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个人简介
My interest in visualization was sparked while learning Euclidean geometry. Later, while being a Ph.D. student in Mathematics at the University of Illinois (Champaign-Urbana), and studying multi-dimensional geometry I became frustrated by the absence of visualization. Basically, we were doing Algebra which was being interpreted as Geometry but without the fun and benefit of pictures. I kept wondering about ways to make accurate “multi-dimensional pictures” and derive insights about what may or may not be true in the multi-dimensional worlds. Since parallelism is the fundamental concept in geometry, and not orthogonality which uses the plane very fast, I experimented with putting the coordinate axes parallel to each other.
In 1959 Prof. S.S.Cairns, during a lecture in his Topology course, lamented our inability to visualize “high-dimensions” and prompted us for suggestions. I shared with the class the idea of parallel coordinates (abbr. ||-coords). In turn Prof. Cairns mentioned it to another topologist Prof. D. Bourgin and they both encouraged me to pursue the idea. Other than deriving the basics like the point ↔ line duality, it took me many years to take their advice seriously. It was in 1977 while giving a Linear Algebra course that I was challenged by my students to “show” them some multi-dimensional spaces. This was the catalyst leading to the subsequent development of the methodology : How do multi-dimensional lines, planes, curves, surfaces etc look in ||-coords ? Later I had the good fortune to collaborate with Bernard Dimsdale (an associate of John von Neuman) , at the IBM Los Angeles Science Center, who made many important contributions.
In 1959 Prof. S.S.Cairns, during a lecture in his Topology course, lamented our inability to visualize “high-dimensions” and prompted us for suggestions. I shared with the class the idea of parallel coordinates (abbr. ||-coords). In turn Prof. Cairns mentioned it to another topologist Prof. D. Bourgin and they both encouraged me to pursue the idea. Other than deriving the basics like the point ↔ line duality, it took me many years to take their advice seriously. It was in 1977 while giving a Linear Algebra course that I was challenged by my students to “show” them some multi-dimensional spaces. This was the catalyst leading to the subsequent development of the methodology : How do multi-dimensional lines, planes, curves, surfaces etc look in ||-coords ? Later I had the good fortune to collaborate with Bernard Dimsdale (an associate of John von Neuman) , at the IBM Los Angeles Science Center, who made many important contributions.
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mag(2013)
Handbook of Computational Statisticspp.299-333, (2012)
DATApp.297-319, (2012)
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