We study the following problem: given a polynomial order of approximation n and the corresponding Bézier tensor product patches over an unstructured quadrilateral mesh made of convex quadrilaterals with vertices of any valence , is there a solution to the G 1 ( and as a consequence the C 1 ) approximation (resp. interpolation ) problem ? To illustrate the interpolation case , constraints defining regularity conditions across patches have to be satisfied. The resulting number of free degrees of freedom must be such that the interpolation problem has a solution! This is similar to studying the minimal determining set (MDS) for a C 1 continuity construction. *

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An advantage of digital media is the flexibility to personalize the presentation of text to an individual’s needs and embed tools that support pedagogy and practice. The goal of this study was to develop a tablet-based reading tool, grounded in the principles of phonics-based instruction, and determine whether struggling readers could leverage this technology to improve their decoding skills. The tool presents a small icon below each vowel to represent its sound. Forty struggling child readers were randomly assigned to an intervention or control group to test the efficacy of the phonemic cues. We found that struggling readers could leverage the cues to improve pseudoword decoding: after two weeks of practice, the intervention group showed greater improvement than controls. This study demonstrates the efficacy of a text annotation, grounded in intervention research, to help children decode novel words. These results highlight the opportunity for educational technologies to support and supplement classroom instruction.

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ClearType is a subpixel-rendering method designed to improve the perceived quality of text. The method renders text at subpixel resolution and then applies a one-dimensional symmetric mean-preserving filter to reduce color artifacts. This paper describes a computational method and experimental tests to assess user preferences for different filter parameters. The computational method uses a physical display simulation and a perceptual metric that includes a model of human spatial and chromatic sensitivity. The method predicts experimentally measured preferences for filters for a range of characters, fonts, and displays.