Day 3 — Boolean Operations: Carving Shapes Like a Programmer

⏱ 15 min read + hands-on

Quick Recap

You can place primitives and move them with translate, rotate, and scale. But real-world objects aren't just floating spheres and boxes — they have holes, merged bodies, and intersecting geometry. That's what today covers.

The Big Three: union, difference, intersection

OpenSCAD gives you three Boolean set operations on geometry. If you've ever worked with sets in Java (Set.addAll, Set.retainAll, Set.removeAll), the mental model transfers directly.

All three use the same child scope syntax you learned with transforms — the operation wraps the shapes it applies to:

operation() {
    shape_A();
    shape_B();
}

Let's look at each one on its own first.

union() — Merging Shapes

union() joins all children into one continuous solid.

union() {
    cube([20, 10, 5]);
    translate([10, 5, 5])
        sphere(r = 6, $fn = 32);
}

A box with a sphere fused on top. They become one solid — no seam, no internal boundary. Run it and rotate the view to confirm they're merged, not just touching.

Worth knowing: Multiple shapes at the top level of a file are implicitly unioned. Writing union() explicitly does the same thing — you'll need the explicit form once we combine operations later.

difference() — Cutting Holes

difference() takes the first child as the base solid and subtracts every child after it.

difference() {
    cube([30, 30, 10]);
    translate([15, 15, -1])
        cylinder(h = 12, r = 5, $fn = 32);
}

A box with a circular hole through it. The cylinder is the drill bit — it never appears in the result.

Critical rule: order matters. First child = base. Everything else = cutter. Swap them and you get the inverse — a cylinder with a box-shaped void.

Java analogy: Think of the first child as this — the object being modified. The rest are arguments. difference(A, B, C) = A - B - C.

The Z-fighting trick

Make your cutter slightly taller than the base and start it 1 mm below (z = -1). This prevents z-fighting — a rendering flicker that happens when two faces sit exactly on the same plane.

difference() {
    cube([30, 30, 10]);             // base is 10mm tall
    translate([15, 15, -1])
        cylinder(h = 12, r = 5, $fn = 32);  // cutter: 12mm, starts at -1
}

You'll use this pattern every single time you drill a hole. File it away now.

intersection() — Keeping Only the Overlap

intersection() keeps only the volume that exists inside all children at the same time.

intersection() {
    sphere(r = 15, $fn = 32);
    cube([22, 22, 22], center = true);
}

Result: a sphere with its corners shaved flat — a rounded cube. The cube acts as a boundary; anything outside it is discarded. This is a clean trick for rounded shapes without complex maths.

Combining Them — A Real Example

Now that each operation makes sense on its own, here's where they work together.

Say you want a base plate with a cylindrical boss on it, and a bolt hole through the boss. That's three ideas: merge plate + boss, then drill a hole through the combined body.

difference() {
    // Base: plate and boss merged into one solid first
    union() {
        cube([40, 30, 6]);                              // flat plate
        translate([20, 15, 6])
            cylinder(h = 10, r = 6, $fn = 32);         // boss on top
    }
    // Drill a hole through the boss (and into the plate)
    translate([20, 15, -1])
        cylinder(h = 18, r = 3, $fn = 32);
}

Why the union() here? Without it, difference() would treat the boss cylinder as a cutter and subtract it from the plate — the opposite of what you want. The union() tells OpenSCAD: these two shapes together are the base, before anything gets subtracted.

This difference( union(...), cutter ) pattern comes up constantly in real models.

Today's Exercise

Build a hollow box — open at the top, with walls and a floor:

• Outer dimensions: 30 × 30 × 20
• Wall and floor thickness: 3mm

Use difference() with a smaller cube as the cutter. Think carefully: the cutter needs to leave a 3mm floor, so it shouldn't start at z = 0.

Expected result: rotate the view and look down — you should see a hollow interior with walls and a solid base.

Key Takeaway

Learn each Boolean cleanly before combining them. difference() is what you'll reach for most — base first, cutters after, always extend ±1mm to avoid z-fighting. union() merges solids, intersection() keeps overlaps. When you need to subtract from a composite body, wrap the base in union() first — that's the one case where they combine.

Tomorrow: variables and parameters — making your models reusable and dimension-driven, which is where OpenSCAD starts to feel genuinely like programming.