N-D binary search of [][][]...{} to find the closest vector(int x,y,z,...) to v(double x,y,z,...)?

Question

I'm making a physics simulated 2D animation with JAVA GUI. And here're some open questions for curiosity:  

1. how do you implement n-dimensional binary search of [][][]...{}to find out the closest vector(int x,y,z,...) to vector(double x,y,z,...)? #algorithm    

 2. How do you visualize: z = f(x,y) = vector(x,y)? Are there any 3D multi-variable graphing web-app? Then, how do you sort a curved surface represented by [][][]{} based on z value? #datavisualization

N-D binary search of [][][]...{} to find the closest vector(int x,y,z,...) to v(double x,y,z,...)?

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