Learning By ExamplesTetrahedron

Tetrahedron

Method used

In this example we will use the “Cut Cube” method for making a tetrahedron using extrusions only. The idea is to start from a cube. On that cube we can look at the opposite corners (ie a set of corners that are not connected by an edge). If we define a plane going through 3 of these corners, we get 4 faces of a tetrahedron.

Helper assembly

The helper assembly displays the cube and the opposite corners.

Full Code

Explanations

Step 1: Making a cube

def add_cube(self):
        sketch = Sketch(self.xy())
        square = Square.from_center_and_side(sketch.origin, self.cube_side)
        extrusion = Extrusion(square, -self.cube_side / 2, self.cube_side / 2)
        self.add_operation(extrusion)

After creating the component we add a cube to it using a simple extrusion.

Step 3: Get the Cube Points

We can then use the following code to obtain the 8 corners of the cube.

def get_cube_points(self):
        points = []
        for i in range(2):
            for j in range(2):
                for k in range(2):
                    points.append(
                        Point3D(
                            i * self.cube_side - self.cube_side / 2,
                            j * self.cube_side - self.cube_side / 2,
                            k * self.cube_side - self.cube_side / 2,
                        )
                    )
        return points

They come in a list of 8 points and we select the following ones :

tetra_indices = [0, 3, 5, 6]

to be the corners of the tetrahedron.

Step 4: Define Cutting Planes

def cut_plane_from_3_points(self, points, cut=True):
        p1, p2, p3 = points
        plane = self.pf.get_plane_from_3_points(self.head._frame, [p1, p2, p3])
        sketch = Sketch(plane)
        # cut almost everything one one side of the plane
        square = Square.from_center_and_side(sketch.origin, self.side * 4)
        extrusion = Extrusion(square, -self.side, cut=True)
        self.add_operation(extrusion)

Using the corners we create a list of 4 sets of 3 points. Each set of 3 points defines a plane that will cut the cube. We can use the helper function from the PlaneFactory.get_plane_from_3_points function to create planes from 3 points. We then just draw a large square to cut each of the sides of the tetrahedron.

⚠️

The order of the points in the plane definition maters as it will define the direction of plane normal and thus the side of the half-space that will be cut.

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