The Mathematical Structure of Raster Graphics presents a mathematical characterization of the structure of raster graphics, a popular and diverse form of computer graphics. The semantics and theory of the mathematical structure of raster graphics are discussed. Notations that help to clarify some of the concepts generally considered to be fundamental to computer graphics are included. Comprised of seven chapters, this book begins with a description of a general framework for specifying and manipulating scenes. Basic graphic entities, called primitive graphic objects, are defined using a simple notation over a Euclidean space. The reader is then introduced to a semantics of visibility; a mathematical semantics of rendering, developed using the very basic notion of measure; and a mathematical formalization of bit-mapped graphics. A framework for specifying illumination models is also described, along with the complexity of abstract ray tracing. This monograph will be a useful resource for undergraduate and graduate students, researchers, and practitioners in the fields of mathematics and computer graphics, and to those with some basic computer graphics background.
This book begins with an account of the author's ancestral roots in Norway, Denmark and Great Britain and ends which his retirement in Happy Valley, Oregon, where he served as its Mayor from 1998 to 2006. His ancestors emigrated to America and fought and died in its wars, pioneered newly acquired territories and states, eventually reaching Eugene, Oregon, for which the author was named. His history includes surviving his oftentimes grim childhood in a dysfunctional family beset with serious domestic abuse and mental illness. The author describes his joy of discovering the stories of his ancestors' triumphs and tragedies. Their stories have all the drama of murder, suicide, war, crime, persecution, poverty, addiction, illicit affairs, abandonment, arson, insanity, domestic abuse, and other tragedies but also many triumphs. The sublime and spiritual contrasts with the carnal and depraved. It includes the sad story of the expanding frontier experience of American pioneers displacing native Americans and enslaving Blacks. The heart of this book is the creation of the author's immediate family and struggling to be successful as a prominent Oregon lawyer, local politician, local Mormon religious leader, and most importantly a father and husband. In part this is a religious autobiography. It is like biblical stories, an accounting and evaluation of being in the World but not of the World, an acknowledgement of how he has seen God's hand in the details of his life, the story of his religious conversion and path of discipleship through this veil of tears, seeking salvation. His story, therefore, ends with his evaluation, for the reader's benefit, of his lessons learned. His hope is that these lessons will help the reader appreciate his perspective and hopefully avoid his mistakes not the least of which were his conflicts, especially with political and religious extremists who increasingly bedeviled him during the highly polarized first two decades of the 21st century. This is also his intellectual and political autobiography. His faith was not one of withdrawal from the world into monastic simplicity, but rather one of enthusiastically engaging a complex world by gaining a higher education and using his knowledge and values to help the City of Happy Valley become a thriving and attractive community for likeminded families. It includes the story of how he led Happy in becoming Oregon's fastest growing city. It is also the story of his interaction with the leaders of Clackamas County and all its cities, including both allies and opponents. Lastly, this book includes the story of his legal career. He was fortunate to play a significant role in two leading law firms and his 40-year career helped shape the built environment of the City of Portland, the Metro Region, and the State of Oregon. He worked with many prominent and interesting Oregonians in the process. His legal career was completed by serving for almost two years as a senior legal missionary for his church in the Pacific Area including Australia, New Zealand, and the South Pacific islands.
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