PWrong wrote:btw, those pictures are great, but they're making the screen really long. Couldn't you split them into two pictures?
Marek14 wrote:((22)1) is the circle#tiger. That said, I don't like the definition of spheration anyway.
A#B isn't valid unless B is a sphere in some dimension. The reason is you need unique axes to align the tiger, but not a sphere.
Well, it's the shape you get when you replace each point of tiger with a circle - not the other way around. And this operation is not commutative - replacing each point of circle with sphere is something different from replacing each point of sphere with a circle. And, as mentioned, you really cannot replace each point with a tiger since tiger has unique axes. I suspect there's some confusion in definitions here.
Marek14 wrote:Rob wrote:Well, that's a bit silly, how is a line curved, let alone a torus?
LINE itself is not - but it's border, i.e. two points, are The same way as disk is not curved, but a circle is.
bo198214 wrote:Hey Marek and Rob,
give you a jerk! Wouldnt it be a great idea to have a program where you can choose out of a list of 4d toratopes (and where you can put in a shape in CSG notation), and it shows you a 3d slice moving through the shape?
That would be novel and a really appreciable distribution to the 4d community.
PS: Programming language java, then you can put it online everywhere.
thigle wrote:yep guys common ! bo's right ! do it and become tetraStars!
i don't like shit like rob says "that's a secret what do i do this output in". godam wakeup child ! this is internet - we share ! information restriction is stupid, especially when it ain't worth shit. just what deficit proble does it make to you to answer someone's question about the tools you use ?
if i was your father i would slap you gently and tell you to behave dud
But in fact, you are incorrect, because 1 doesn't mean "line" but "two points".
(21) parsed like this would result in cartesian product of circle and two points, resulting in two circles in parallel planes.
The same way, (11) would lead to four circles in this way.
PWrong wrote:But in fact, you are incorrect, because 1 doesn't mean "line" but "two points".
Sigh, 1 comes in two forms: "line" and "two points".(21) parsed like this would result in cartesian product of circle and two points, resulting in two circles in parallel planes.
Which is just the 1D form of a cylinder.The same way, (11) would lead to four circles in this way.
The four circles are the 1D form of a cubinder.
PWrong wrote:In general, the equations of these cuts are high order polynomials. Toric sections are quartic curves, and mathworld describes them as looking like kidneys. http://mathworld.wolfram.com/ToricSection.html. I doubt it's possible to find a parametrisation for them.
The general cross sections of 4D toratopes would be really interesting, but even harder to work out. And mathematica isn't very good at plotting implicit equations.
#version 3.6;
#include "colors.inc"
global_settings {assumed_gamma 1.0}
camera {
location <4,8,8>
look_at <0,0,0>
}
background { color White }
light_source {<-30, 30, -30> color rgb <1, 1, 1> }
#declare a = 1; // parameters
#declare b = 1; // ...
#declare r = 0.2; // ...
#declare w = 0; // value of W for cross section
#declare fn_A = function(x,y,z) { pow(sqrt(x*x+y*y) - a,2) + pow(sqrt(z*z+w*w) - b,2) - r*r } // formula for tiger
isosurface {
function { fn_A(x, y, z) }
contained_by { box { -4, 4 } }
accuracy 0.001
max_gradient 9
pigment {Blue}
scale 2
}
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