Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines
Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines
复制标题
特征曲线的尖点以及路径和条纹线的交叉感知可视化
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
O. Sorkine
中科院分区：
文献类型：
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作者：
T. Weinkauf;H. Theisel;O. Sorkine
我们分析了向量场的特征曲线，并报告了它们在空间投影中具有顶点的位置，即曲线上具有突然转向切线方向的孤立点。尖点出现在相应切线向量场的投影呈现临界点的地方。我们证明这样的顶点只可能出现在条纹线和路径线上，而它们不能出现在流和时间线上。结果表明，尖点与特征曲线的自交密切相关。我们在一个新的算法中利用这些信息来创建路径和条纹线的整洁的静态可视化。
We analyze characteristic curves of vector fields and report on locations where they have cusps in their spatial projection, i.e., isolated points on the curve with abruptly turning tangent direction. Cusps appear in places where a projection of the corresponding tangent curve vector field exhibits critical points. We show that such cusps are only possible for streak and path lines, whereas they cannot appear on stream and time lines. Cusps turn out to be closely related to self-intersections of characteristic curves. We utilize this information in a new algorithm to create uncluttered static visualizations of path and streak lines.