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Unfold a Sliced Cone

  •  A tutorial to demonstrate advanced concepts.
    • The advanced 3D drawing contains:
      • Draw an Intersecting Plane with Extrude and Resizing Handles
      • Contour Line
      • Slice by Custom Plane
      • Vector Convert
      • Preset Sticky handles
      • Divide Arc with Tickmarks
      • Duplicate and place with Handles
  •  Step 1
    • Start by creating a 3D Cone that fits your window with plenty of room to unfold it.
      • Actual dimensions are unimportant. I used the same cone from Unfold Simple Cone.
      • Determining the lengths is done the same, but should be done AFTER the Slice operation. (Add the 2 sliced line segments together)
    • See the next steps to create the 'Slice Plane'
  •  Step 2
    • In Side View first put your cursor on the point of the cone and hit the Comma key. (Gravity Move)
      • This will position your cursor at the Z value of the center of the cone without setting a point.
    • Draw a Vector intersecting the cone.
      • For precision you could use Point Control or Point Polar to set Angle and Position of this line, not necessary for this example.
  •  Step 3
    • In Top View select the Vector and hit 'X'.
    • Have Ortho ON. (hotkey 'H')
    • Gravity Snap to one end of the Vector and then set a 2nd point straight up.
    • Hit ENTER.

 

  •  Step 4
    • In Top View select resizing Handles and then drag the lower handle straight down till the Plane is exceeding the Cone extents.
    • Back in the Main 3D window you can now use Contour Line (OR Surface Intersection) to project the Angled Ellipse on the cone.
      • See result in Step 1.
    • Then use Solid->Slice with Custom Plane to slice the Cone.
      • For Contour Line and Slice just Snap to 3 corners of the Plane.
      • Hit ENTER.

 

  • Step 2
    • Select the lower part of the Cone and use Vector Convert to break it into Vectors.
    • Go back to Top View window.
      • I numbered the Vectors for reference.
  •  Step 3
    • In OPTIONS, the item Enable Stick Handles needs to be ON.
      • This lets the handles stay active even after you unselect an object.
    • Now select each Vector and set Handles at the Bottom first and a 2nd Handle at the Cone Peak (where the 1 is)
      • We want the handles to be the TOTAL length of the cone.

  •  Step 4
    • Next to the Cone in Top View created the flat pattern Arc with the same procedure as before.
    • I add Tickmarks defining 12 sections and a Pointmark at the Radius Point.
      • The Tickmarks can be a little tricky in 3D, you can switch to 2D and set the plane to YZ in OPTIONS to make this easier.
  •  Step 5
    • Starting with the longest Vector (# 1 in the numbered example) duplicate each one in turn between a Tickmark and the Pointmark.
  •  Step 6
    • The last Vector (# 13) is # 1 used again.
    • Delete the Pointmarks.
  •  Step 7
    • Draw a Curve (Hotkey 'C') along the top ends of the Vectors.
      • Move your cursor close to each end and hit the Period key for each point. Should take about 5 seconds to do.
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