C++ :: Good Object Oriented Approach To Meshing?

I'm a newbie to C++ and I've been working on this Delaunay tree in C for some time. I'm ready to port it to C++ which does not mean that the code itself is completed or done.

But I was wondering, how could I design my code to fully utilize C++?

For one, I'm using C++'s built-in stack/queue/vector functions because it's a lot nicer than building my own stacks or queues lol.

So, here's an overview of the code.

The mesh is built of tetrahedrons so I have a "struct tetra" which stores pointers to vertices ("struct particle") and its 4 neighbours. Working in half-plane data, we have:

Code:
struct particle {
double x, y, z;
};

struct tetra {
struct particle *p[4];//vertices
struct tetra *ngb[4];//neighbours

double a[4], b[4], c[4], d[4];//half-plane data
};

I'm fracturing these tetrahedrons by inserting vertices so I can get anywhere from 2 to 4 children per fracture per tetraheron. I'm mapping this history to a quadtree. This looks like :

Code:

struct tree {
int level;
struct tree *parent;
struct tree *children[4];
struct tetra *t;
};

What would be the best OO approach to this problem?

I thought about just using this object,

Code:
struct mesh {
struct tree *root; //pointer to root
/* insert all functions to be used by mesh here */
};

But I'm not sure how effectively this would be taking advantage of the OO paradigm.