Geometry of Curves and Surfaces with MAPLE

1. Front Matter

   Pages i-x

   PDF

2. MAPLE V: A Quick Reference

   1. MAPLE V: A Quick Reference

      • Vladimir Rovenski

      Pages 1-4

3. Functions and Graphs with MAPLE

   1. Front Matter

      Pages 5-5

      PDF

   2. Graphs of Tabular and Continuous Functions

      • Vladimir Rovenski

      Pages 7-20

   3. Graphs of Composed Functions

      • Vladimir Rovenski

      Pages 21-32

   4. Interpolation of Functions

      • Vladimir Rovenski

      Pages 33-40

   5. Approximation of Functions

      • Vladimir Rovenski

      Pages 41-44

4. Curves with MAPLE

   1. Front Matter

      Pages 45-45

      PDF

   2. Plane Curves in Rectangular Coordinates

      • Vladimir Rovenski

      Pages 47-60

   3. Curves in Polar Coordinates

      • Vladimir Rovenski

      Pages 61-74

   4. Asymptotes of Curves

      • Vladimir Rovenski

      Pages 75-78

   5. Space Curves

      • Vladimir Rovenski

      Pages 79-94

   6. Tangent Lines to a Curve

      • Vladimir Rovenski

      Pages 95-109

   7. Singular Points on Curves

      • Vladimir Rovenski

      Pages 111-116

   8. Length and Center of Mass of a Curve

      • Vladimir Rovenski

      Pages 117-123

   9. Curvature and Torsion of Curves

      • Vladimir Rovenski

      Pages 125-132

   10. Fractal Curves and Dimension

       • Vladimir Rovenski

       Pages 133-149

   11. Spline Curves

       • Vladimir Rovenski

       Pages 151-171

   12. Non-Euclidean Geometry in the Half-Plane

       • Vladimir Rovenski

       Pages 173-187

   13. Convex Hulls

       • Vladimir Rovenski

       Pages 189-190

This concise text on geometry with computer modeling presents some elementary methods for analytical modeling and visualization of curves and surfaces. The author systematically examines such powerful tools as 2-D and 3-D animation of geometric images, transformations, shadows, and colors, and then further studies more complex problems in differential geometry. Well-illustrated with more than 350 figures---reproducible using Maple programs in the book---the work is devoted to three main areas: curves, surfaces, and polyhedra. Pedagogical benefits can be found in the large number of Maple programs, some of which are analogous to C++ programs, including those for splines and fractals. To avoid tedious typing, readers will be able to download many of the programs from the Birkhauser web site. Aimed at a broad audience of students, instructors of mathematics, computer scientists, and engineers who have knowledge of analytical geometry, i.e., method of coordinates, this text will be an excellent classroom resource or self-study reference. With over 100 stimulating exercises, problems and solutions, {\it Geometry of Curves and Surfaces with Maple} will integrate traditional differential and non- Euclidean geometries with more current computer algebra systems in a practical and user-friendly format.

• Computational Geometry
• Geometry
• Modeling & Simulations
• ksa
• animation
• Area
• computational geometry
• computer algebra
• Dragon curve
• fractal
• Geometrie
• mathematics
• modeling
• Peano curve
• plane
• polygon
• simulation
• Spline
• visualization

"I was hunting for a book that would provide a set of practical exercises for the students of a graduate course entitled 'Geometric Modeling for Computer Graphics'.... The title of [this] book sounds appealing for such a purpose.... Almost every topic you could imagine about curves and surfaces is somewhere inside: this includes common, and less common, definitions and properties (parametric and implicit form, rectangular and polar form, tangent, asymptote, envelope, normal, curvature, torsion, twist, length, center of mass, evolute and involute, pedal and podoid, etc) as well as the whole menagerie of usual, and less usual, curves and surfaces (polynomials and rational polynomials, B-splines, Bezier,  Hermite, Catmul--Rom, Beta-splines, scalar and vector fields, polygons and  polyhedra, fractals, etc).

Of course 310 pages is a bit short to present all these topics deeply, but for each of them, there is at least a definition, an example, a piece of Maple source code and the resulting figure generated by the code (note that all the code pieces can be downloaded from the author’s web page).... The index is rich enough to easily find a topic you are interested in. 

To conclude, the book is clearly valuable for at least three kinds of people: first, people who are familiar with the mathematical aspect of curves and surfaces but unfamiliar with the computation and plotting possibilities providing by Maple; second, people who are familiar with Maple but unfamiliar with curves and surfaces; third, people who are unfamiliar with both topics."
— Computer Graphics Forum

“The book can be recommended to students ofmathematics, engineering or computer science, who have already a basic knowledge of MAPLE and are interested in the visualization of geometry.” (Anton Gfrerrer, zbMATH 0960.53001, 2021)

• Department of Mathematics, University of Haifa and Technion, Haifa, Israel

  Vladimir Rovenski

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