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I have created a plane, then have created grease pencil and configured it to constraint drawings to that plane. Unfortunately, I can't contraint draw behavior to the plane too:

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I.e. while I am drawing a rectangle, it looks rectangular only from that side view I was looking to the scene

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Can I simulate 2D vector drawing more natural?

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This is a great question, and had to think about it, but I think I have a simple solution:

  1. Go to Draw Mode
  2. With the box tool draw a rectangle at any location and orientation you want in the 3D Viewport.
  3. Hit Enter to confirm the box location, orientation, size
  4. Optional: change your view so you can understand this technique is not dependent on world view
  5. Enter Edit Mode
  6. With the Selection Tool active set the Selection Mode to Select Only Points or Select all Stroke Point

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  1. Select the whole rectangle you just created

  2. Now switch the Cursor tool

  3. With the Cursor tool selected go to the tools Settings and and set the Transformation Orientaion to Local

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  1. From the 3D Viewport Menu chose Grease Pencil > Snap > Cursor To Selected (you can also use the shortcut key: Shift + S )

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  1. Go back to Draw Mode
  2. Draw with any tool on the rectangle and then move your view to see that the strokes are in the same drawing plane.

You can see the drawing plane by turning on the 3D Canvas in the Viewport Overlay (In the Edit Grease Pencil section, put a checkmark next to Canvas to turn it on)

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