We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of userspecified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.

We solve the form-finding problem for polyhedral meshes in a way which combines form, function and fabrication; taking care of userspecified constraints like boundary interpolation, planarity of faces, statics, panel size and shape, enclosed volume, and last, but not least, cost. Our main application is the interactive modeling of meshes for architectural and industrial design. Our approach can be described as guided exploration of the constraint space whose algebraic structure is simplified by introducing auxiliary variables and ensuring that constraints are at most quadratic. Computationally, we perform a projection onto the constraint space which is biased towards low values of an energy which expresses desirable "soft" properties like fairness. We have created a tool which elegantly handles difficult tasks, such as taking boundary-alignment of polyhedral meshes into account, planarization, fairing under planarity side conditions, handling hybrid meshes, and extending the treatment of static equilibrium to shapes which possess overhanging parts.

BackgroundThe use of adjunct rasagiline in levodopa-treated patients with Parkinson’s disease and motor fluctuations is supported by findings from large-scale clinical studies. This study is to investigate the efficacy and safety of adjunct rasagiline in Chinese patients with Parkinson’s disease, as a product registration study.MethodsThis 16-week, randomized, double-blind, parallel-group, multicenter, placebo-controlled study of rasagiline 1 mg/day included levodopa-treated patients with Parkinson’s disease and motor fluctuations. The primary efficacy endpoint was mean change from baseline in total daily OFF time over 16 weeks. Secondary endpoints were Clinical Global Impressions – Improvement (CGI-I), and change in Unified Parkinson’s Disease Rating Scale (UPDRS) Activities of daily living (ADL) and Motor scores. Patient well-being (EQ-5D), and the frequency of adverse events were also assessed.ResultsIn total, 324 levodopa-treated patients were randomized to rasagiline 1 mg/day (n = 165) or placebo (n = 159). Over 16 weeks, rasagiline statistically significantly reduced the mean [95% confidence interval] total daily OFF time versus placebo (− 0.5 h [− 0.92, − 0.07]; p = 0.023). There were also statistically significant improvements versus placebo in CGI-I (− 0.4 points [− 0.61, − 0.22]; p < 0.001), UPDRS-ADL OFF (− 1.0 points [− 1.75, − 0.27]; p = 0.008), and UPDRS-Motor ON (− 1.6 points [− 3.05, − 0.14]; p = 0.032) scores, as well as the EQ-5D utility index (p < 0.05). Rasagiline was safe and well tolerated.ConclusionsIn levodopa-treated Chinese patients with Parkinson’s disease and motor fluctuations, adjunct rasagiline 1 mg/day statistically significantly reduced OFF time, and improved daily function and overall well-being, versus placebo. Consistent with findings in other countries, adjunct rasagiline was proven efficacious and well tolerated in Chinese patients.Trial registration numberNCT01479530. Registered 22 November 2011.

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