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    • 4. 发明授权
    • System, method and computer program product for modeling at least one section of a curve
    • 用于对曲线的至少一个部分进行建模的系统,方法和计算机程序产品
    • US07333109B2
    • 2008-02-19
    • US10309969
    • 2002-12-04
    • Thomas A. GrandineThomas A. Hogan
    • Thomas A. GrandineThomas A. Hogan
    • G06T11/20G06F19/00
    • G06T11/203
    • A system, method and computer program product are provided for modeling at least one section of a curve. Each section can be modeled by initially providing a pair of positions (fi, fi+1) of the section of the curve including associated directions (di, di+1) and curvatures (κi, κi+1). Then, points b0, b1, b2, b3 and b4 can be identified based upon the pair of positions (fi, fi+1) and associated directions (di, di+1) and curvatures (κi, κi+1). Thereafter, a quartic interpolant p(t) can be determined over an interval (i≦t≦i+1) based upon points b0, b1, b2, b3 and b4 to thereby model the section of the curve. The quartic interpolant can be determined such that the interpolant p(t) has a position, direction and curvature equal to fi, di and κi, respectively, at t=i, and the interpolant p(t) has a position, direction and curvature equal to fi+1, di+1, and κi+1, respectively, at t=i+1.
    • 提供了用于对曲线的至少一个部分进行建模的系统,方法和计算机程序产品。 每个部分可以通过初始提供包括相关联的方向(d i)的曲线的部分的一对位置(f i,i,i,i, (i + 1)和曲率(kappa,i,i,i + 1)。 然后,点b 0,b 1,b 2,b 3 3和b 4, 可以基于一对位置(f i,i,i,i + 1)和相关联的方向(d i,i, SUB&gt; i + 1&gt;)和曲率(kappa,i,i + 1)。 此后,可以基于点b 0,b 1,b 2的区间(i <= t i = 1 + 1)来确定四次内插器p(t) 2&lt; 2&gt;,b 3&lt; 3&gt;和b 4&gt;之间,从而对曲线的部分进行建模。 可以确定四次内插器,使得内插器p(t)具有等于f i,i i,i i的位置,方向和曲率, SUB>,在t = i,并且内插p(t)具有等于f 1 i + 1,i i + 1的位置,方向和曲率, 和kappa i + 1分别在t = i + 1。
    • 6. 发明申请
    • PARAMETRIC GEOMETRY MODEL FOR A BLENDED WING BODY
    • 用于混合身体的参数几何模型
    • US20090152392A1
    • 2009-06-18
    • US11958143
    • 2007-12-17
    • Thomas A. HoganChristopher K. DroneyDino Roman
    • Thomas A. HoganChristopher K. DroneyDino Roman
    • B64C1/00
    • B64C39/10B64C2039/105B64F5/00G06F17/5095
    • Lofting of a Blended Wing Body air vehicle is accomplished by first determining the required payload volume of the air vehicle. The payload volume is then analyzed to determine a list of corner points of the payload volume. The list of points is passed to a Loft Module as keep-out points and a body portion of the blended wing body is established using a faceted minimum volume which encloses all of the provided keep-out points. A trapezoidal wing shape and size is then determined to accommodate aerodynamic performance requirements. A leading edge of the body portion and trapezoidal wing leading edge are trimmed and a trailing edge of the body portion and trapezoidal wing trailing edge are blended. A leading edge elevation is established and with leading edge radius as an input all other point coordinates and all tangents and remaining curvatures to smoothly enclose the payload volume in a first set of aerodynamic sections are defined. The aerodynamic requirements of the trapezoidal wing including Wing Thickness, Camber, Twist and Shear establish a second set of aerodynamic sections and sections in a transition region between the body portion and the trapezoidal wing are then defined. The blended wing body is then lofted based on the first plurality of sections, second plurality of sections and transition sections.
    • 混合翼的车身通过首先确定空中车辆的所需有效载荷体积来实现车身空中车辆。 然后分析有效载荷体积以确定有效载荷体积的角点列表。 点数列表作为保留点传递给阁楼模块,并且使用包围所有提供的保留点的面最小体积来建立混合翼体的身体部分。 然后确定梯形翼形和尺寸以适应空气动力学性能要求。 主体部分和梯形翼前缘的前缘被修剪,并且主体部分的后缘和梯形翼后缘被混合。 确定了前缘高程,并以前缘半径作为输入,定义所有其他点坐标以及所有切线和剩余曲率以平滑地将有效负载体积包围在第一组空气动力学截面中。 然后定义梯形翼片的空气动力学要求,包括翼厚度,弯度,扭转和剪切,建立第二组空气动力学截面和在主体部分和梯形翼之间的过渡区域中的截面。 然后,混合翼体基于第一多个部分,第二多个部分和过渡部分而放置。
    • 7. 发明授权
    • System, method and computer program product for modeling a transition between adjoining surfaces
    • 用于建模相邻表面之间过渡的系统,方法和计算机程序产品
    • US07518609B2
    • 2009-04-14
    • US11420581
    • 2006-05-26
    • Thomas A. GrandineThomas A. Hogan
    • Thomas A. GrandineThomas A. Hogan
    • G09G5/00G06T11/20G06T15/40
    • G06T17/30
    • According to one aspect of exemplary embodiments of the present invention, a method is provided for modeling a transition between adjoining surfaces. The method includes determining a curve of intersection of two adjoining surfaces, where the curve includes a plurality of points. For each of at least some of the points, the method includes selecting a point of the curve of intersection, and determining end points of a section of the transition located at the selected point, where each end point is located on a respective one of the adjoining surfaces. The method also includes determining a shape of the section of the transition, where the shape of the section for each of at least some of the points models the transition between the adjoining surfaces. The transition is curvature continuous with a first curvature at the end points and a second, different curvature at a portion therebetween.
    • 根据本发明的示例性实施例的一个方面,提供了一种用于对相邻表面之间的过渡进行建模的方法。 该方法包括确定两个相邻表面的交点的曲线,其中曲线包括多个点。 对于至少一些点中的每一个,所述方法包括选择交叉曲线的点,以及确定位于所选择的点处的转变的部分的终点,其中每个终点位于相应的一个 相邻的表面。 该方法还包括确定过渡部分的形状,其中至少一些点中的每一个的部分的形状对相邻表面之间的过渡进行建模。 该转变是在端点处具有第一曲率的连续曲率和在它们之间的部分处的第二不同曲率。