create a solid from a shell

[raydeleu]

I am having difficulty creating a solid out of a shell. I wanted to use this functionality to create a socalled icosphere or geodesic dome. I used some code that I found on the internet to create these shapes. To create an icosphere with a certain subdivision level you have to start with an icosahedron. I created all faces using the standard Polygon() function of CascadeStudio. Then I sewed all faces to a shell. I confirmed that the shell is closed. Then I tried to create a solid out of the closed shell using oc.BRepBuilderAPI_MakeSolid(). After this I checked that indeed a solid was created.

The following scene shows my result. I get a shape that I can scale and translate. The scene contains three shapes, namely a box, a sphere and the icosphere. All three shapes are identified as solids (ShapeType()=2). A boolean operation between the box and the sphere works, but if you uncomment the last line in my code, containing a boolean of the icosphere with the resulting shape, the icosphere disappears.

What am I doing wrong?

// icospheres

function ProjectSphere(radius, vertex)
// function to project a vertex on to a sphere with radius "radius"
{
    let x = vertex[0];
    let y = vertex[1];
    let z = vertex[2];
    let currentRadius = Math.sqrt(Math.pow(x,2)+Math.pow(y,2)+Math.pow(z,2))
    let scale = radius/currentRadius;
    let scaledVertex = [scale*x , scale*y, scale*z]
    return  scaledVertex
}

function Icosahedron(radius)
{
    let golden = (1+Math.sqrt(5))/2
    let v = []
    // vertices determined by 4 rectangles
    v[0] = ProjectSphere(radius,[-1,  golden, 0]);
    v[1] = ProjectSphere(radius,[ 1,  golden, 0]);
    v[2] = ProjectSphere(radius,[-1, -golden, 0]);
    v[3] = ProjectSphere(radius,[ 1, -golden, 0]);

    v[4] = ProjectSphere(radius,[ 0, -1, golden]);
    v[5] = ProjectSphere(radius,[ 0,  1, golden]);
    v[6]= ProjectSphere(radius,[ 0, -1,-golden]);
    v[7] = ProjectSphere(radius,[ 0,  1,-golden]);

    v[8] = ProjectSphere(radius,[ golden,0, -1]);
    v[9] = ProjectSphere(radius,[ golden,0,  1]);
    v[10]= ProjectSphere(radius,[ -golden,0, -1]);
    v[11] = ProjectSphere(radius,[ -golden,0, 1]);

    // faces added so that they always have an edge in common
    // with the previous ones
    let f = []
    f[0] = [v[0],v[11],v[5]]
    f[1] = [v[0],v[5],v[1]]
    f[2] = [v[0],v[10],v[11]]
    f[3] = [v[0],v[7],v[10]]
    f[4] = [v[5],v[11],v[4]]
    f[5] = [v[4],v[9],v[5]]
    f[6] = [v[3],v[9],v[4]]
    f[7] = [v[3],v[8],v[9]]
    f[8] = [v[3],v[6],v[8]]
    f[9] = [v[3],v[2],v[6]]
    f[10] = [v[6],v[2],v[10]]
    f[11] = [v[10],v[7],v[6]]
    f[12] = [v[8],v[6],v[7]]
    f[13] = [v[0],v[1],v[7]]  
    f[14] = [v[1],v[5],v[9]]  
    f[15] = [v[11],v[10],v[2]] 
    f[16] = [v[7],v[1],v[8]]  
    f[17] = [v[3],v[4],v[2]]  
    f[18] = [v[2],v[4],v[11]] 
    f[19] = [v[9],v[8],v[1]]  

    // create polygons/faces out of the 20 * three vertices
    // and sew them together to a closed shell
    let icosphere = new oc.BRepBuilderAPI_Sewing()
    for(let i=0; i<=19 ;i++)
    {
        face = Polygon(f[i])
        icosphere.Add(face)
        sceneShapes.pop(face)  // to avoid that Polygon() puts faces in the scene
    }
    icosphere.Perform()
    let sewedsphere = icosphere.SewedShape()
    console.log(sewedsphere.ShapeType())  // check type 3 (shell) of the result
    console.log(sewedsphere.Closed())  // check if the shell is closed (true)
    
    // create a solid
    let result = new oc.BRepBuilderAPI_MakeSolid()
    result.Add(sewedsphere)
    let finalresult = result.Solid() 
    console.log(finalresult.ShapeType())
    return finalresult
}

// draw the isosphere
let test= Icosahedron(2.0);

test = Scale(50,test,false)
test = Translate([20,20,220],test,false)
console.log(test.ShapeType())

// draw a box
let box = Box(200,200,200)
console.log(box.ShapeType())

// draw a standard sphere
let studioSphere = Translate([50,30,20],Sphere(100))
console.log(studioSphere.ShapeType())

box = Difference(box,[studioSphere])
// let experiment = Difference(box,[test])

[Lisztes]

The problem is causeb by the Scale command. If we chose a bigger radius, and do not apply the Scale command, the code works.
Why?

I reproduced the problem with a simpler example. The Scale command might have issues.
The problem has nothing to do with the icospheres (size of radius, rounding error). If the scale factor equals 1, the result might be good.

// Faces
let face1 = Polygon([[0, 0, 0], [25, 50, 0], [50, 0, 0]])
let face2 = Polygon([[0, 0, 30], [50, 0, 30], [25, 50, 30]])
let face3 = Polygon([[0, 0, 0], [50, 0, 0], [50, 0, 30], [0, 0, 30]])
let face4 = Polygon([[50, 0, 0], [25, 50, 0], [25, 50, 30], [50, 0, 30]])
let face5 = Polygon([[25, 50, 0], [0, 0, 0], [0, 0, 30], [25, 50, 30]])
console.log(face1.ShapeType()) // 4

// Shell
let builder = new oc.BRepBuilderAPI_Sewing()
builder.Add(face1)
builder.Add(face2)
builder.Add(face3)
builder.Add(face4)
builder.Add(face5)
builder.Perform()
let shell = builder.SewedShape()
console.log(shell.ShapeType())  // 3

// Solid
let solid_builder = new oc.BRepBuilderAPI_MakeSolid()
solid_builder.Add(shell)
let solid = solid_builder.Solid()
console.log(solid.ShapeType())  // 2

// Scale
let solidS = Scale(1.2, solid, false)
console.log(solidS.ShapeType())  // 2

// FilletEdges
let solid_filleted = FilletEdges(solidS, 15, [1, 5])
sceneShapes = [solid_filleted]
console.log(solid_filleted.ShapeType())  // 0

[raydeleu]

Might also be caused by the size of the radius? Something like rounding errors? So what happens if you use an even larger radius and scale the shape down? Or scale with factor 1? Then we would know for sure that the Scale function is the culprit.