CAREER: Theory and Practice of Applied Geometric Computing

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Computational geometry arose out of the need for manyscience and engineering applications of geometric computing.Over the last two decades, the field has emerged as a rich,mature, and mathematically rigorous discipline. However,despite its impressive achievements well-received in thetheoretical computer science community, computationalgeometry has had limited impact in the practical areas ofgeometric computing. As advocated by the recentComputational Geometry Task Force Report, it is important toreorient the field towards providing more practicalsolutions to the specific needs of the applications that usegeometric computing, and towards focusing on new"bottleneck" problems of identifiably important practicalareas. In this proposed career plan, we intend to developour research career toward this goal, by working on the fullcomputational pipelines of some important real-worldapplications of geo-metric computing, including air trafficmanagement (conflict prediction), graphics and scientificvisualization (I/O-efficient isosurface extraction, I/O-efficient direct volume rendering, external-memory view-dependent surface simplification), and manufacturing(maximum scatter traveling salesperson problem (TSP)). Animportant aspect of the work is to examine the fullcomputational pipelines of the practical applications toidentify and formulate critical tasks into new algorithmicquestions, extend computational geometry methodologies todevise novel solutions, and finally implement and integratethe developed algorithms into the pipelines to evaluatetheir practical ef-fectiveness in the original real-lifeapplications. Key components of the plan are the expectedrich interactions between theory and practice, and the aimof designing simple, easy-to-implement geometric algorithmsthat are efficient both practically and theoretically. Inthe long term, we expect to be able to have real impact onthese important practical areas of geometric computing, andat the same time enrich the knowledge body of the field ofcomputational geometry. The proposed educational planincludes introduction of new courses, involvement of bothgraduate and undergraduate students in the proposed researchprojects, participation in an outreach program, and furtherdevelopment of a research laboratory.