No Arabic abstract
We present a technique for designing 3D-printed perforated lampshades, which project continuous grayscale images onto the surrounding walls. Given the geometry of the lampshade and a target grayscale image, our method computes a distribution of tiny holes over the shell, such that the combined footprints of the light emanating through the holes form the target image on a nearby diffuse surface. Our objective is to approximate the continuous tones and the spatial detail of the target image, to the extent possible within the constraints of the fabrication process. To ensure structural integrity, there are lower bounds on the thickness of the shell, the radii of the holes, and the minimal distances between adjacent holes. Thus, the holes are realized as thin tubes distributed over the lampshade surface. The amount of light passing through a single tube may be controlled by the tubes radius and by its direction (tilt angle). The core of our technique thus consists of determining a suitable configuration of the tubes: their distribution across the relevant portion of the lampshade, as well as the parameters (radius, tilt angle) of each tube. This is achieved by computing a capacity-constrained Voronoi tessellation over a suitably defined density function, and embedding a tube inside the maximal inscribed circle of each tessellation cell. The density function for a particular target image is derived from a series of simulated images, each corresponding to a different uniform density tube pattern on the lampshade.
We present a method for the efficient processing of contact and collision in volumetric elastic models simulated using the Projective Dynamics paradigm. Our approach enables interactive simulation of tetrahedral meshes with more than half a million elements, provided that the model satisfies two fundamental properties: the region of the models surface that is susceptible to collision events needs to be known in advance, and the simulation degrees of freedom associated with that surface region should be limited to a small fraction (e.g. 5%) of the total simulation nodes. Despite this conscious delineation of scope, our hypotheses hold true for common animation subjects, such as simulated models of the human face and parts of the body. In such scenarios, a partial Cholesky factorization can abstract away the behavior of the collision-safe subset of the face into the Schur Complement matrix with respect to the collision-prone region. We demonstrate how fast and accurate updates of penalty-based collision terms can be incorporated into this representation, and solved with high efficiency on the GPU. We also demonstrate the opportunity to iterate a partial update of the element rotations, akin to a selective application of the local step, specifically on the smaller collision-prone region without explicitly paying the cost associated with the rest of the simulation mesh. We demonstrate efficient and robust interactive simulation in detailed models from animation and medical applications.
Repetitive patterns are ubiquitous in natural and human-made objects, and can be created with a variety of tools and methods. Manual authoring provides unmatched degree of freedom and control, but can require significant artistic expertise and manual labor. Computational methods can automate parts of the manual creation process, but are mainly tailored for discrete pixels or elements instead of more general continuous structures. We propose an example-based method to synthesize continuous curve patterns from exemplars. Our main idea is to extend prior sample-based discrete element synthesis methods to consider not only sample positions (geometry) but also their connections (topology). Since continuous structures can exhibit higher complexity than discrete elements, we also propose robust, hierarchical synthesis to enhance output quality. Our algorithm can generate a variety of continuous curve patterns fully automatically. For further quality improvement and customization, we also present an autocomplete user interface to facilitate interactive creation and iterative editing. We evaluate our methods and interface via different patterns, ablation studies, and comparisons with alternative methods.
Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches have not been widely adopted in graphics mainly due to the underlying inaccuracy, instability and inflexibility. In this paper, we try to tackle these problems in order to make kinetic approaches practical for graphical applications. To achieve more accurate and stable simulations, we propose to employ the non-orthogonal central-moment-relaxation model, where we develop a novel adaptive relaxation method to retain both stability and accuracy in turbulent flows. To achieve flexibility, we propose a novel continuous-scale formulation that enables samples at arbitrary resolutions to easily communicate with each other in a more continuous sense and with loose geometrical constraints, which allows efficient and adaptive sample construction to better match the physical scale. Such a capability directly leads to an automatic sample construction which generates static and dynamic scales at initialization and during simulation, respectively. This effectively makes our method suitable for simulating turbulent flows with arbitrary geometrical boundaries. Our simulation results with applications to smoke animations show the benefits of our method, with comparisons for justification and verification.
We introduce a large scale benchmark for continuous collision detection (CCD) algorithms, composed of queries manually constructed to highlight challenging degenerate cases and automatically generated using existing simulators to cover common cases. We use the benchmark to evaluate the accuracy, correctness, and efficiency of state-of-the-art continuous collision detection algorithms, both with and without minimal separation. We discover that, despite the widespread use of CCD algorithms, existing algorithms are either: (1) correct but impractically slow, (2) efficient but incorrect, introducing false negatives which will lead to interpenetration, or (3) correct but over conservative, reporting a large number of false positives which might lead to inaccuracies when integrated in a simulator. By combining the seminal interval root finding algorithm introduced by Snyder in 1992 with modern predicate design techniques, we propose a simple and efficient CCD algorithm. This algorithm is competitive with state of the art methods in terms of runtime while conservatively reporting the time of impact and allowing explicit trade off between runtime efficiency and number of false positives reported.
Using (casual) images to texture 3D models is a common way to create realistic 3D models, which is a very important task in computer graphics. However, if the shape of the casual image does not look like the target model or the target mapping area, the textured model will become strange since the image will be distorted very much. In this paper, we present a novel texturing and deforming approach for mapping the pattern and shape of a casual image to a 3D model at the same time based on an alternating least-square approach. Through a photogrammetric method, we project the target model onto the source image according to the estimated camera model. Then, the target model is deformed according to the shape of the source image using a surface-based deformation method while minimizing the image distortion simultaneously. The processes are performed iteratively until convergence. Hence, our method can achieve texture mapping, shape deformation, and detail-preserving at once, and can obtain more reasonable texture mapped results than traditional methods.