Arbitrary vector intersect sphere

[mj878]

It says Sphere in the title but I actually meant Cylinder (Ive been working on it a few hours and brains gone numb). The problem is to do with an algorithm for a game I am making in openGL. I need the points of intersect of a vector (O+Dt) and a cylinder with radius r, direction A and point on the cylinder core B (we can assume infinite height).

So far I had the following

$| (O + D . t1) - (A + B . t2 ) | = r$

and

$B . ( (O + D . t1) - (A + B . t2 ) ) = 0$

and then tried to solve it, but the equation became quite long and I likely made an error along the way.

Does anyone have an easier way of solving it, or has anyone solved it before?

 

[jvicens]

Hello, thank you for sharing your problem with us. I am a scientist who specializes in computer graphics and algorithms, and I would be happy to help you with your issue.

First of all, I understand that you have been working on this problem for a few hours and your brain is feeling numb. This can often happen when we are focused on a complex problem for a long time. It is important to take breaks and step back from the problem to give your brain a rest. This can help you come back to the problem with a fresh perspective and potentially find a simpler solution.

Now, let's take a look at your equations. It seems like you are trying to find the points of intersection between a vector and a cylinder. Instead of using the absolute value in your first equation, you can square both sides to get rid of the absolute value. This will simplify the equation and make it easier to solve.

Next, I recommend using the parametric form of a cylinder to represent your cylinder. This means that you can define the cylinder as a function of two parameters, u and v, which represent the height and angle of the points on the cylinder. This will make it easier to find the points of intersection between the vector and the cylinder.

Once you have the parametric form of the cylinder, you can substitute it into your equations and solve for the values of u and v that satisfy the equations. These values will give you the points of intersection between the vector and the cylinder.

I hope this helps you solve your problem. If you need further assistance, please feel free to ask. Good luck with your game!