3D Analytic Geometry in Code-Ready Algorithms

Analytic geometry is geometry carried out in algebra and trigonometry rather than in drawing. There are algebraic representations of all of the geometrical shapes, e.g., points, lines, rays and vectors; planes, squares, rectangles and circles; spheres, cylinders, rectangular solids.In their algebraic form geometric entities lend themselves to manipulation by algorithms, especially when executed by a computer program. For these reasons analytic geometry (AG) finds wide application in engineering, physics, aviation, rocketry – not to mention computer gaming.3D Analytic Geometry in Code-Ready Algorithms presents the discipline explicitly for software engineers. AG mathematics and object-oriented program design are made for each other. A lexicon inspired by object-oriented programming syntax is a natural and powerful form of expression for the concepts and techniques of AG. For example, a method of the Plane class furnishes the point in space at which a given line intersects the plane. This method is the one place in the program that implements the mathematics of plane/line intersection. Thus it is built-in for use with any instance of Plane and Line, no matter where located or how oriented.To hint further at this, consider the Aglexicon treatment of a common problem in AG. Given a point p in space and a line that does not pass through the point, find the point pc on the line that is closest to p. A very compact expression yields the point: pc = line.GetPoint( line.ProjectOntoMe( Vector( line.PO, p ) ) )In addition, the book presents the mathematics for displaying 3D objects on the 2D surface of a computer screen.This introduction to the subject promises three things. Anyone who studies the material will develop an intuitive grasp of analytic geometry. In addition, those who wish to can work to a thorough understanding of its mathematics. Finally, software developers will find a specification for a library of object-oriented classes that embody the forms and algorithms of analytic geometry, which will outfit their programs with the power and beauty of its methods. Read more