We propose a method to transform unstructured 3D sketches into piecewise smooth surfaces that preserve sketched geometric features. Immersive 3D drawing and sketch-based 3D modeling applications increasingly produce imperfect and unstructured collections of 3D strokes as design output. These 3D sketches are readily perceived as piecewise smooth surfaces by viewers, but are poorly handled by existing 3D surface techniques tailored to well-connected curve networks or sparse point sets. Our algorithm is aligned with human tendency to imagine the strokes as a small set of simple smooth surfaces joined along stroke boundaries. Starting with an initial proxy surface, we iteratively segment the surface into smooth patches joined sharply along some strokes, and optimize these patches to fit surrounding strokes. Our evaluation is fourfold: we demonstrate the impact of various algorithmic parameters, we evaluate our method on synthetic sketches with known ground truth surfaces, we compare to prior art, and we show compelling results on more than 50 designs from a diverse set of 3D sketch sources.

We present CASSIE, a conceptual modeling system in VR that leverages freehand mid-air sketching, and a novel 3D optimization framework to create connected curve network armatures, predictively surfaced using patches with C0 continuity. Our system provides a judicious balance of interactivity and automation, providing a homogeneous 3D drawing interface for a mix of freehand curves, curve networks, and surface patches. Our system encourages and aids users in drawing consistent networks of curves, easing the transition from freehand ideation to concept modeling. A comprehensive user study with professional designers as well as amateurs (N=12), and a diverse gallery of 3D models, show our armature and patch functionality to offer a user experience and expressivity on par with freehand ideation, while creating sophisticated concept models for downstream applications.

Complex 3D curves can be created by directly drawing mid-air in immersive environments (Augmented and Virtual Realities). Drawing mid-air strokes precisely on the surface of a 3D virtual object, however, is difficult, necessitating a projection of the mid-air stroke onto the user “intended” surface curve. We present the first detailed investigation of the fundamental problem of 3D stroke projection in VR. An assessment of the design requirements of real-time drawing of curves on 3D objects in VR is followed by the definition and classification of multiple techniques for 3D stroke projection. We analyze the advantages and shortcomings of these approaches both theoretically and via practical pilot testing. We then formally evaluate the two most promising techniques spraycan and mimicry with 20 users in VR. The study shows a strong qualitative and quantitative user preference for our novel stroke mimicry projection algorithm. We further illustrate the effectiveness and utility of stroke mimicry to draw complex 3D curves on surfaces for various artistic and functional design applications.

We explore the use of hand gestures for authoring animations in virtual reality (VR). We first perform a gesture elicitation study to understand user preferences for a spatiotemporal, bare-handed interaction system in VR. Specifically, we focus on creating and editing dynamic, physical phenomena (e.g., particle systems, deformations, coupling), where the mapping from gestures to animation is ambiguous and indirect. We present commonly observed mid-air gestures from the study that cover a wide range of interaction techniques, from direct manipulation to abstract demonstrations. To this end, we extend existing gesture taxonomies to the rich spatiotemporal interaction space of the target domain and distill our findings into a set of guidelines that inform the design of natural user interfaces for VR animation. Finally, based on our guidelines, we develop a proof-of-concept gesture-based VR animation system, MagicalHands. Our results, as well as feedback from user evaluation, suggest that the expressive qualities of hand gestures help users animate more effectively in VR.

We present SymbiosisSketch, a hybrid sketching system that combines drawing in air (3D) and on a drawing surface (2D) to create detailed 3D designs of arbitrary scale in an augmented reality (AR) setting. SymbiosisSketch leverages the complementary affordances of 3D (immersive, unconstrained, life-sized) and 2D (precise, constrained, ergonomic) interactions for in situ 3D conceptual design. A defining aspect of our system is the ongoing creation of surfaces from unorganized collections of 3D curves. These surfaces serve a dual purpose: as 3D canvases to map strokes drawn on a 2D tablet, and as shape proxies to occlude the physical environment and hidden curves in a 3D sketch. SymbiosisSketch users draw interchangeably on a 2D tablet or in 3D within an ergonomically comfortable canonical volume, mapped to arbitrary scale in AR. Our evaluation study shows this hybrid technique to be easy to use in situ and effective in transcending the creative potential of either traditional sketching or drawing in air.

Sketching in immersive 3D virtual reality (VR) environments has great potential for a variety of interactive 3D design applications. Precisely sketching the intended strokes in mid-air, however, can be a challenge. In this paper, we present a set of controlled studies to analyze the factors affecting human ability to sketch freely in a 3D VR environment. In our first study, we directly compare traditional sketching on a physical surface to sketching in VR, with and without a physical surface to rest the stylus on. Our results indicate that the lack of a physical drawing surface is a major cause of inaccuracies in VR drawing, and that the effect is dependent on the orientation of the drawing surface. In a second experiment, we evaluate the extent to which visual guidance can compensate for the loss of sketching precision in VR. We found that while additional visual guidance improves positional accuracy, it can be detrimental to the aesthetic quality of strokes. We conclude by distilling our experimental findings into design guidelines for sketching tools in immersive 3D environments.

Abstract A hallmark of early stage design is a number of quick‐and‐dirty sketches capturing design inspirations, model variations and alternate viewpoints of a visual concept. We present SketchSoup, a workflow that allows designers to explore the design space induced by such sketches. We take an unstructured collection of drawings as input, along with a small number of user‐provided correspondences as input. We register them using a multi‐image matching algorithm, and present them as a 2D interpolation space. By morphing sketches in this space, our approach produces plausible visualizations of shape and viewpoint variations despite the presence of sketch distortions that would prevent standard camera calibration and 3D reconstruction. In addition, our interpolated sketches can serve as inspiration for further drawings, which feed back into the design space as additional image inputs. SketchSoup thus fills a significant gap in the early ideation stage of conceptual design by allowing designers to make better informed choices before proceeding to more expensive 3D modelling and prototyping. From a technical standpoint, we describe an end‐to‐end system that judiciously combines and adapts various image processing techniques to the drawing domain—where the images are dominated not by colour, shading and texture, but by sketchy stroke contours.

The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph ensures that it has a unique minimum weight perfect matching, with a good probability. We derandomize this lemma for K3,3-free and K5-free bipartite graphs. That is, we give a deterministic log-space construction of such a weight assignment for these graphs. Such a construction was known previously for planar bipartite graphs. Our result implies that the perfect matching problem for K3,3-free and K5-free bipartite graphs is in SPL. It also gives an alternate proof for an already known result – reachability for K3,3-free and K5-free graphs is in UL.