wendy wrote:The equation given for the torocylinder is a (sphere-circle)-comb, while the torocubinder is given as a ((anulus × circle ) crind. The two are different.
The second is an analus-circle crind product. A crind product of X, Y, Z might be represented by overlays of prisms of xX, yY, zZ, ... where x,y,z, ... is the coordinates of a sphere. In the case of an analus, we see that placing an analus-line crind, would give an circle (a+r, a+r, a), with a second ellipsoid (a-r,a-r,a) removed. At the point (0,0,1) the two ellipsoids meet, so four surfaces come together.
The full figure for the torocubinder here is then rss(a+r, a+r, a, a) - rss(a-r,a-r,a,a). which meets at a line-thin junction at (0,0,z,w).
Keiji wrote:[...]Thus they are not named after the shape they are folded up from (since they're both folded up from the same shape), but instead are named because the toratopic notation corresponds with the shape they are named after (see list of toratopes). I learnt this the hard way many years ago.
[...]You then set up a figure up so that its elements are mutually perpendicular at the centre, and then for a general point, its coordinates are, eg (a,b), where eg a is the radius in x,y,z, and b is the radius in (u,v,w).[...]
For our point a,b, then max(a,b) = 4, sum(a,b) = 7, and rss(a,b) = 5. For a standard line, of coordinate (1) to (-1), centre 0, we see that the values of the coordinates of 3,4 gives a radius of 4, 7 and 5, and so the surface crosses the ray (3,4) at (3/4, 4/4), or (3/7, 4/7), or (3/5, 4/5).
Likewise, for a cylinder, = prism(crind(x,y), z) gives max(rss(x,y), z), the point 3,4,5 would then cross the surface at max(rss(3,4),5) = max(5,5) = 5. This is at the notional point (3/5, 4/5, 1).
Secret wrote:But what does the lines sticking together mean e.g. ||
and what does () sticking to lines mean (e.g. (|)|)?
Secret wrote:Also you missed the torinder in that page
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