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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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