Question/Feature request - 3d circle

[Stinosko]

Hey,

I'm wondering if the library has a way to use 3 dimensional circles? I have a program that spit out 3d circles by providing the centerpoint, radius and normal vector of the circle his plane. I want to calculate the intersection of a line in the same plane with the circle, is that possible?

[sylee957]

I think that we should support more wider varieties of geometric primitives
But problem is that that there are multiple ways to draw plane circles in 3D space regarding how it is tilted, so there should be a good way to describe such rotation

[Stinosko]

What do you mean? If you provide a normal, center point and radius than you can only draw one circle as far as i can think off? It might be more tricky for a ellipse as his rotation does matter.

Correct me if I'm wrong!

[sylee957]

No, I mean about how the plane where the circle is drawn is tilted

[sylee957]

Okay, I see you have mentioned to use normal vector

[sylee957]

I’d tell you that I missed your detail of using normal vectors

[oscarbenjamin]

It is possible to do this if you give equations for the circle and line. The equations for the circle are something like:

( r - c ) . n = 0  # circle is in the plane
| r - c |^2 = R^2

where r is the arbitrary position vector, c the centre, n the normal and R the radius. The equation for the line will be something like

r = a + t b

where t is the parameter of the line.

Using the vector module we have:

In [24]: from sympy.vector import CoordSys3D                                                                                      

In [25]: N = CoordSys3D('N')                                                                                                      

In [26]: x, y, z = N.base_scalars()                                                                                               

In [27]: i, j, k = N.base_vectors()                                                                                               

In [28]: c = 1*i                                                                                                                  

In [29]: n = i + j                                                                                                                

In [30]: R = 2                                                                                                                    

In [31]: a = c                                                                                                                    

In [32]: b = i - j                                                                                                                

In [33]: t = Symbol('t')                                                                                                          

In [34]: r = a + t*b                                                                                                              

In [35]: r                                                                                                                        
Out[35]: (t + 1) i_N + (-t) j_N

In [36]: (r - c).dot(n)                                                                                                           
Out[36]: 0

In [37]: r - c                                                                                                                    
Out[37]: (t) i_N + (-t) j_N

In [42]: (r - c).dot(r - c)                                                                                                       
Out[42]: 
   2
2⋅t 

In [43]: solve((r - c).dot(r - c) - R**2, t)                                                                                      
Out[43]: [-√2, √2]

In [44]: r                                                                                                                        
Out[44]: (t + 1) i_N + (-t) j_N

In [45]: sol = solve((r - c).dot(r - c) - R**2, t, dict=True)                                                                     

In [46]: sol                                                                                                                      
Out[46]: [{t: -√2}, {t: √2}]

In [47]: [r.subs(s) for s in sol]                                                                                                 
Out[47]: [(1 - √2) i_N + (√2) j_N, (1 + √2) i_N + (-√2) j_N]

[Stinosko]

Oooh, that comment wasn't present when sending mine comment @sylee957
I'll remove it!

[Stinosko]

@oscarbenjamin I'll give it a try, thank you! :)