Visually depicting light movement in hemispherical shell on a planar substrate

I have ray tracing code that is intended to vectorially follow collimated light beams incident on a semitransparent hemispherical shell on a planar substrate as they undergo reflections and refractions until attenuation. Each ray is described by an origin point, a direction, and an intensity and then the intersection points are calculated. At the intersection the beam is appropriately reflected/refracted and the subsequent beam is then followed similarly. In order to solve bugs in the code visualizing the light beams would be very helpful. I'm unsure of which of the plethora of plotting functions to use in order to plot two hemispheres and the light vectors on the same 3D plot for visualization. The sphere function produces a 3D plot but I have no idea how to limit it to only the hemispherical top part of the sphere or how to plot light ray vectors onto the same plot. Any direction would be helpful.

[darova]

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