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In the design process, different problem statements result in different problem-solving strategies. A proper problem statement is the key to effective problem-solving. Based on the characteristics of the product design process, we divided design problem statements into open-ended (OE), decision-making (DM), and constrained (CO) statements and attempted to investigate the influences of different problem statements on designers’ cognitive behaviors from three perspectives, namely divergent thinking, convergent thinking, and mental workload. Then we provided quantification description to these influences based on electroencephalography (EEG) technology. We conducted experiments on 19 participants and used the BrainProduct™ actiChamp-32 to record the EEG data. Results are as follows: (1) The higher task-related α power was found in the temporal and occipital regions in the OE task compared with that in the DM and CO tasks. The OE statement also would help designers get novel ideas by strengthening their divergent thinking. (2) In the DM and CO tasks, there was no significant difference in the impact of the brain region on convergent thinking, but activities in the left hemisphere were stronger than that in the right hemisphere. The DM and CO tasks have better performance in convergent thinking than the OE task. (3) In the CO task, the designer's mental workload is the highest and mainly related to the activation of the centroparietal and occipital regions. These findings help designers understand the design problem-solving process from the perspective of cognitive science and monitor their thinking modes in the design process so as to improve their design performance.

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We develop a novel isotropic remeshing method based on constrained centroidal Delaunay mesh (CCDM), a generalization of centroidal patch triangulation from 2D to mesh surface. Our method starts with resampling an input mesh with a vertex distribution according to a user-defined density function. The initial remeshing result is then progressively optimized by alternatively recovering the Delaunay mesh and moving each vertex to the centroid of its 1-ring neighborhood. The key to making such simple iterations work is an efficient optimization framework that combines both local and global optimization methods. Our method is parameterization-free, thus avoiding the metric distortion introduced by parameterization, and generating more well-shaped triangles. Our method guarantees that the topology of surface is preserved without requiring geodesic information. We conduct various experiments to demonstrate the simplicity, efficacy, and robustness of the presented method.

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Image triangulation aims to generate an optimal partition with triangular elements to represent the given image. One bottleneck in ensuring approximation quality between the original image and a piecewise approximation over the triangulation is the inaccurate alignment of straight edges to the curved features. In this paper, we propose a novel variational method called curved optimal triangulation, where not all edges are straight segments, but may also be quadratic Bézier curves. The energy function is defined as the total approximation error determined by vertex locations, connectivity and bending of edges. The gradient formulas of this function are derived explicitly in closed form to optimize the energy function efficiently. We test our method on several models to demonstrate its efficacy and ability in preserving features. We also explore its applications in the automatic generation of stylization and Lowpoly images. With the same number of vertices, our curved optimal triangulation method generates more accurate and visually pleasing results compared with previous methods that only use straight segments.

Vector image representation methods that can faithfully reconstruct objects and color variations in a raster image are desired in many practical applications. This paper presents triangular configuration B-spline (referred to as TCB-spline)-based vector graphics for raster image vectorization. Based on this new representation, an automatic raster image vectorization paradigm is proposed. The proposed framework first detects sharp curvilinear features in the image and constructs knot meshes based on the detected feature lines. It iteratively optimizes color and position of control points and updates the knot meshes. By using collinear knots at feature lines, both smooth and discontinuous color variations can be efficiently modeled by the same set of quadratic TCB-splines. A variational knot mesh generation method is designed to adaptively introduce knots and update their connectivity in order to satisfy the local reconstruction quality. Experiments and comparisons show that our framework outperforms the existing state-of-the-art methods in providing more faithful reconstruction results. In particular, our method is able to model undetected features and subtle or complicated color variations in-between features, which the previous methods cannot handle efficiently. Our vectorization representation also facilitates a variety of editing operations performed directly over vector images.