This text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many applications in engineering analysis, approximation, and curve plotting problems. Because of its usefulness for computing, the algebraic approach is the main theme, but a brief discussion of the synthetic approach is also presented as a way of gaining additional insight before proceeding with the algebraic manipulation. The authors start with simple interpolation, including splines, and extend this in an intuitive fashion to the production of conic sections. They then introduce projective coordinates as tools for dealing with higher order curves and singular points. They present many applications and concrete examples, including parabolic interpolation, geometric approximation, and the numerical solution of trajectory problems. In the final chapter, they apply the basic theory to the construction of finite element basis functions and surface interpolants over nonregular shapes. Professionals, students, and researchers in applied mathematics, solid modeling, graphics, robotics, and engineering design and analysis will find this a useful reference.
Review of the hardback: 'The authors have displayed considerable erudition and ability in dealing with a difficult topic. Their practical, step-by-step approach to algebraic curves and surface interpolation is very commendable in view of the complexity of the subject.' J. A. Prescott, Robotica
Review of the hardback: 'This looks like a delightful way to introduce students to the subject.' The Mathematical Association of America
Review of the hardback: '... an elegant and serious introduction to the basic concepts and results of (elementary) algebraic geometry.' European Maths Society Journal
"The whole thing is fascinating...a delightful way to introduce students to the subject." MAA Online
"This work serves quite well as a textbook on algebraic and projective geometry and their applications to computer-aided design." Mathematical Reviews