We present a comprehensive system to author planar section structures, common in art and engineering. A study on how planar section assemblies are imagined and drawn guide our design principles: planar sections are best drawn in-situ, with little foreshortening, orthogonal to intersecting planar sections, exhibiting regularities between planes and contours. We capture these principles with a novel drawing workflow where a single fluid user stroke specifies a 3D plane and its contour in relation to existing planar sections. Regularity is supported by defining a vocabulary of procedural operations for intersecting planar sections. We exploit planar structure properties to provide real-time visual feedback on physically simulated stresses, and geometric verification that the structure is stable, connected and can be assembled. This feedback is validated by real-world fabrication and testing. As evaluation, we report on over 50 subjects who all used our system with minimal instruction to create unique models.

True2Formis a sketch-based modeling system that reconstructs 3D curves from typical design sketches. Our approach to infer 3D form from 2D drawings is a novel mathematical framework of insights derived from perception and design literature. We note that designers favor viewpoints that maximally reveal 3D shape information, and strategically sketch descriptive curves that convey intrinsic shape properties, such as curvature, symmetry, or parallelism. Studies indicate that viewers apply these properties selectively to envision a globally consistent 3D shape. We mimic this selective regularization algorithmically, by progressively detecting and enforcing applicable properties, accounting for their global impact on an evolving 3D curve network. Balancing regularity enforcement against sketch fidelity at each step allows us to correct for inaccuracy inherent in free-hand sketching. We perceptually validate our approach by showing agreement between our algorithm and viewers in selecting applicable regularities. We further evaluate our solution by: reconstructing a range of 3D models from diversely sourced sketches; comparisons to prior art; and visual comparison to both ground-truth and 3D reconstructions by designers.

Various algorithms have been proposed to create planar abstractions of 3D models, but there has been no systematic effort to evaluate the effectiveness of such abstractions in terms of perception of the abstracted surfaces. In this work, we perform a large crowd-sourced study involving approximately 70k samples to evaluate how well users can orient gauges on planar abstractions of commonly occurring models. We test four styles of planar abstractions against ground truth surface representations, and analyze the data to discover a wide variety of correlations between task error and measurements relating to surface-specific properties such as curvature, local thickness and medial axis distance, and abstraction-specific properties. We use these discovered correlations to create linear models to predict error in surface understanding at a given point, for both surface representations and planar abstractions. Our predictive models reveal the geometric causes most responsible for error, and we demonstrate their potential use to build upon existing planar abstraction techniques in order to improve perception of the abstracted surface.

Minimalist object representations or shape-proxies that spark and inspire human perception of shape remain an incompletely understood, yet powerful aspect of visual communication. We explore the use of planar sections, i.e., the contours of intersection of planes with a 3D object, for creating shape abstractions, motivated by their popularity in art and engineering. We first perform a user study to show that humans do define consistent and similar planar section proxies for common objects. Interestingly, we observe a strong correlation between user-defined planes and geometric features of objects. Further we show that the problem of finding the minimum set of planes that capture a set of 3D geometric shape features is both NP-hard and not always the proxy a user would pick. Guided by the principles inferred from our user study, we present an algorithm that progressively selects planes to maximize feature coverage, which in turn influence the selection of subsequent planes. The algorithmic framework easily incorporates various shape features, while their relative importance values are computed and validated from the user study data. We use our algorithm to compute planar slices for various objects, validate their utility towards object abstraction using a second user study, and conclude showing the potential applications of the extracted planar slice shape proxies.

Recently, research in 3D computer graphics and interaction has started to move beyond the narrow domain of single object authoring and inspection, and has begun to consider complex multiscale objects and environments. This generalization of problem scope calls for more general solutions, which are more akin to information visualization techniques than traditional computer graphics approaches.

We present a comprehensive system for multiscale navigation of 3-dimensional scenes, and demonstrate our approach on multiscale datasets such as the Earth. Our system incorporates a novel image-based environment representation which we refer to as the cubemap. Our cubemap allows consistent navigation at various scales, as well as real-time collision detection without pre-computation or prior knowledge of geometric structure. The cubemap is used to improve upon previous work on proximal object inspection (HoverCam), and we present an additional interaction technique for navigation which we call look-and-fly. We believe that our approach to the navigation of multiscale 3D environments offers greater flexibility and ease of use than mainstream applications such as Google Earth and Microsoft Virtual Earth, and we demonstrate our results with this system.

This article presents a method for real-time line drawing of deforming objects. Object-space line drawing algorithms for many types of curves, including suggestive contours, highlights, ridges, and valleys, rely on surface curvature and curvature derivatives. Unfortunately, these curvatures and their derivatives cannot be computed in real-time for animated, deforming objects. In a preprocessing step, our method learns the mapping from a low-dimensional set of animation parameters (e.g., joint angles) to surface curvatures for a deforming 3D mesh. The learned model can then accurately and efficiently predict curvatures and their derivatives, enabling real-time object-space rendering of suggestive contours and other such curves. This represents an order-of-magnitude speedup over the fastest existing algorithm capable of estimating curvatures and their derivatives accurately enough for many different types of line drawings. The learned model can generalize to novel animation sequences and is also very compact, typically requiring a few megabytes of storage at runtime. We demonstrate our method for various types of animated objects, including skeleton-based characters, cloth simulation, and blend-shape facial animation, using a variety of nonphotorealistic rendering styles. An important component of our system is the use of dimensionality reduction for differential mesh data. We show that Independent Component Analysis (ICA) yields localized basis functions, and gives superior generalization performance to that of Principal Component Analysis (PCA).