Graphics3D[{AbsolutePointSize[5], Point[p]}],. Graphics3D[{{Red, Arrow[{p, p + 2 Normalize[t]}]},. {Green, Arrow[{p, p + 2 Normalize[b]}]}, {Cyan, Arrow[{p, p + 2 ...
Differential characteristics of spatial curves given as an intersection of two surfaces with Mathematica In[37]:=
Out[37]=
DiffCharx2 + y2 + z2 ⩵ 6, x2 - y2 + z2 ⩵ 4, {x, y, z} // Simplify // PowerExpand 1, 0, -
x z
, -
x (x2 + z2 ) z4
, 0, -
x2 + z2 z3
, 0,
x2 + z2 z3
, 0,
In[38]:=
sis = x2 + y2 + z2 ⩵ 6, x2 - y2 + z2 ⩵ 4; p = {1, 1, 2};
In[39]:=
{t, n, b, κ, τ} = DiffChar[sis, {x, y, z}, Point → p]
Out[39]=
1, 0, -
1 2
, -
5 16
, 0, -
5 8
, 0,
5 8
, 0,
1 5
, 0
x2 + z2 1 +
x2 z2
3/2
, 0 z3
2
In[40]:=
SketchCurve3Dsis, {x, - 3.5, 3.5}, y, -
Out[40]=
6,
6 , {z, - 3.5, 3.5}, z, Surfaces → # & /@ {True, False}
,
3
In[41]:=
Show SketchCurve3Dsis, {x, - 3.5, 3.5}, y, -
6,
6 , {z, - 3.5, 3.5}, z,
Graphics3D[{AbsolutePointSize[5], Point[p]}], Graphics3D[{{Red, Arrow[{p, p + 2 Normalize[t]}]}, {Green, Arrow[{p, p + 2 Normalize[b]}]}, {Cyan, Arrow[{p, p + 2 Normalize[n]}]}}]
Out[41]=
4
In[42]:=
Show SketchCurve3Dsis, {x, - 3.5, 3.5}, y, -
6,
6 , {z, - 3.5, 3.5}, z,
Graphics3D[{AbsolutePointSize[5], Point[p]}], Graphics3D[{{Red, Arrow[{p, p + 2 Normalize[t]}]}, {Green, Arrow[{p, p + 2 Normalize[b]}]}, {Cyan, Arrow[{p, p + 2 Normalize[n]}]}}]
Out[42]=
