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    • 12. 发明授权
    • Constructing solid models using implicit functions defining connectivity
relationships among layers of an object to be modeled
    • 使用隐式函数构建实体模型,定义要建模的对象的层之间的连接关系
    • US6100893A
    • 2000-08-08
    • US862216
    • 1997-05-23
    • Mark T. EnszMark A. GanterChek T. LimDuane W. StortiGeorge M. Turkiyyah
    • Mark T. EnszMark A. GanterChek T. LimDuane W. StortiGeorge M. Turkiyyah
    • G06T17/20G06T17/00
    • G06T17/20
    • A solid model is constructed from surface point data that represent layers of an object. The model is represented as the level set of an implicit function that is fitted to the surface point data. In the two-dimensional application of the technique, a Delaunay triangulation is performed for each layer. In this step, surface points are connected to form Delaunay triangles; the data points are the vertices of the Delaunay triangles. A circumcircle is then created around each Delaunay triangle, passing through the three vertices of the triangle. To decimate the circumcircle data, overlapping circumspheres are merged according to a merging criterion. A pseudo-union of implicit functions for the reduced number of circumcircles provides an initial implicit function for the layer. Errors in the implicit function are substantially reduced by optimizing the position and/or radii of the circumcircles. The implicit functions for a plurality of adjacent layers are blended to define an implicit function for the object that is used for reconstruction or modeling of the object. The technique is generally extended to n dimensional objects by using simplices instead of the Delaunay triangles and hyperspheres instead of the circumcircles. The method is capable of constructing solid models with highly localized surface curvature.
    • 实体模型由表示对象层的表面点数据构成。 该模型表示为拟合到表面点数据的隐式函数的级别集合。 在该技术的二维应用中,对于每个层执行Delaunay三角测量。 在此步骤中,表面点连接形成Delaunay三角形; 数据点是Delaunay三角形的顶点。 然后在每个Delaunay三角形周围创建一个外接圆,穿过三角形的三个顶点。 为了抽取外接圆周数据,根据合并标准合并重叠的圆周。 减少数量的外接圆的隐式函数的伪联合提供了层的初始隐式函数。 通过优化外接圆的位置和/或半径来显着减少隐含函数中的错误。 混合多个相邻层的隐含函数以定义用于对象的重构或建模的对象的隐式函数。 该技术通常通过使用简单代替Delaunay三角形和超球体而不是外接圆来扩展到n维对象。 该方法能够构建具有高度局部化表面曲率的实体模型。
    • 13. 发明授权
    • 3D objects morphing employing skeletons indicating symmetric differences
to define intermediate objects used in morphing
    • 3D对象变形使用指示对称差异的骨架来定义在变形中使用的中间对象
    • US6094199A
    • 2000-07-25
    • US862621
    • 1997-05-23
    • George M. TurkiyyahDuane W. StortiMark A. Ganter
    • George M. TurkiyyahDuane W. StortiMark A. Ganter
    • G06T3/40G06T15/00
    • G06T3/0093G06T3/4007
    • The present invention provides a unified, automated approach to 3D object interpolation and 3D morphing based on a geometric descriptor known as the skeleton. The skeleton of an object consists of the closure of the set of points minimally equidistant from two points on the object's boundary. An "intermediate 3D object" between a pair of two other 3D objects is obtained as the (trimmed) skeleton of the symmetric difference of the pair of objects. By applying this process recursively, any desired number of intermediate 3D objects between a first and a last object may be obtained to produce a discrete 3D morph. A discrete morph can be thought of as an animation starting from the initial object and ending with the final object after a given number of the intermediate objects. Alternatively, the skeleton is used to identify corresponding points on the surfaces of the objects. Interpolation between the location of the corresponding points is then used to determine a continuum of intermediate 3D objects.
    • 本发明提供了一种基于被称为骨架的几何描述的3D对象插值和3D变形的统一的自动化方法。 对象的骨架包括从对象边界上的两个点最小等距的点集合的闭合。 获得一对另外的3D对象之间的“中间3D对象”作为该对对象的对称差异的(修剪)骨架。 通过递归地应用该过程,可以获得在第一和最后一个对象之间的任何期望数量的中间3D对象以产生离散的3D变形。 离散变体可以被认为是从初始对象开始的动画,并在给定数量的中间对象之后以最终对象结束。 或者,骨架用于识别对象表面上的相应点。 然后使用对应点的位置之间的插值来确定中间3D对象的连续体。