Determining IF & WHERE a line intersects with a 2D plane (in 3D space)

Question

The following problem im working on is for one of my favorite past-times: game development.

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Problem: We're in 3D space. I'm trying to determine if a line between two vectors in said space is passing through a circle; the latter of which consists of: center vector, radius, yaw & pitch.

In order to determine that, my aim is to convert the circle to a plane which can either be infinite or just have the diameter of the circle for all it's sides.

Should the line between the two vectors in fact pass through that plane, i am left with the simple task of determining wether that intersection point is within the radius of the circle, in which case i can return either true or false.

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What's already working: I have my circles set up and the general framework is there. The circles are appearing/rendered in the 3D space exactly as specified, great!

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What was already tried: Copied some github gist codes and tried to make them work for my purposes. I kinda worked, sometimes at least. Unfortunately due to the nature of how the code was written, i had no idea what it was doing and just scrapped all of that. Researched the topic a lot, too. But due to me not really understanding the language people speak when talking about line/plane intersections, i could have read the answer without recognizing it as such.

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Question: I'm stuck at line intersections. No idea where to go and how it works logically, So? where do i go from here and how can one comprehend all of this?

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Note: I did tag this issue as "java", but i'm not looking for spoon-fed code. It's a logical issue i'm trying to get past. If explained well enough, i will make the code work with trial and error!

Answer 1

Say if your circle is a circle in the XY plane with its centre on (0,0,0) and radius 1. How would you solve that? You would check the values of X and Y when Z is equal to zero. And X squared plus Y squared would be less than 1 (radius squared) if the line passes through the circle.

In other words, you could transform the 3D coordinates to a simpler reference frame. So I think you need to learn transformation of 3D coordinates, which is really not too hard to do. You need to rotate the 3D space around until the centre vector only has a Z component, and yaw and pitch are zero. And then offset the coordinates so the circle centre is in (0, 0, 0). Then apply the same transformation to the line. You could lastly scale by radius, but to be honest that is not so important since the circle math is easy.