Inertia matrix

[TawhiriMaetea]

I am investigating the idea of an optimization script, which modifies the shape of an object considering its mass and inertia properties. For this I obviously need the inertia matrix of the body. I would appreciate any helpful ideas how this could be extracted.

Here is what I tried:

• One option would be to get the volume and coordinates of the individual voxels. Unfortunately the Voxels object does not expose the indiviual voxels
• Another way I thought of is to create a ConformalCellArray, which has a similar shape to the body, and get the coordinates and the volume of the individual cells. Here I am struggling with making the ConformalCellArray's shape to follow the body, as it only accepts only a few simple shapes as input.

Any ideas are greatly appreciated.

[LinKayser]

If you want to do this for an arbitrary voxels object, the easiest way to query the voxel values is to create a ScalarField from the Voxels object.

Voxels vox = new(...); // existing voxel field
ScalarField oField = new(vox);

// You can now iteratve over the bounding box 
BBox3 oBounds = oField.oBoundingBox();

// As an example, let's retrieve the value at the center
// of the bounding box
oField.bGetValue(oBounds.vecCenter(), out float fValue);
if (fValue <= 0)
{
    // Negative values are inside
    // Positive values are outside
    // 0.0 is exactly at the surface
}

I specifically didn't expose a voxel probing/setting function for the Voxels object, as it is a discretized signed distance field and didn't want to people to think of it as on/off and settable.

The next question you will have is how to remove individual voxels, which you cannot. However you can subtract a very small object, for example a tiny lattice, and I think this is the the easiest way to deal with your process.

Let me know if this helps.

Best,
Lin

[TawhiriMaetea]

Works perfectly, thank you. A brute force grid search to check whether the point is inside the solid is a little slow for reasonable accuracy, but hopefully an octree will solve this too.

[TawhiriMaetea]

I've been experimenting further and ran into a strange issue:
When querying the solid/void state of the scalar field, the boundary is shifted by 2mm.

For example: given a R=15 sphere, the ScalarField.getValue returns False until 13, and True for larger values.
The 2mm seems constant and independent from the general voxel size:

            float sphereRadius = 15.0f;

            Lattice latBody = new();

            latBody.AddSphere(new Vector3(0, 0, 0), sphereRadius);

            Voxels VoxBody = new(latBody);

            ScalarField oField = new(VoxBody); // Create a scalar field from the voxels

            BBox3 oBounds = oField.oBoundingBox(); // Get the bounding box of the field

            Console.WriteLine($"Sphere radius: {sphereRadius}");

            float testValue;
            bool isVoid = oField.bGetValue(new Vector3(0, 0, 0), out testValue);

            // query points close to the sphere radius
            isVoid = oField.bGetValue(new Vector3(0, 0, 0), out testValue);
            Console.WriteLine($"R = 0 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(12.999f, 0, 0), out testValue);
            Console.WriteLine($"R = 12.9 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(13.0f, 0, 0), out testValue);
            Console.WriteLine($"R = 13 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(13.1f, 0, 0), out testValue);
            Console.WriteLine($"R = 13.1 is outside the body: {isVoid}");

            isVoid = oField.bGetValue(new Vector3(-12.999f, 0, 0), out testValue);
            Console.WriteLine($"R = -12.9 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(-13.0f, 0, 0), out testValue);
            Console.WriteLine($"R = -13 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(-13.1f, 0, 0), out testValue);
            Console.WriteLine($"R = -13.1 is outside the body: {isVoid}");

            // try with 2mm offset
            float offset = 2.0f; // Offset in mm
            Vector3 vecOffset = new Vector3(-oBounds.vecCenter().X,
                                 -oBounds.vecCenter().Y,
                                 -oBounds.vecCenter().Z);
            Voxels VoxBodyOffset = VoxBody.voxOffset(2.0f); // Offset the voxels radially by 2mm
            VoxBody = VoxBodyOffset;
            oField = new(VoxBody);

            Console.WriteLine($"Sphere radius with 2mm offset: {sphereRadius + offset}");

            isVoid = oField.bGetValue(new Vector3(14.999f, 0, 0), out testValue);
            Console.WriteLine($"R = 14.9 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(15.0f, 0, 0), out testValue);
            Console.WriteLine($"R = 15 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(15.1f, 0, 0), out testValue);
            Console.WriteLine($"R = 15.1 is outside the body: {isVoid}");

            isVoid = oField.bGetValue(new Vector3(-14.999f, 0, 0), out testValue);
            Console.WriteLine($"R = -14.9 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(-15.0f, 0, 0), out testValue);
            Console.WriteLine($"R = -15 is outside the body: {isVoid}");
            isVoid = oField.bGetValue(new Vector3(-15.1f, 0, 0), out testValue);
            Console.WriteLine($"R = -15.1 is outside the body: {isVoid}");
            try
            {

                SolidBody shaft = new SolidBody(20,10, 100, 50, 60, 20, 20);

                PicoGK.Library.Go(
                    0.05f,
                    () => Library.oViewer().Add(VoxBody)
                    );

            }
            catch (Exception e)
            {
                Console.WriteLine("Failed to run Task.");
                Console.WriteLine(e.ToString());
            }

Applying the offset solves it, but it might cause issues later.
Do you know what causes this?

[LinKayser]

Dear @TawhiriMaetea the return value of bGetValue just says whether there is a value at that position or not (the underlying data structure of the Scalar Field stores the values sparsely if no value is set).

You need to evaluate the value as I did in my example. If it is less or equal than 0, you are inside the object, if it is larger than 0, you are outside the object. What you discovered is that the voxel field sparsely stores the distance to the surface in a narrow band of 3 voxels. But that's irrelevant for your use case. You can ignore the return value of bGetValue and just evaluate the value:

oField.bGetValue(oBounds.vecCenter(), out float fValue);
if (fValue <= 0)
{
    // Negative values are inside
    // Positive values are outside
    // 0.0 is exactly at the surface
}

Best,
Lin

[TawhiriMaetea]

Makes sense, thank you!
Cheers, Andras