Revisions to Solve for the intersection point of 3 surfaces

deleted 3 characters in body

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edited May 8, 2013 at 17:15

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You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

The 3 "tori"torus and a the point :

enter image description here

You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

The 3 "tori" and a the point :

enter image description here

You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

The 3 torus and the point :

enter image description here

graphic added

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edited May 8, 2013 at 16:49

andre314

19k
1
37
73

You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

The 3 "tori" and a the point :

enter image description here

You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

The 3 "tori" and a the point :

enter image description here

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created May 8, 2013 at 16:35

andre314

19k
1
37
73

You can minimize the distances between 3 points that each belong to a torus :

res = NMinimize[
        Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
      + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
      {x1, y1, x2, y2, x3, y3}]

(* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
   torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

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