Is there a known way to determine the smallest sphere to completely encapsulate any triangle in 3D?
Obviously I did not consider the obtuse triangle, if you have a triangle on the circle Vertex (point), then the circle is not the smallest bounding circle (hence the smallest bounding sphere).
Now I believe you are looking for the minimum bounding sphere, which is a known and researched problem in mathematics, And computer graphics. “Smallest Enclosing Circle Problem” is a description of O(n ^ {2}) and linear O(n) algorithms.
As far as I know, the smallest bounding circle does produce the smallest bounding sphere, Use the same parameters (center point and radius) for projection to three dimensions.
First, I think you add the vertex and the scale by 1/3 to find the origin and then go from the vertex to The maximum distance to the origin. This produces a sphere containing a triangle, but it is not necessarily the smallest.
Is there a known way to determine the smallest sphere to completely encapsulate the 3D Arbitrary triangle?
Assuming that the sphere is just a trivial extension of a circle (2-D) to 3-D (using the same center point and the same radius), I believe What you are looking for is circumscribed circle of a triangle.
Obviously I did not consider the obtuse triangle. If you have triangle vertices (points) on the circle, then the circle is not the smallest bounding circle (Hence the smallest bounding sphere).
Now I believe you are looking for the minimum bounding sphere, which is a known and studied problem in mathematics, and computer graphics. “Smallest Enclosing Circle Problem” is O (n ^ (2)) and a description of the linear O(n) algorithm.
As far as I know, the smallest bounding circle does produce the smallest bounding sphere, using the same parameters projected to three dimensions (center point and radius ).