在3D对象的外部查找三角形

Question

I am trying to take a set of vertices (vi = xi,yi,zi) and make a solid object out of them. To draw the object, I use triangles, so I need to find a set of triangles t = v1, v2, v3, which forms a solid surface.

I know that if I construct every possible triangle from the vertices, I will see a solid surface, but this wastes a lot of resources on triangles which are hidden in the interior of the object, and calculating them all costs O(N^3) where N is the number of vertices. How do I find the triangles only on the exterior?

Here is my code (java) to generate all the triangles in an object with random vertices.

public class myObject {

    public ArrayList<float[]> Vertex_Coords;
    ArrayList<float[]> Vertex_Colors;
    ArrayList<int[]> triangles;


    public myObject() {

        Vertex_Colors = new ArrayList<float[]>();
        Vertex_Coords = new ArrayList<float[]>();
        triangles = new ArrayList<int[]>();

        addball(20);
    }

    public void addvertex() {
        float[] coords = new float[3];
        float[] colors = new float[4];
        int i;

        for (i = 0; i < 3; i++)
            coords[i] = maxModelSize * ((float) Math.random()-0.5f);

        for (i = 0; i < 4; i++)
            colors[i] =  (float) Math.random();

        Vertex_Coords.add(coords);
        Vertex_Colors.add(colors);
    }

    public void addball(int numpoints)
    {
        int i;
        for(i = 0;i<numpoints;i++)
        {
            addvertex(false,true);
        }
        connectalltriangles();
    }

    public void connectalltriangles()
    {
        int i,j,k;
        int [] tri;
        for(i=0;i<Vertex_Coords.size();i++)
        for(j=i+1;j<Vertex_Coords.size();j++)
            for(k=j+1;k<Vertex_Coords.size();k++)
        {
            tri = new int[3];
            tri[0]=i;
            tri[1]=j;
            tri[2]=k;
            triangles.add(tri);
        }
    }

}

Answer 1

What you exactly need is a Convex Hull algorithm, if you are sure if your geometry is always convex.

Convex Hull: This algorithm creates a mesh by connecting only the outermost vertices of a given set of points in 3d space. Obviously you will loose the vertices which are inside the convex structure and will not be used in any triangles. This only works for convex shapes.

Below is a good example for a convex hull construction.

There are many Libraries that implement Convex hulling algorithm. Ex: CGAL, BulletPhysics and OpenMesh. If you are looking for a quick way to build a convex hull, QuickHull is the best place. http://www.qhull.org