In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAH...In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAHT） B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., t^n-5}, n 7〉 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.展开更多
苹果刚用一个经过重新设计的程序,替代了原先的故障诊断软件。你可能已经知道,可以用AHT（苹果硬件测试Apple Hardware Test）来对苹果电脑内部的硬件进行检查和调试。如果安装的是OS X 10.7或更新的操作系统,你可以在重启电脑时立刻快...苹果刚用一个经过重新设计的程序,替代了原先的故障诊断软件。你可能已经知道,可以用AHT（苹果硬件测试Apple Hardware Test）来对苹果电脑内部的硬件进行检查和调试。如果安装的是OS X 10.7或更新的操作系统,你可以在重启电脑时立刻快速按下D键进入该程序。如果很不巧这么做没成功的话,你还可以通过在启动时按下Option和D键来进行尝试。若想了解更多有关AHT的详情（例如如何在较早期的苹果电脑上启动AHT）,请参看这篇文章（http：//support.apple.com/kb/HT1509）。如果诊断发现可能有潜在的硬件问题,该诊断软件会提供相关建议,告知你具体遇到的问题是什么,以及应该如何处理。展开更多
基金This work is supported by the National Natural Science Foundation of China under Grant Nos.60473130,10371110the National Grand Fundamental Research 973 Program of China under Grant No.2004CB318000.
文摘In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric （ AHT） Bezier curves and non-uniform algebraic hyperbolic trigonometric （ NUAHT） B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., t^n-5}, n 7〉 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.
文摘苹果刚用一个经过重新设计的程序,替代了原先的故障诊断软件。你可能已经知道,可以用AHT（苹果硬件测试Apple Hardware Test）来对苹果电脑内部的硬件进行检查和调试。如果安装的是OS X 10.7或更新的操作系统,你可以在重启电脑时立刻快速按下D键进入该程序。如果很不巧这么做没成功的话,你还可以通过在启动时按下Option和D键来进行尝试。若想了解更多有关AHT的详情（例如如何在较早期的苹果电脑上启动AHT）,请参看这篇文章（http：//support.apple.com/kb/HT1509）。如果诊断发现可能有潜在的硬件问题,该诊断软件会提供相关建议,告知你具体遇到的问题是什么,以及应该如何处理。
