Is there a way to digitally capture a 3d point of view image of all directions in a sphere? Your eyes take in light from the fields of view, approximately 160 degrees but you cannot capture the other 200 degrees at the same time or can you?
Yes you can.
The technique you use depends on 2 things. If you need a high resolution option or you want a realtime one.
For the high resolution option you can take a series of shoots rotating the camera and after that stilching it on a special program.
You can use Hugin that its free.
You need some technique to do this. Here are some notes I did sometime ago: http://www.otake.com.mx/Apuntes/Imagen/EnviromentMaps/
If you need exact aligment in an interior shoot you need a special head Do I "need" a panoramic head to shoot 360 panoramas?
For a realtime shoot, lets say people is walking arround or you need video you can take a shoot from a ball mirror. That projection is called a Hemispherical probe.
You can transform that projection in a spherical one but the resolution, specially on the borders is very low.
You can make an array of cameras too. sometimes the images will not align very well. Like google street view.
The 3D part
You can project this into a 3D sphere to make a panorama or environmental sphere, which is 3D.
But the position of the point of view is exactly the center of this sphere.
If you need to make a 3D model of that you need multimpe shoots or a moving video so a program can calculate the diference and starting to create a 3D model.
It is possible to create spherical 3D views with a lot of cameras in precise arrangement, post processing and a VR headset. See this blog post by the esteemed Vi Hart for the gritty details: http://elevr.com/stereo-polygons/
It's possible with multiple cameras taking a shot at the same time.
One option is a ball with cameras facing outwards in all directions.
It is possible to capture a full 360 x 180 degree panorama (allowing you to see in every possible direction), using either multiple cameras or specialized reflectors. However it will not be "3-D" in the sense that the image will contain no depth information, you couldn't turn it into a 3D model of a room and rotate it etc.