Inside-outside determination is a basic building block for higher-level geometry processing operations. Generalized winding numbers provide a robust answer for triangle meshes, regardless of defects such as self-intersections, holes or degeneracies. In this paper, we further generalize the winding number to point clouds. Previous methods for evaluating the winding number are slow for completely disconnected surfaces, such as triangle soups or-in the extreme case- point clouds. We propose a tree-based algorithm to reduce the asymptotic complexity of generalized winding number computation, while closely approximating the exact value. Armed with a fast evaluation, we demonstrate the winding number in a variety of new applications: voxelization, signing distances, generating 3D printer paths, defect-tolerant mesh booleans and point set surfaces.

Interactive, smart objects-customized to individuals and uses-are central to many movements, such as tangibles, the internet of things (IoT), and ubiquitous computing. Yet, rapid prototyping both the form and function of these custom objects can be problematic, particularly for those with limited electronics or programming experience. Designers often need to embed custom circuitry; program its workings; and create a form factor that not only reflects the desired user experience but can also house the required circuitry and electronics. To mitigate this, we created Pineal, a design tool that lets end-users: (1) modify 3D models to include a smart watch or phone as its heart; (2) specify high-level interactive behaviours through visual programming; and (3) have the phone or watch act out such behaviours as the objects' "smarts". Furthermore, a series of prototypes show how Pineal exploits mobile sensing and output, and automatically generates 3D printed form-factors for rich, interactive, objects.

We present ChronoFab, a 3D modeling tool to craft motion sculptures, tangible representations of 3D animated models, visualizing an object's motion with static, transient, ephemeral visuals that are left behind. Our tool casts 3D modeling as a dynamic art-form by employing 3D animation and dynamic simulation for the modeling of motion sculptures. Our work is inspired by the rich history of stylized motion depiction techniques in existing 3D motion sculptures and 2D comic art. Based on a survey of such techniques, we present an interface that enables users to rapidly explore and craft a variety of static 3D motion depiction techniques, including motion lines, multiple stroboscopic stamps, sweeps and particle systems, using a 3D animated object as input. In a set of professional and non-professional usage sessions, ChronoFab was found to be a superior tool for the authoring of motion sculptures, compared to traditional 3D modeling workflows, reducing task completion times by 79%.

This paper presents an interactive design interface for three-dimensional free-form musical wind instruments. The sound of a wind instrument is governed by the acoustic resonance as a result of complicated interactions of sound waves and internal geometries of the instrument. Thus, creating an original free-form wind instrument by manual methods is a challenging problem. Our interface provides interactive sound simulation feedback as the user edits, allowing exploration of original wind instrument designs. Sound simulation of a 3D wind musical instrument is known to be computationally expensive. To overcome this problem, we first model the wind instruments as a passive resonator, where we ignore coupled oscillation excitation from the mouthpiece. Then we present a novel efficient method to estimate the resonance frequency based on the boundary element method by formulating the resonance problem as a minimum eigenvalue problem. Furthermore, we can efficiently compute an approximate resonance frequency using a new technique based on a generalized eigenvalue problem. The designs can be fabricated using a 3D printer, thus we call the results "print-wind instruments" in association with woodwind instruments. We demonstrate our approach with examples of unconventional shapes performing familiar songs.

3D modelers often wish to showcase their models for sharing or review purposes. This may consist of generating static viewpoints of the model or authoring animated fly-throughs. Manually creating such views is often tedious and few automatic methods are designed to interactively assist the modelers with the view authoring process. We present a view authoring assistance system that supports the creation of informative view points, view paths, and view surfaces, allowing modelers to author the interactive navigation experience of a model. The key concept of our implementation is to analyze the model's workflow history, to infer important regions of the model and representative viewpoints of those areas. An evaluation indicated that the viewpoints generated by our algorithm are comparable to those manually selected by the modeler. In addition, participants of a user study found our system easy to use and effective for authoring viewpoint summaries.

3D printers offer extraordinary flexibility for prototyping the shape and mechanical function of objects. We investigate how 3D models can be modified to facilitate the creation of interactive objects that offer dynamic input and output. We introduce a general technique for supporting the rapid prototyping of interactivity by removing interior material from 3D models to form internal pipes. We describe this new design space of pipes for interaction design, where variables include openings, path constraints, topologies, and inserted media. We then present PipeDream, a tool for routing such pipes through the interior of 3D models, integrated within a 3D modeling program. We use two distinct routing algorithms. The first has users define pipes' terminals, and uses path routing and physics-based simulation to minimize pipe bending energy, allowing easy insertion of media post-print. The second allows users to supply a desired internal shape to which we fit a pipe route: for this we describe a graph-routing algorithm. We present several prototypes created using our tool to show its flexibility and potential.

This paper introduces novel interactive techniques for designing original hand-launched free-flight glider airplanes which can actually fly. The aerodynamic properties of a glider aircraft depend on their shape, imposing significant design constraints. We present a compact and efficient representation of glider aerodynamics that can be fit to real-world conditions using a data-driven method. To do so, we acquire a sample set of glider flight trajectories using a video camera and the system learns a nonlinear relationship between forces on the wing and wing shape. Our acquisition system is much simpler to construct than a wind tunnel, but using it we can efficiently discover a wing model for simple gliding aircraft. Our resulting model can handle general free-form wing shapes and yet agrees sufficiently well with the acquired airplane flight trajectories. Based on this compact aerodynamics model, we present a design tool in which the wing configuration created by a user is interactively optimized to maximize flight-ability. To demonstrate the effectiveness of our tool for glider design by novice users, we compare it with a traditional design workflow.

Abstract We propose a method for interactive cloning of 3D surface geometry using a paintbrush interface, similar to the continuous cloning brush popular in image editing. Existing interactive mesh composition tools focus on atomic copy‐and‐paste of preselected feature areas, and are either limited to copying surface displacements, or require the solution of variational optimization problems, which is too expensive for an interactive brush interface. In contrast, our GeoBrush method supports real‐time continuous copying of arbitrary high‐resolution surface features between irregular meshes, including topological handles. We achieve this by first establishing a correspondence between the source and target geometries using a novel generalized discrete exponential map parameterization. Next we roughly align the source geometry with the target shape using Green Coordinates with automatically‐constructed cages. Finally, we compute an offset membrane to smoothly blend the pasted patch with C continuity before stitching it into the target. The offset membrane is a solution of a bi‐harmonic PDE, which is computed on the GPU in real time by exploiting the regular parametric domain. We demonstrate the effectiveness of GeoBrush with various editing scenarios, including detail enrichment and completion of scanned surfaces.

In this article we derive an equation for the velocity of an arbitrary time-evolving implicit surface. Strictly speaking, only the normal component of the velocity is unambiguously defined. This is because an implicit surface does not have a unique parametrization. However, by enforcing a constraint on the evolution of the normal field we obtain a unique tangential component. We apply our formulas to surface tracking and to the problem of computing velocity vectors of a motion blurred blobby surface. Other possible applications are mentioned at the end of the article.

We describe a novel approach to inferring 3D curves from perspective drawings in an interactive design tool. Our methods are based on a traditional design drawing style known as analytic drawing , which supports precise image-space construction of a linear 3D scaffold. This scaffold in turn acts as a set of visual constraints for sketching 3D curves. We implement analytic drawing techniques in a pure-inference sketching interface which supports both single-and multi-view incremental construction of complex scaffolds and curve networks. A new representation of 3D drawings is proposed, and useful interactive drawing aids are described. Novel techniques are presented for deriving constraints from single-view sketches drawn relative to the current 3D scaffold, and then inferring 3D line and curve geometry which satisfies these constraints. The resulting analytic drawing tool allows 3D drawings to be constructed using exactly the same strokes as one would make on paper.

Abstract We present a system for creating and manipulating layered procedural surface editing operations, which is motivated by the limited support for iterative design in free‐form modeling. A combination of sketch‐based and traditional modeling tools are used to design soft displacements, sharp creases, extrusions along 3D paths, and topological holes and handles. Using local parameterizations, these edits are combined in a dynamic hierarchy, enabling procedural operations like linked copy‐and‐paste and drag‐and‐drop layer‐based editing. Such dynamic, layered “surface compositing” is formalized as a Surface Tree, an analog of CSG trees which generalizes previous hierarchical surface modeling techniques. By “anchoring” tree nodes in the parameter space of lower layers, our surface tree implementation can better preserve the semantics of an edit as the underlying surface changes. Details of our implementation are described, including an efficient procedural mesh data structure.

Abstract We present an interface for 3D object manipulation in which standard transformation tools are replaced with transient 3D widgets invoked by sketching context‐dependent strokes. The widgets are automatically aligned to axes and planes determined by the user's stroke. Sketched pivot‐points further expand the interaction vocabulary. Using gestural commands, these basic elements can be assembled into dynamic, user‐constructed 3D transformation systems. We supplement precise widget interaction with techniques for coarse object positioning and snapping. Our approach, which is implemented within a broader sketch‐based modeling system, also integrates an underlying “widget history” to enable the fluid transfer of widgets between objects. An evaluation indicates that users familiar with 3D manipulation concepts can be taught how to efficiently use our system in under an hour.

A method is described for texturing surfaces using decals , images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O ( N log N ) discrete approximation to the exponential map which requires only a single additional step in Dijkstra's graph-distance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/feature-matching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.

Complex implicit CSG models can be represented hierarchically as a tree of nodes (the BlobTree) . However, current methods cannot be used to visualize changes made to these models at interactive rates due to the large number of potential field evaluations required. A hierarchical spatial caching technique is presented which accelerates evaluations of the potential function. This method introduces the concept of a caching node inserted into the implicit model tree. Caching nodes store exact potential field values at the vertices of a voxel grid and rely on tri-linear and tri-quadratic reconstruction filters to locally approximate the potential field of a sub-tree. A lazy evaluation scheme is used to avoid expensive pre-computation. Polygonization timings with and without caching are compared for a complex model undergoing manipulation in an interactive modeling tool. An order-of-magnitude improvement in visualization time is achieved for complex implicit models containing thousands of primitives.