Surveys, tutorials, and research papers from a summer 2002 workshop examine a range of topics in algebraic geometry and geometric modeling. Papers are divided into sections on modeling curves and surfaces, multisided patches, implicitization and parametrization, topic varieties, and mixed volume and resultants, and papers from both disciplines are included in each section. Some specific topics include polar forms, interference analysis of conics and quadrics, rational M-patches and tensor-border patches, and toric ideals, real toric varieties, and the moment map. A translation of an 1841 paper which foreshadows the modern application of mixed volumes in algebraic geometry is also included.