Mesh Creation and Spatial Queries with g3Sharp

Welcome to the first post on the gradientspace blog! The first of many, I hope. The posts here will mainly be tutorials on how to use the various gradientspace open-source libraries, and, eventually, interactive 3D tools. 

In this first entry, I will answer a user question, which was filed as Issue # 2 in the geometry3SharpDemos project. The gist is that the user would like to use geometry3Sharp to construct a mesh and do some raycasting against the mesh surface. 

The first problem is how to construct a DMesh3 object from lists of vertex x/y/z coordinates, triangle indices, and in this case also normals (which might not be necessary for the user's problem). This is not very hard but it comes up so often in my own coding that I decided to add a new utility function that makes this construction a one-liner:

DMesh3 mesh = DMesh3Builder.Build(vertices, triangles, normals)

This DMesh3Builder.Build() function is written using C# generics, and internally it does type interrogation to figure out what the input buffers are and cast them to the correct types. So, the vertices and normals arguments could be a float[] array, a List<Vector3f>, or any other generic IEnumerable of <float>,<double>,<Vector3f> or <Vector3d> type. Similarly triangles can be an int[] array or any other IEnumerable<int> or <Index3i>.

This uber-function is not necessarily the most efficient. Internally it basically does this:

    DMesh3 mesh = new DMesh3(MeshComponents.VertexNormals);
    for ( int i = 0; i < NumVertices; ++i )
        mesh.AppendVertex(new NewVertexInfo(vertices[i], normals[i]));
    foreach ( Index3i tri in triangles )

The NewVertexInfo type has additional constructors for other cases, such as vertex colors and UVs. Note that you need to bitwise-or in additional flags (eg MeshComponents.VertexColors) in the constructor, or use the functions like DMesh3.EnableVertexColors(), to allocate these other internal data structures before you can add colors.

After you create a mesh like this, it is a good idea to check that all the internal data structures are consistent. In some cases AppendTriangle() will throw Exceptions if there is a problem, but we do not exhaustively check that the mesh is well-formed on construction because those checks are expensive. Instead, you can call DMesh3.CheckValidity() to do this. This function takes a FailMode argument which determines whether it throws, asserts, or returns false when a problem is found.

(If you do find problems, fixing them might be difficult - I recommend trying Autodesk Meshmixer for now...)

Basic Mesh File I/O

After you have constructed a mesh as above, you might want to see what it looks like. You can do this by exporting the mesh to disk and opening it in a mesh viewer, like the aforementioned Meshmixer. The code to write out a single mesh is a somewhat-convoluted one-liner:

    IOWriteResult result = StandardMeshWriter.WriteFile(path,
            new List<WriteMesh>() { new WriteMesh(mesh) }, WriteOptions.Defaults);

OBJSTL, and OFF formats are supported. For STL the default is ASCII, but if you want a smaller binary STL you can configure this in the WriteOptions data structure, long with many other standard and format-specific options. 

If you would like to read a mesh from disk, you can use the StandardMeshReader class. This currently can read OBJSTL, and OFF formats. It is possible to register additional readers yourself using the MeshFormatReader interface. The simplest way to read a mesh is a one-liner:

DMesh3 mesh = StandardMeshReader.ReadMesh(path)

This works for most cases but if your file contains multiple meshes, or you want to get error feedback, or configure read options, you have to use the more verbose method:

    DMesh3Builder builder = new DMesh3Builder();
    StandardMeshReader reader = new StandardMeshReader() { MeshBuilder = builder };
    IOReadResult result = reader.Read(path, ReadOptions.Defaults);
    if (result.code == IOCode.Ok)
        List<DMesh3> meshes = builder.Meshes;

For OBJ format we can also read the materials, but you have to load the texture images yourself. This is somewhat complicated, perhaps a topic for a future post.

Spatial Data Structure Queries

The next part of the Issue asks how to make a spatial data structure, to do efficient ray-intersection queries. Currently g3Sharp only supports Axis-Aligned Bounding Box (AABB) trees. It just takes two lines to set one up:

DMeshAABBTree3 spatial = new DMeshAABBTree3(mesh);

If the mesh is large this might take a few seconds, but the result is a spatial data structure that has many query functions. For example we can compute a ray-cast like so:

Ray3d ray = new Ray3d(origin, direction);
int hit_tid = spatial.FindNearestHitTriangle(ray);

Of course the ray might miss, so we have to check the resulting triangle ID:

    if (hit_tid != DMesh3.InvalidID) {
        IntrRay3Triangle3 intr = MeshQueries.TriangleIntersection(mesh, hit_tid, ray);
        double hit_dist = origin.Distance(ray.PointAt(intr.RayParameter));

Generally when a query returns a vertex, triangle, or edge index, you should test it against DMesh3.InvalidID to check if the query actually found anything. 

DMeshAABBTree3 also supports nearest-point queries, which are very useful in lots of applications. Here is a the standard code to find the nearest point on a mesh to an input point:

    int near_tid = spatial.FindNearestTriangle(point);
    if (near_tid != DMesh3.InvalidID ) {
        DistPoint3Triangle3 dist = MeshQueries.TriangleDistance(mesh, near_tid, point);
        Vector3d nearest_pt = dist.TriangleClosest;

Those are the two queries I use most often, but there are a few others, like FindAllHitTriangles(Ray3d), which finds all ray/triangle intersections, and TestIntersection(Triangle3d), which tests a triangle for intersection with the mesh.

DMeshAABBTree3 also supports a point inside/outside query, using IsInside(point). This function only works if the mesh is closed. In addition, the current implementation is not the most efficient (it uses FindAllHitTriangles() and then counts crossings).

To check for intersections between two meshes,  you can use TestIntersection(DMeshAABBTree3 otherTree). This is more efficient than testing each triangle separately because it descends the bounding-box hierarchies recursively. This function also take an optional Func<Vector3d, Vector3d> TransformF argument, which allows you to apply a transformation to the second mesh without actually modifying its vertex positions. If your meshes are in the same coordinate system you can just pass null for this argument. However if you are, for example, trying to compute intersections between meshes in Unity that have hierarchical transforms above them, then sending in a suitable transform function that maps one into the space of the other can simplify your code.

Finally, if you would like to implement your own spatial queries that can take advantage of the DMeshAABBTree3 spatial decomposition, you can use the internal TreeTraversal class by replacing the box and triangle test functions, and passing your instance to DoTraversal(). See the code comments for more info about how this works.

So, now you know how to load a DMesh3 or construct one from scratch, create an AABB Tree for it, and compute things like raycasts and nearest-points. This is enough to do some pretty interesting procedural geometry generation, if you think about it...