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1. 发明申请

US20050062763A1 System and method for contiguous images from polygons 失效
标题翻译：来自多边形的连续图像的系统和方法
公开(公告)号：US20050062763A1
公开(公告)日：2005-03-24
申请号：US10963868
申请日：2004-10-13
申请人： Daniel Keim , Stephen North , Christian Panse
发明人： Daniel Keim , Stephen North , Christian Panse
IPC分类号： G06T15/50 , G09B29/00 , G09G5/00
CPC分类号： G09B29/005 , G09B29/00 , G09B29/001
摘要： A system, method and computer-readable media are disclosed for generating an image from another image of contiguous polygons and a vector containing values to which areas of corresponding polygons are scaled. The method embodiment relates to generating an image from a plurality of contiguous polygons having vertices. The method comprises calculating a shape value associated with a polygon, calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon, calculating a shape distortion by comparing the shape value and the altered shape value and determining whether to accept the altered polygon based on the calculated shape distortion.
摘要翻译：公开了用于从邻接多边形的另一图像生成图像的系统，方法和计算机可读介质，以及包含对应多边形的区域进行缩放的值的向量。方法实施例涉及从具有顶点的多个相邻多边形生成图像。该方法包括计算与多边形相关联的形状值，计算与改变的多边形相关联的改变的形状值，改变的多边形是多边形的改变版本，通过比较形状值和改变的形状值来计算形状失真并确定是否基于计算出的形状失真来接受改变的多边形。

2. 发明授权

US07737998B1 System and method for contiguous images from polygons 失效
标题翻译：来自多边形的连续图像的系统和方法
公开(公告)号：US07737998B1
公开(公告)日：2010-06-15
申请号：US11857097
申请日：2007-09-18
申请人： Daniel Keim , Stephen Charles North , Christian Panse
发明人： Daniel Keim , Stephen Charles North , Christian Panse
IPC分类号： G09G5/00 , G06T11/20
CPC分类号： G09B29/005 , G09B29/00 , G09B29/001
摘要： A system, method and computer-readable media are disclosed for generating an image from another image of contiguous polygons and a vector containing values to which areas of corresponding polygons are scaled. The method embodiment relates to generating an image from a plurality of contiguous polygons having vertices. The method comprises calculating a shape value associated with a polygon, calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon, calculating a shape distortion by comparing the shape value and the altered shape value and determining whether to accept the altered polygon based on the calculated shape distortion.
摘要翻译：公开了用于从邻接多边形的另一图像生成图像的系统，方法和计算机可读介质，以及包含对应多边形的区域进行缩放的值的向量。方法实施例涉及从具有顶点的多个相邻多边形生成图像。该方法包括计算与多边形相关联的形状值，计算与改变的多边形相关联的改变的形状值，改变的多边形是多边形的改变版本，通过比较形状值和改变的形状值来计算形状失真，并确定是否基于计算出的形状失真来接受改变的多边形。

3. 发明授权

US06853386B1 Method for generating contiguous cartograms 有权
标题翻译：生成连续图形的方法
公开(公告)号：US06853386B1
公开(公告)日：2005-02-08
申请号：US10371714
申请日：2003-02-21
申请人： Daniel Keim , Stephen Charles North , Christian Panse
发明人： Daniel Keim , Stephen Charles North , Christian Panse
IPC分类号： G06T15/50 , G09B29/00 , G09G5/00
CPC分类号： G09B29/005 , G09B29/00 , G09B29/001
摘要： The present invention is a method for generating cartograms using a base map of contiguous polygons and a vector containing values to which areas of corresponding polygons are scaled. The general problem is intractable, so an iterative heuristic is proposed. The heuristic is based on “scanlines.” The scanlines may be defined automatically (typically, by placing a grid over the map) or entered manually (to provide finer control over the results). At each step, one scanline is chosen and a new candidate map is made by adjusting the vertices of polygons intersected by the scanline, moving them orthogonally to the scanline. A candidate solution is accepted if it improves the solution and preserves the input mesh's topology. Improvement depends on metrics for area and shape error. The solver is run until the improvement falls below some threshold, or a time limit or maximum number of iterations is reachedThe method determines shape error created by a candidate iterative step by first estimating a curvature function of the polygon and then performing a Fourier transform on the function to yield a shape representation that is relatively independent of scale, translation and rotation of the polygon. The proposed iterative step is accepted or discarded based in part on the magnitude of the resulting shape error.
摘要翻译：本发明是一种使用邻接多边形的基本映射生成图形的方法，以及包含对应多边形的区域进行缩放的值的向量的方法。一般的问题是棘手的，所以提出了迭代启发式。启发式是基于“扫描线”。可以自动定义扫描线（通常通过在地图上放置网格）或手动输入扫描线（以便对结果提供更好的控制）。在每个步骤中，选择一条扫描线，并通过调整与扫描线相交的多边形的顶点，将它们与扫描线正交移动，从而形成新的候选图。如果改进解决方案并保留输入网格的拓扑，则接受候选解决方案。改进取决于面积和形状误差的度量。解算器运行直到改进低于某个阈值，或者达到时间限制或最大迭代次数。该方法通过首先估计多边形的曲率函数然后对该多边形进行傅立叶变换，来确定由候选迭代步骤产生的形状误差用于产生相对独立于多边形的尺度，平移和旋转的形状表示。部分地基于所得到的形状误差的大小来接受或丢弃所提出的迭代步骤。

4. 发明授权

US07286144B2 System and method for contiguous images from polygons 失效
标题翻译：来自多边形的连续图像的系统和方法
公开(公告)号：US07286144B2
公开(公告)日：2007-10-23
申请号：US10963868
申请日：2004-10-13
申请人： Daniel Keim , Stephen Charles North , Christian Panse
发明人： Daniel Keim , Stephen Charles North , Christian Panse
IPC分类号： G09G5/00 , G06T11/20
CPC分类号： G09B29/005 , G09B29/00 , G09B29/001
摘要： A system, method and computer-readable media are disclosed for generating an image from another image of contiguous polygons and a vector containing values to which areas of corresponding polygons are scaled. The method embodiment relates to generating an image from a plurality of contiguous polygons having vertices. The method comprises calculating a shape value associated with a polygon, calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon, calculating a shape distortion by comparing the shape value and the altered shape value and determining whether to accept the altered polygon based on the calculated shape distortion.
摘要翻译：公开了用于从邻接多边形的另一图像生成图像的系统，方法和计算机可读介质，以及包含对应多边形的区域进行缩放的值的向量。方法实施例涉及从具有顶点的多个相邻多边形生成图像。该方法包括计算与多边形相关联的形状值，计算与改变的多边形相关联的改变的形状值，改变的多边形是多边形的改变版本，通过比较形状值和改变的形状值来计算形状失真并确定是否基于计算出的形状失真来接受改变的多边形。

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