order to achieve the desired output. We present guided procedural modeling, a new approach that allows a high level of top‐down control by breaking the system into smaller building blocks that communicate. In our work we generalize the concept of the environment. The user creates a set of guides. Each guide defines a region in which a specific procedural model operates. These guides are connected by a set of links that serve for message passing between the procedural models attached to each guide. The entire model consists of a set of guides with procedural models, a graph representing their connection, and the method in which the guides interact. The modeling process is performed by modifying each of the described elements. The user can control the high‐level description by editing the guides or manipulate the low‐level description by changing the procedural rules. Changing the connectivity allows the user to create new complex forms in an easy and intuitive way. We show several examples of procedural structures, including an ornamental pattern, a street layout, a bridge, and a model of trees. We also demonstrate interactive examples for quick and intuitive editing using physics‐based mass‐spring system.

Abstract We present an important step towards the solution of the problem of inverse procedural modeling by generating parametric context‐free L‐systems that represent an input 2D model. The L‐system rules efficiently code the regular structures and the parameters represent the properties of the structure transformations. The algorithm takes as input a 2D vector image that is composed of atomic elements, such as curves and poly‐lines. Similar elements are recognized and assigned terminal symbols of an L‐system alphabet. The terminal symbols' position and orientation are pair‐wise compared and the transformations are stored as points in multiple 4D transformation spaces. By careful analysis of the clusters in the transformation spaces, we detect sequences of elements and code them as L‐system rules. The coded elements are then removed from the clusters, the clusters are updated, and then the analysis attempts to code groups of elements in (hierarchies) the same way. The analysis ends with a single group of elements that is coded as an L‐system axiom. We recognize and code branching sequences of linearly translated, scaled, and rotated elements and their hierarchies. The L‐system not only represents the input image, but it can also be used for various editing operations. By changing the L‐system parameters, the image can be randomized, symmetrized, and groups of elements and regular structures can be edited. By changing the terminal and non‐terminal symbols, elements or groups of elements can be replaced.

Abstract This paper presents a new technique for modification of 3D terrains by hydraulic erosion. It efficiently couples fluid simulation using a Lagrangian approach, namely the Smoothed Particle Hydrodynamics (SPH) method, and a physically‐based erosion model adopted from an Eulerian approach. The eroded sediment is associated with the SPH particles and is advected both implicitly, due to the particle motion, and explicitly, through an additional velocity field, which accounts for the sediment transfer between the particles. We propose a new donor‐acceptor scheme for the explicit advection in SPH. Boundary particles associated to the terrain are used to mediate sediment exchange between the SPH particles and the terrain itself. Our results show that this particle‐based method is efficient for the erosion of dense, large, and sparse fluid. Our implementation provides interactive results for scenes with up to 25,000 particles.