The potential advantages of freehand sketches have been widely recognized and exploited in many fields especially in engineering design and analysis. This is mainly because the freehand sketches are an efficient and natural way for users to visually communicate ideas. However, due to a lack of fundamental techniques for understanding them, sketch-based interfaces have not yet evolved as the preferred computing platform over traditional menu-based tools. In this paper, we address the specific challenge of transforming informal and ambiguous freehand inputs to more formalized and structured representations. We present a domain-independent, multi-stroke, multi-primitive beautification method which detects and uses the spatial relationships implied in the sketches. Spatial relationships are represented as geometric constraints and satisfied by a geometric constraint solver. To demonstrate the utility of this technique and also to build a natural working environment for structural analysis in early design, we have developed FEAsy (acronym for Finite Element Analysis made easy) as shown in Fig. 1. This tool allows the users to transform, simulate and analyze their finite element models quickly and easily through freehand sketching, just as they would draw on paper. Further, we have also developed simple, domain specific rules-based algorithms for recognizing the commonly used symbols and for understanding the different contexts in finite element modeling. Finally, we illustrate the proposed approach with a few examples.
BackgroundDuring the past decade, the computed tomography has been successfully applied to various fields especially in medicine. The estimation of view angles for projections is necessary in some special applications of tomography, for example, the structuring of viruses using electron microscopy and the compensation of the patient's motion over long scanning period.MethodsThis work introduces a novel approach, based on the spherical multidimensional scaling (sMDS), which transforms the problem of the angle estimation to a sphere constrained embedding problem. The proposed approach views each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. By using SMDS, then each projection vector is embedded onto a 1D sphere which parameterizes the projection with respect to view angles in a globally consistent manner. The parameterized projections are used for the final reconstruction of the image through the inverse radon transform. The entire reconstruction process is non-iterative and computationally efficient.ResultsThe effectiveness of the sMDS is verified with various experiments, including the evaluation of the reconstruction quality from different number of projections and resistance to different noise levels. The experimental results demonstrate the efficiency of the proposed method.ConclusionOur study provides an effective technique for the solution of 2D tomography with unknown acquisition view angles. The proposed method will be extended to three dimensional reconstructions in our future work. All materials, including source code and demos, are available on https://engineering.purdue.edu/PRECISE/SMDS.
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