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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.

We present a novel approach to sketching 2D curves with minimally varying curvature as piecewise clothoids. A stable and efficient algorithm fits a sketched piecewise linear curve using a number of clothoid segments with G^2 continuity based on a specified error tolerance. Further, adjacent clothoid segments can be locally blended to result in a G^3 curve with curvature that predominantly varies linearly with arc length. We also handle intended sharp corners or G^1 discontinuities, as independent rotations of clothoid pieces. Our formulation is ideally suited to conceptual design applications where aesthetic fairness of the sketched curve takes precedence over the precise interpolation of geometric constraints. We show the effectiveness of our results within a system for sketch-based road and robot-vehicle path design, where clothoids are already widely used.

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).

True2Form is 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.

We apply traditional bimanual curve modeling using French curves to the problem of automatic neatening of sketched strokes. Given a sketched input stroke and a set of template French curves we present an approach that fits the stroke using an optimal number of French curve segments. Our algorithm operates in both curvature and point space, reconstructing the salient curvature profiles of French curve segments, while limiting error accumulation resulting from curvature integration. User-controlled parameters allow the neatened stroke to model G2 continuous curves, capture G1 discontinuities, define closed curves and explore the trade-off between fitting error and the number of French curve segments used. We present an interactive sketch stroke neatening implementation to demonstrate the real-time performance of our algorithm and evaluate the quality of its results.