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Need help developing a routine to map a 3D sphere out of blocks

Started by QuadMV Aug 23, 2008 at 1:19 PM 3 replies 1k views

Original Post

Aug 23, 2008 at 1:19 PM

Hey all. I want to draw a 3D Sphere out of a bunch of blocks. What I’m looking for is a function that will return me a list of 3D coordinates where if I placed a block at each coordinate it’ll create the shape of a 3D sphere. I’m assuming I’d pass into this function the radius of the sphere and the density (ie: size of block relative to radius, is it 5 blocks wide or 100 blocks wide). The result would be a list of 3D coordinates. Let’s assume this is in object space, so the center most point will be 0,0,0. I also want a second version that just returns the outer coordinates, without any of the inner points. I hope that makes sense. If anyone is willing to help me with this I’d really appreciate it. I’m not asking you to write the entire function, but at least help with the math enough for me to understand it then I can run with it. Of course if you feel so obliged to write the whole function I’d be most appreciative as it would allow me to focus more on the logic and game play, but I understand if you just want to point me in the right direction. I’ll leave it to your own prerogative. Thanks!

oliii

Aug 24, 2008 at 7:02 AM

nope, you lost me. I'm sure it all makes sense, but if you can explain it another way.

SiCrane

Aug 24, 2008 at 9:18 AM

Did you try the obvious brute-force solution?

#include <set>struct Point {  Point(int i, int j, int k) : x(i), y(j), z(k) {}  int x, y, z;};bool operator<(const Point & lhs, const Point & rhs) {  if (lhs.x < rhs.x) return true;  if (lhs.x > rhs.x) return false;  if (lhs.y < rhs.y) return true;  if (lhs.y > rhs.y) return false;  return lhs.z < rhs.z;}std::set<Point> get_sphere_blocks(int radius) {  std::set<Point> to_return;  int r2 = radius * radius;  for (int i = 0; i <= radius; i++) {    for (int j = 0; j <= radius; j++) {      for (int k = 0; k <= radius; k++) {        int sum = i * i + j * j + k * k;        if (sum <= radius) {          to_return.insert(Point( i,  j,  k));          to_return.insert(Point( i,  j, -k));          to_return.insert(Point( i, -j,  k));          to_return.insert(Point( i, -j, -k));          to_return.insert(Point(-i,  j,  k));          to_return.insert(Point(-i,  j, -k));          to_return.insert(Point(-i, -j,  k));          to_return.insert(Point(-i, -j, -k));        }      }    }  }  return to_return;}

Emergent

Aug 24, 2008 at 11:29 AM

It sounds like QuadMV wants two routines: One, to rasterize a sphere onto a voxel grid, including all the interior points; and another, to rasterize just the surface of the sphere to the voxel grid.

The brute force solution is probably just fine. You could also be a little more intelligent about it and instead slice your sphere into circles, and those circles into strips. The equations will look like, r=sqrt(R^2 - z^2), etc.

QuadMV

Aug 24, 2008 at 11:50 AM

I think the brute force will give me what I want. I was originally thinking of that but didn't want it to return a cube, but a sphere instead. I think the addition of:

int sum = i * i + j * j + k * k;
if (sum <= radius) {
.
.
.
}

Is what I was missint in my head to make it a sphere.

Thanks, I'll give this a try and let you all know how it goes.

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