![]() Using the equations of the two spheres takes you right back to step one, so you’d need to find a different pair of equations to describe this same circle. A single implicit three-dimensional Cartesian equation generally describes a surface, not a curve you need two such equations to describe a curve. The real complications arise when you try to describe this intersection circle with equations. Actually, because of the symmetry of the 2-d problem, you really only need one intersection point since the other circle intersection, if any, will generate the same circle in 3-d. By symmetry, one can see that the intersection of the two spheres lies in a plane perpendicular to the line joining their centers, therefore once you have the solutions to the restricted circle intersection problem, rotating them around the line joining the sphere centers produces the other sphere intersection points. Indeed, if you restrict your attention to a plane that passes through the centers of both spheres, then you have precisely that two dimensional problem of finding the intersections of two circle. Given that you only know their position and radii.īecause of the radial symmetry of the problem, it’s not substantially different from the two-dimensional one. To sum up : I would like to know a solution to solve a suitable intersection along a circle when two spheres intersect in a 3 dimensional space, and how to change it, explained in a way that would make sense. I would also like to refrain from using trigonometric functions such as $sin$ and $cos$ since I would like to explain it to other people using RBX.Lua. If when you explain could show and explain your logic and reasoning behind what you are doing, that would be very helpful, and also explaining what everything means. Which is what is being used to calculate the 2 dimensional intersection, however the 3 dimensional intersection is much more complex, and is what I need help with. Local cmx, cmy = x1 + (cd*DX)/d, y1 + (cd*DY)/d Local x2, y2 = p2.Position.X, p2.Position.Y Local x1, y1 = p1.Position.X, p1.Position.Y Here is what I have so far in RBX.Lua for 2D intersection: function calculateIntersect(p1, p2, j1, j2, el) I am aware that in a 3D space with two spheres intersecting there is an infinite number of possible solution along a circle. Right now, I have the equation for working out the two intersects of two circles in 2D space, however when I was studying and reading about the 3D intersection it did not make much sense it what they are doing.
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