In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that ...In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc展开更多
为使纬编针织物具有更真实的力学效果和体积感,在改进的弹簧-质点模型基础上对线圈进行结构建模。同时采用插值算法,在相邻型值点间插入2个新的型值点,用非均匀有理B样条曲线(NURBS)连接线圈型值点,解决了NURBS不能穿过所有型值点的问...为使纬编针织物具有更真实的力学效果和体积感,在改进的弹簧-质点模型基础上对线圈进行结构建模。同时采用插值算法,在相邻型值点间插入2个新的型值点,用非均匀有理B样条曲线(NURBS)连接线圈型值点,解决了NURBS不能穿过所有型值点的问题。为模拟股线的捻度,以此样条曲线为几何中心,用4根圆柱围绕,通过对相邻型值点的空间坐标计算3个相对欧拉角,对圆柱进行相应的旋转变换。测量了真实线圈的形变量,分析出线圈形变量与质点位移量的关系来模拟线圈变形。用Velocity-Verlet数值积分方法求解力学方程,计算各质点位移。借助于Microsoft Visual Studio 2010集成开发工具和Open GL三维绘图函数库,在计算机上实现了纬编织物的三维建模和变形仿真。展开更多
文摘In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc
文摘为使纬编针织物具有更真实的力学效果和体积感,在改进的弹簧-质点模型基础上对线圈进行结构建模。同时采用插值算法,在相邻型值点间插入2个新的型值点,用非均匀有理B样条曲线(NURBS)连接线圈型值点,解决了NURBS不能穿过所有型值点的问题。为模拟股线的捻度,以此样条曲线为几何中心,用4根圆柱围绕,通过对相邻型值点的空间坐标计算3个相对欧拉角,对圆柱进行相应的旋转变换。测量了真实线圈的形变量,分析出线圈形变量与质点位移量的关系来模拟线圈变形。用Velocity-Verlet数值积分方法求解力学方程,计算各质点位移。借助于Microsoft Visual Studio 2010集成开发工具和Open GL三维绘图函数库,在计算机上实现了纬编织物的三维建模和变形仿真。
