Curve Flow

Discover the remarkable story of an orphaned Black boy who grew up to become the groundbreaking architect to the stars, Paul R. Williams. A stunning nonfiction picture-book biography from the Caldecott Honor–winning author and NAACP Image Award–nominated artist. As an orphaned Black boy growing up in America in the early 1900s, Paul R. Williams became obsessed by the concept of "home." He not only dreamed of building his own home, he turned his dreams into drawings. Defying the odds and breaking down the wall of racism, Williams was able to curve around the obstacles in his way to become a world-renowned architect. He designed homes for the biggest celebrities of the day, such as Frank Sinatra and Lucille Ball, and created a number of buildings in Los Angeles that are now considered landmarks. From Andrea J. Loney, the author of the Caldecott Honor Book Double Bass Blues, and award-winning artist Keith Mallett comes a remarkable story of fortitude, hope, and positivity.

Discover the remarkable story of an orphaned Black boy who grew up to become the groundbreaking architect to the stars, Paul R. Williams. A stunning nonfiction picture-book biography from the Caldecott Honor–winning author and NAACP Image Award–nominated artist. As an orphaned Black boy growing up in America in the early 1900s, Paul R. Williams became obsessed by the concept of "home." He not only dreamed of building his own home, he turned his dreams into drawings. Defying the odds and breaking down the wall of racism, Williams was able to curve around the obstacles in his way to become a world-renowned architect. He designed homes for the biggest celebrities of the day, such as Frank Sinatra and Lucille Ball, and created a number of buildings in Los Angeles that are now considered landmarks. From Andrea J. Loney, the author of the Caldecott Honor Book Double Bass Blues, and award-winning artist Keith Mallett comes a remarkable story of fortitude, hope, and positivity.

In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.

The Soil Conservation Service (SCS) curve number (CN) method is one of the most popular methods for computing the runoff volume from a rainstorm. It is popular because it is simple, easy to understand and apply, and stable, and accounts for most of the runoff producing watershed characteristics, such as soil type, land use, hydrologic condition, and antecedent moisture condition. The SCS-CN method was originally developed for its use on small agricultural watersheds and has since been extended and applied to rural, forest and urban watersheds. Since the inception of the method, it has been applied to a wide range of environments. In recent years, the method has received much attention in the hydrologic literature. The SCS-CN method was first published in 1956 in Section-4 of the National Engineering Handbook of Soil Conservation Service (now called the Natural Resources Conservation Service), U. S. Department of Agriculture. The publication has since been revised several times. However, the contents of the methodology have been nonetheless more or less the same. Being an agency methodology, the method has not passed through the process of a peer review and is, in general, accepted in the form it exists. Despite several limitations of the method and even questionable credibility at times, it has been in continuous use for the simple reason that it works fairly well at the field level.

Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.