Geometric concepts for geometric design

Description

Often a solution to a problem lies simply in finding its correct description. It is this underlying concept that consolidates the text of this unique and lively survey of geometric ideas. In Geometric Concepts for Geometric Design, its authors provide a way in which to visualize a variety of geometric problems and present the tools for their accurate representation. Disassociating fundamental ideas and methods from special applications, they clarify these concepts for the reader and allow him to apply the material to other problems of a geometric nature. Relying on the idea that a picture is worth a thousand words, the text is beautifully illustrated with a variety of elucidating figures and diagrams. Anyone attracted to or wishing a deeper understanding of the beauty of geometric mysteries will find this book an engaging and invaluable guide.  Read more... pt. I. Some linear algebra. 1. Linear systems -- 2. Linear spaces -- 3. Least squares -- pt. II. Images and projections. -- 4. Parallel projections -- 5. Moving the object -- 6. Perspective drawings -- 7. The mapping matrix -- 8. Reconstruction -- pt. III. Affine geometry. 9. Affine space -- 10. The barycentric calculus -- 11. Affine maps -- 12. Affine figures -- 13. Quadrics in affine spaces -- 14. More on affine quadrics -- 15. Homothetic pencils -- pt. IV. Euclidean geometry. 16. The euclidean space -- 17. Some euclidean figures -- 18. Quadrics in euclidean space -- 19. Focal properties -- pt. V. Some projective geometry. 20. The projective space -- 21. Projective maps -- 22. Some projective figures -- 23. Projective quadrics -- pt. VI. Some descriptive geometry. 24. Associated projections -- 25. Penetrations -- pt. VII. Basic algebraic geometry. 26. Implicit curves and surfaces -- 27. Parametric curves and surfaces -- 28. Some elimination methods -- 29. Implicitization, inversion and intersection -- pt. VIII. Differential geometry. 30. Curves -- 31. Curves on surfaces -- 32. Surfaces.