Sphere and hyperboloid intersection

[malenkylizard]

Hello all,

I'm not sure if there's a simple answer to this, and if there isn't, I won't waste your time; I have so much more to do that I can only devote so much time to this little subproblem. I'm trying to model an eggplant in C++, using a graphics library called Renderman, by way of two partial spheres of different sizes, connected by a hyperboloid. So my first attempt was to have the two ruling points of the hyperboloid be at the equator of one sphere, and the equator of the other, offset by 90 degrees. So for example, in my case, one sphere is of r=1, the other sphere is of r=0.7, and their centers are at coordinates (0,0,0) and (0,0,2), that is, their centers are separated by a distance of 2 units, along the Z axis. Then the two points of the hyperboloid are at (1,0,0) and (0,0.7,2). The result is seen here: http://userpages.umbc.edu/~fraha1/eggplant.jpg

This isn't quite what I was hoping for. I was hoping that the derivatives at the intersecting circles would be the same; instead there's a ridge I'd like to do away with. Any ideas for how I could change the parameters to make this look nicer? Thanks!

 

[pat_connell]

</code>One way to improve the look of the eggplant is to increase the radius of the smaller sphere. By increasing the radius of the smaller sphere, you can create a smoother transition between the two spheres and eliminate the ridge. You can then adjust the positions of the spheres and hyperboloid to ensure that they still intersect at the equator of the two spheres. You may also want to tinker with the shape of the hyperboloid to get the desired result. You can do this by adjusting the parameters that define the hyperboloid, such as its eccentricity and its curvature. Finally, you can experiment with different materials and textures for the eggplant to give it a more realistic look. I hope this helps!