二次曲面

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

Expression methods and growing rules accord with self-organization way are studied for binominal curves and surfaces such as arc, spiral, helicoid, ellipsoid and fractal curves such as snow-form curve.

研究了圆弧、螺旋线、螺旋面、椭球面等常规二次曲线/曲面以及雪花曲线等分形曲线的自组织表达和生长规则，实现并验证了其生长算法。

MethodsBy means of orthogonally rotational combination design, microwave extraction mathematical simulation model was concluded by the linear regression analysis. In order to obtain the optimum extraction of flavonoids, the regression equation of the relationship between the four factors were established.

方法通过二次回归正交旋转组合试验设计，得到了微波提取苦丁茶中黄酮的数学回归方程；利用模型的响应曲面图及等高线图，对影响微波提取苦丁茶黄酮提取率的关键因素及相互作用进行探讨，得到最佳提取工艺条件。

On the basis of the single-factor experiment, the quaternionic quadratic rotational combination was used to optimize the extraction process of total relative flavone that came from fermentation fluid of citrus, and we had used the response surface methodology to study the best horizontal extent of solid-to-liquid ratio, extraction time, alcohol density, the microwave power which affected the rate of total flavone relative extraction.

在单因素试验的基础上，采用四元二次通用旋转组合试验优化柑橘皮渣发酵液总黄酮的提取工艺，用曲面响应法对影响总黄酮得率的料液比，提取时间，乙醇浓度，微波功率的最佳水平范围进行研究。

MethodsGuided by the contents of mannitol in Sparganium stoloniferum, uniform design, response surface analysis and path analysis were used to optimize microwave extraction process by combining with single factor experiment.

方法以甘露醇含量为响应指标，通过均匀试验设计，采用二次响应曲面和通径分析并结合单因素实验优化三棱中甘露醇的微波辅助萃取工艺。

objective to optimize microwave extraction process of mannitol from sparganium stoloniferum.methodsguided by the contents of mannitol in sparganium stoloniferum, uniform design, response surface analysis and path analysis were used to optimize microwave extraction process by combining with single factor experiment.resultsobtained response surface equation is notable at the level a.01 and the relative error of the predicted value from the model was smaller than 1%.

目的优化三棱中甘露醇的微波辅助萃取工艺。方法以甘露醇含量为响应指标，通过均匀试验设计，采用二次响应曲面和通径分析并结合单因素实验优化三棱中甘露醇的微波辅助萃取工艺。

Analysis indicates that the adjacent channel power is a quadratic function of predistorter efficients. A new optimization method is given which uses the predicted ACP surface to obtain fast convergence and simulation results show that a 20dB reduction in the third IMD and a 10dB reduction in the quatic IMD are achievable.

得出结论为：分析表明功放输出的邻信道功率是预失真器系数的二次函数；利用了新的自适应算法即使用预测的ACP曲面以提供更快的收敛速度；仿真结果表明，3阶产物可获得20dB以上的改善，5阶产物可获得10dB以上的改善。

Some specific problems in connection with blade modeling, such as spanning characteristic mesh, interpolation of curve face modeling, precise presentation arc by second order NURBS curve, node interpolation algor...

深入探讨了在叶片构造过程中遇到的剖分网格确定、插值曲面构造、圆弧的二次NURBS曲线精确表示、NURBS曲线节点插入算法及其升降阶等关键性技术问题。

Through practical application, this system can deal with the cutter tool path file of counters, groves, holes, curves and surfaces directly, not need to do second-managing.

通过实践验证，本系统能够直接处理轮廓、内槽、孔系、曲线及曲面的刀具路径文件，不需人工再做二次处理。

Traditionally ellipsoids and hyperboloids are modeled as implicit surfaces or through the use of rational surface schemes. The existing methods for generating spheres or quadrics have shortcoming such as the rational parameterizations for these surfaces are non-uniform, the resulting scheme cannot represent these surfaces in their natural acr-length parameterization and the implementation of the scheme is complex.

长久以来，Subdivision方法对一些看似简单却又在计算机图形学中有着重要作用的曲线曲面的造型非常困难，即使是对简单的圆和球的生成也很困难，已有的一些生成球或二次曲面的Subdivision方法一般都有太复杂、不能自然弧长参数化或者计算量太大等缺点。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新