Abstract We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing for map distortions or multiple patches. Instead, we propose a geometric relaxation of the problem: We modify the input shape until it admits an overlap‐free unfolding. We achieve this by locally displacing vertices and collapsing edges, guided by the unfolding process. We validate our algorithm quantitatively and qualitatively on a large dataset of complex shapes and show its proficiency by fabricating real shapes from paper.

We propose a computational design approach for covering a surface with individually addressable RGB LEDs, effectively forming a low-resolution surface screen. To achieve a low-cost and scalable approach, we propose creating designs from flat PCB panels bent in-place along the surface of a 3D printed core. Working with standard rigid PCBs enables the use of established PCB manufacturing services, allowing the fabrication of designs with several hundred LEDs. Our approach optimizes the PCB geometry for folding, and then jointly optimizes the LED packing, circuit and routing, solving a challenging layout problem under strict manufacturing requirements. Unlike paper, PCBs cannot bend beyond a certain point without breaking. Therefore, we introduce parametric cut patterns acting as hinges, designed to allow bending while remaining compact. To tackle the joint optimization of placement, circuit and routing, we propose a specialized algorithm that splits the global problem into one sub-problem per triangle, which is then individually solved. Our technique generates PCB blueprints in a completely automated way. After being fabricated by a PCB manufacturing service, the boards are bent and glued by the user onto the 3D printed support. We demonstrate our technique on a range of physical models and virtual examples, creating intricate surface light patterns from hundreds of LEDs. The code and data for this paper are available at https://github.com/mfremer/pcbend.

While 3D printing enables the customization and home fabrication of a wide range of shapes, fabricating freeform thin-shells remains challenging. As layers misalign with the curvature, they incur structural deficiencies, while the curved shells require large support structures, typically using more material than the part itself. We present a computational framework for optimizing the internal structure of 3D printed plates such that they morph into a desired freeform shell when heated. This exploits the shrinkage effect of thermoplastics such as PLA, which store internal stresses along the deposition directions. These stresses get released when the material is heated again above its glass transition temperature, causing an anisotropic deformation that induces curvature. Our inverse design method takes as input a freeform surface and finds an optimized set of deposition trajectories in each layer such that their anisotropic shrinkage deforms the plate into the prescribed surface geometry. We optimize for a continuous vector field that varies across the plate and within its thickness. The algorithm then extracts a set of deposition trajectories from the vector field in order to fabricate the flat plates on standard FFF printers. We validate our algorithm on freeform, doubly-curved surfaces.

Abstract This paper proposes a method for simulating liquids in large bodies of water by coupling together a water surface wave simulator with a 3D Navier‐Stokes simulator. The surface wave simulation uses the equivalent sources method (ESM) to efficiently animate large bodies of water with precisely controllable wave propagation behavior. The 3D liquid simulator animates complex non‐linear fluid behaviors like splashes and breaking waves using off‐the‐shelf simulators using FLIP or the level set method with semi‐Lagrangian advection. We combine the two approaches by using the 3D solver to animate localized non‐linear behaviors, and the 2D wave solver to animate larger regions with linear surface physics. We use the surface motion from the 3D solver as boundary conditions for 2D surface wave simulator, and we use the velocity and surface heights from the 2D surface wave simulator as boundary conditions for the 3D fluid simulation. We also introduce a novel technique for removing visual artifacts caused by numerical errors in 3D fluid solvers: we use experimental data to estimate the artificial dispersion caused by the 3D solver and we then carefully tune the wave speeds of the 2D solver to match it, effectively eliminating any differences in wave behavior across the boundary. To the best of our knowledge, this is the first time such a empirically driven error compensation approach has been used to remove coupling errors from a physics simulator. Our coupled simulation approach leverages the strengths of each simulation technique, animating large environments with seamless transitions between 2D and 3D physics.

Abstract This paper introduces a simple method for simulating highly anisotropic elastoplastic material behaviors like the dissolution of fibrous phenomena (splintering wood, shredding bales of hay) and materials composed of large numbers of irregularly‐shaped bodies (piles of twigs, pencils, or cards). We introduce a simple transformation of the anisotropic problem into an equivalent isotropic one, and we solve this new “fictitious” isotropic problem using an existing simulator based on the material point method. Our approach results in minimal changes to existing simulators, and it allows us to re‐use popular isotropic plasticity models like the Drucker‐Prager yield criterion instead of inventing new anisotropic plasticity models for every phenomenon we wish to simulate.

This paper investigates the use of fundamental solutions for animating detailed linear water surface waves. We first propose an analytical solution for efficiently animating circular ripples in closed form. We then show how to adapt the method of fundamental solutions (MFS) to create ambient waves interacting with complex obstacles. Subsequently, we present a novel wavelet-based discretization which outperforms the state of the art MFS approach for simulating time-varying water surface waves with moving obstacles. Our results feature high-resolution spatial details, interactions with complex boundaries, and large open ocean domains. Our method compares favorably with previous work as well as known analytical solutions. We also present comparisons between our method and real world examples.

We propose an efficient method to model paper tearing in the context of interactive modeling. The method uses geometrical information to automatically detect potential starting points of tears. We further introduce a new hybrid geometrical and physical-based method to compute the trajectory of tears while procedurally synthesizing high resolution details of the tearing path using a texture based approach. The results obtained are compared with real paper and with previous studies on the expected geometric paths of paper that tears.

We present a phenomenological model for the real-time simulation of paper tearing and sound. The model uses as input rotations of the hand along with the index and thumb of left and right hands to drive the position and orientation of two regions of a sheet of paper. The motion of the hands produces a cone shaped deformation of the paper and guides the formation and growth of the tear. We create a model for the direction of the tear based on empirical observation, and add detail to the tear with a directed noise model. Furthermore, we present a procedural sound synthesis method to produce tearing sounds during interaction. We show a variety of paper tearing examples and discuss applications and limitations.

We present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations.