3D-XplorMath (formerly 3D-Filmstrip) is a highly interactive museum for exploring the visual aspects of the exciting and beautiful universe of mathematical objects and processes. It has been under continual development for over ten years by an international team of renowned mathematical researchers and educators, the 3DXM Consortium. It was originally developed for use in teaching and research, but recently the Consortium has been working hard to make it easy and enjoyable to use by anyone with mathematical curiosity and an appreciation for the visual and logical beauty of mathematics. This museum contains literally hundreds
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3D-XplorMath (formerly 3D-Filmstrip) is a highly interactive museum for exploring the visual aspects of the exciting and beautiful universe of mathematical objects and processes. It has been under continual development for over ten years by an international team of renowned mathematical researchers and educators, the 3DXM Consortium. It was originally developed for use in teaching and research, but recently the Consortium has been working hard to make it easy and enjoyable to use by anyone with mathematical curiosity and an appreciation for the visual and logical beauty of mathematics. This museum contains literally hundreds of well-known (and some not so well-known) mathematical objects, arranged logically into numerous "galleries", referred to as Categories. These include: Surfaces, Planar Curves, Space Curves, Polyhedra, Conformal Maps, Dynamical Systems, Waves, and (the latest) Fractals & Chaos. The "3D" in its name refers to the fact that 3D objects can be viewed in strikingly realistic stereo. If you would like to visit a Gallery of just some of the remarkable surfaces that can be created and manipulated with the program, go to: http://rsp.math.brandeis.edu/3D-XplorMath/Surface/gallery.html 3D-XplorMath differs from programs such as Mathematica, Maple, and Matlab that provide visualization back-ends for viewing objects, but require the user to first program the object and its visualization. 3D-XplorMath emphasizes ease of use and does not even require the user to have a pre-existing knowledge of the mathematical definition of an object in order to see it. Every mathematical object in its massive collection is not only pre-programmed, but also has carefully chosen default parameters and associated animations. Merely selecting a gallery object by its name from a menu presents an excellent initial view of the object. The user may then optionally use simple dialogs, controls, and menu choices to customize and animate this default view, perhaps after first learning about its background by choosing About This Object from the Documentation menu. Users can also create and animate new objects on their own by entering simple algebraic formulas into dialogs. All objects including user defined objects can be saved in several graphic formats, and animations can be saved as Quicktime movies. While The 3DXM Consortium is not asking a monetary payment for you to use 3D-XplorMath, we are asking for payment of a different sort: Please send us reports of any difficulties you have with the program and any suggestions you have for new mathematical objects or for improving the user interface and the documentation. Either send email to firstname.lastname@example.org, or if you prefer write your comments as a MacUpdate review.
We have improved the documentation.
We would very much like to know the extent to which our program is being used on "old" systems and hardware.
he new Free Pascal compilation runs on OS 10.4.11 and later.
Since our point clouds have been used for Monte Carlo typpe numerical computations, we have switched to the Mersenne Twister, a state of the art random number generator.
The control of the playback speed for movies was too hidden, so we added a slider control (visible only while a movie is playing).
The Plane Curve Category:
A demo showing rotating gear wheels has been added. The teeth of the gear wheels have circle involute flanks.
The Surface Category:
We have added more "decorations", in particular to the Implicit Surfaces: Families of Curvature lines, polar geodesic grids and parallel geodesic grids which can be moved with the mouse over the surface.
Surfaces such as the Boy Surface are difficult to grasp as a whole; we have developped a new morph-with-background where the whole surface is rendered as point cloud and the Meridian Bands are now visibly moving on the surface. This led us to improved morphs for various other surfaces (Cross Cap, Right Conoid, Bianchi-Pinkall).
We experimented with rendering Implicit Surfaces by putting tangential disks at the points of a point cloud. These renderings are fast enough for mouse rotation, but since we cannot take these disks too small, the quality is still not quite as good as that of a flat shaded parametrized surface.
The Fractals & Chaos Category:
The Henon Attractor can now be rendered in Hit-Count-Mode. This gives some impression of the invariant density on this complicated set.