Skip to main content
MathOverflow

Return to Answer

Added hull of two curves.
Source Link
Joseph O'Rourke
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar.
      (Image due to Frank Sottile, Philip Rostalski.)
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves. Here is a crude attempt on your two curves $A$:
      ![CurveHull][2]

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar.
      (Image due to Frank Sottile, Philip Rostalski.)
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves.

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar.
      (Image due to Frank Sottile, Philip Rostalski.)
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves. Here is a crude attempt on your two curves $A$:
      ![CurveHull][2]
Image credit added.
Source Link
Joseph O'Rourke
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$.The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar. The green surface has degree $16$. 
The pink triangle is planar.      (Image due to Frank Sottile, Philip Rostalski.)
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves.

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar.
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves.

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar.  
      (Image due to Frank Sottile, Philip Rostalski.)
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves.
Source Link
Joseph O'Rourke
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958

You might see if this paper helps:

Ranestad, Kristian, and Bernd Sturmfels. "On the convex hull of a space curve." arXiv:0912.2986 (2009). (arXiv abstract link)

      ![CurveHull][1]
      The yellow surface is $z - 4x^3 + 3x = 0$. The green surface has degree $16$. The pink triangle is planar.
If an approximate hull would suffice, it is "easy" to compute the 3D convex hull of many points along your curves.