How do I draw a 3D curve in 2D? Or rather, how do I algorithmically draft an arbitrary 3D curve from a 2D perspective?
I have a line that curves in three dimensions simultaneously and want to figure out how to determine how to display it in two dimensions (i.e. drafting on paper) without perspective (i.e. vanishing points).
I've run into this issue a couple of times and have a prior unfinished project waiting on developing this skill.
This time, I am designing a wooden window sash
and have muntin sections with a moulding profile(the 1915 muntin profile shown here
) that overlay and meet each other at various angles. I am trying to determine how to draft the coped profiles (this is the curve in 3D space) from an isometric view. The "bottom" section will be a straight cut with a coped overlay on the "top" section. To add insult to injury, I also have an area where three muntin sections meet in an even more complex profile.
I know craftsmen used to be able to do this by hand (so I should too, goddamnit!). I'm moving from 2D to 3D modeling of this design and want to determine the profile before
modeling it. Again, I'm also interested in the big-picture method for my other stalled and future projects.
Yes, I could cheat and use a 3D composite of these shapes to figure out how it "should" look and back-fill the construction, but what I'm primarily interested in is how to do this by hand. My goal is to design forward instead of empirically determine how to do it and extract the design from that.
I've had some luck with "mechanical drawing" resources (mostly books from the early 1900s), but figured that, of anyone, MeFites will know who and where to look for the information.
For example, there is a way to use a compass at specific points to draw a (2D) circle isometrically, and I want to be able to do the same for an arbitrary 3D curve.
Anyone have resources, keywords, and/or tutorials on how to do this algorithmically?