After taking a little break from doing posts during February I got around to exploring the 3D graphics capabilities of Mathcad 11 a little further. One can make models of solid objects and I started out with a simple torus.
This simple torus can be morphed into more complicated shapes by modifying the mathematical equations used to define the surface.
To create a surface one starts by defining a simple curved line, x, that forms the "backbone" for the surface. The curve's tangent, t, and a normal, e, perpendicular to the unit vector in the direction of the third axis are needed to define a matrix, y, specifying some of the points of the surface. The 3D plotter uses the matrices specifying the set of coordinates (ξ, η, ζ) to create a surface graph.
The 3D plotter's dialog box can be used to change the appearance of the object's surface and one can make the shape of the surface more complicated. One can also use lighting to add a little more realism.
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