Merging Houses

My mother really likes playing those mobile merging games.

For the ones who don’t know, the goal of those games is to put together 2 objects of the same type to create another. In most cases, the game gives you tasks to complete, which you need to make different objects for.

I noticed that there is always a limit to how much you can merge objects. Mainly because it requires a lot of people to design and draw that many assets.

So the question is: can we automate that process? And can we create a merging game with an infinite number of objects?

The tools

#

For this project, I’ll be using the gmsh python library, as well as pygmsh for a simpler code syntax. Here are the 2 repositories:

Building a house

#

For this project, we’ll try to make houses of infinite sizes. So first, we need a house!

The first cube

#

A good house starts with a cube. So we’ll start by trying to make a cube using gmsh. Here is the python script that does so:

import gmsh
import pygmsh

# Starts describing the geometry
with pygmsh.occ.Geometry() as geom:
    # Add a cube to it
    mesh = geom.add_box(
        (0, 0, 0), # position
        (1, 1, 1)  # scale
    )

    # Convert the geometry to a real mesh
    geom.generate_mesh()

    # Write the generated mesh to the 'out.msh' file
    gmsh.write("out.msh")
    gmsh.clear()

When opening the generated out.msh with gmsh, we get this beautiful cube:

Better with a roof

#

Now our house needs a roof. Unfortunatly, we do not have any basic 3D form to put on top of it.

That’s why we’ll use extrusion.

Extrusion

#

The goal of extrusion is to extend a 2D face into 3D. For example, turning a square into a cube.

Here are the different steps of extrusion:

1. make a copy of the object you want to extrude, and move it to the desired position;
2. link each vertices from the 2 objects to create the missing faces.

Making the roof

#

To use extrusion, we first need our 2D object. We’ll start by drawing a triangle on top of the cube:

triangle = geom.add_polygon([
    [-0.1, -0.1,   1], # Removed -0.1 from each side of the roof
    [-0.1,  1.1,   1], # for a little offset with the main cube
    [-0.1,  0.5, 1.5],
], mesh_size=1)

Now we need to make the extrusion. Thankfully, pygmsh has a method to do just that:

# The copy is moved by 1.2 on the x axis
geom.extrude(triangle, (1.2, 0, 0))

This will give us our final roof:

How to get in

#

To make it seem like there is an entrance to the house, we need to carve a rectangle inside the house cube to imply its presence.

To do that, we’ll need boolean operations.

Boolean operations

#

There is 2 types of boolean operations we need for this project:

• union, which combines 3D objects;
• difference, which carves a object into the other.

It is identical to union and difference between 2 mathematical sets:

Making the door

#

To create our door, we’ll use a boolean diffenrece. We first need to highlight the space we want to remove:

door = geom.add_box(
    (0.4,   0,   0),
    (0.4, 0.1, 0.6)
)

Here is the result with only edges for more visibility:

Once the space is delimited properly, we simply remove it with the boolean difference.

geom.boolean_difference(mesh, door)

A complete house

#

Here is the final script for our building house:

import gmsh
import pygmsh

# Starts describing the geometry
with pygmsh.occ.Geometry() as geom:
    # Add a cube to it
    mesh = geom.add_box(
        (0, 0, 0), # position
        (1, 1, 1)  # scale
    )

    # Create the door box
    door = geom.add_box(
        (0.4,   0,   0),
        (0.4, 0.1, 0.6)
    )

    # Remove it from the body
    geom.boolean_difference(mesh, door)

    # Create the triangle
    triangle = geom.add_polygon([
        [-0.1, -0.1,   1],
        [-0.1,  1.1,   1],
        [-0.1,  0.5, 1.5],
    ], mesh_size=1)

    # Extrude it
    geom.extrude(triangle, (1.2, 0, 0))

    # Convert the geometry to a real mesh
    geom.generate_mesh()

    # Write the generated mesh to the 'out.msh' file
    gmsh.write("out.msh")
    gmsh.clear()

Define a merge pattern

#

Now that we are able to build a house, let’s define a pattern that will allow us to describe any type of house.

We’ll consider the house built earlier to be of level 0.

Here is the pattern we will use:

• a level 1 house has a larger base;
• a level 2 house has a flower pot;
• a level 3 house has a little balcony.

On level 4, we create a new level 0 floor for the house. Then the cycle continues: a level 5 house is composed of a level 3 base and a level 1 floor, a level 6 house is composed of a level 3 base and a level 2 floor, etc.

A larger house

#

To make a larger house, we simply to transform our base cube into a cuboid.

We also need to account for the change in the door placement.

Adding some plants

#

For the plants, we’ll add a cuboid at the front of the house to act as a pot, and 3 random ellipsoids to fill it. You can see the 3 different variations below:

A little balcony

#

For the balcony, same principle: we’ll combine cuboids with a boolean union:

New floor

#

This is where things gets fun.

New floors follow the same rules, with one small detail: we can’t have a door.

To keep a consistent level of details, we’ll add a window with the same method used for the door.

We create a window shaped form:

And remove it with boolean difference:

Here is the code used to do so:

# Add a cube for the floor
mesh = geom.add_box(
    (0, 0, 0), # position
    (1, 1, 1)  # scale
)

# Create the window frame
window_frame = geom.add_box((0.2, -0.1, 0.25), (0.6, 0.15, 0.5))

# Window glasses
glasslb = geom.add_box((0.225, -0.1, 0.275), (0.25, 0.2, 0.2))
glasslt = geom.add_box((0.525, -0.1, 0.275), (0.25, 0.2, 0.2))
glassrb = geom.add_box((0.225, -0.1, 0.525), (0.25, 0.2, 0.2))
glassrt = geom.add_box((0.525, -0.1, 0.525), (0.25, 0.2, 0.2))

# Combine the window with boolean union
window = geom.boolean_union([window_frame, glasslb, glasslt, glassrb, glassrt])

# Remove it with a boolean difference
geom.boolean_difference(mesh, window)

We’re missing one final detail to make the house truly complete.

Currently, we have this big empty space next to the last floor:

To fix this problem, we simply need to add a little roof section next to it.

Adding some variations

#

As a final touch, we’ll add some variations to the details. We’ll alternate the side of the window and the balcony on each floor.

Here is a level 8 house to illustrate:

Finishing notes

#

The script works well, but it isn’t perfect. You may have noticed when opening a file with gmsh, but the generated house is composed of way too many triangles.

The script also does not have great performances due to the many boolean operations in play:

If you want to tackle those problems, you can find the final of the script here: