Primitive modelling
A primitive is a basic solid that a 3D program gives you at once. The common ones are:
- Box (cuboid): 6 flat faces, 12 edges, 8 corners (vertices).
- Sphere: one curved surface.
- Cylinder: 2 flat circles and 1 curved side.
- Cone: 1 flat circle, 1 curved side and 1 tip.
Primitive modelling means making an object by placing, sizing, turning and joining these solids. A chair is a flat box (seat), four thin cylinders (legs) and a box (back): 6 primitives. A snowman is 3 spheres, a cone nose and two cylinders for a hat. You can also subtract one primitive from another, like drilling a hole with a cylinder. Good tips: name every part, keep the sizes in real units (cm), and start with the biggest part.
For a box the numbers fit Euler's rule: corners − edges + faces = 8 − 12 + 6 = 2.
Profile modelling
Some shapes are hard to build from primitives. Then we draw a flat outline, the profile, and turn it into a solid.
- Extrude: pull the profile straight out, like squeezing dough through a mould. The solid has the same cross-section all along. Volume = area of profile × depth. An L-shaped profile gives an L-shaped beam.
- Revolve (lathe): spin the profile around an axis. A curve with a wide belly and a narrow neck becomes a vase. A rectangle spun around one edge becomes a cylinder, with volume = π × r² × h.
Tip: a revolve profile must be drawn on one side of the axis only. A partial revolve (say 180 degrees) gives a half-vase, which is handy for checking the inside. Other profile tools are sweep (move a shape along a path, like a pipe) and loft (blend between two different profiles).
Assembly
Real products have many parts. We build each part as its own model, then put them together in an assembly.
- Make parts: seat, leg, ring.
- Fix one part: the base or the biggest part stays still. It is the reference.
- Add mates (constraints): rules that say how parts touch, such as "the top of the leg meets the underside of the seat", "this hole lines up with that pin", "these two faces are flush".
- Check: that parts do not overlap and that moving parts move the right way.
Our stool has 5 parts: 1 seat, 3 legs and 1 ring that braces the legs. In the 3D, slide to bring each part home. Making a part once and re-using it (3 legs from one leg) saves time. This also means a change to the leg changes all three.
Exploded views
An exploded view moves the parts of an assembly apart along straight lines, in the order and direction they would be assembled. It shows every part and how it fits without hiding anything.
- Parts move along the axis they slide on (up for the seat, outward for the legs).
- Thin guide lines show where each part goes.
- Parts are numbered and listed in a parts list (a bill of materials).
You will see exploded views in furniture instructions, phone repair guides, engine manuals and product adverts. The ring in our stool is hidden when closed, but it shows clearly when exploded.
Parametric models and a quick workflow
In a parametric model the shapes depend on numbers (parameters) such as leg height and seat width. Change one number and every part updates, as in the free-play step. This saves hours when a design changes.
Workflow: plan on paper, build primitives, add profile solids, name and colour parts, assemble with mates, check, create the exploded view, and export (for example for 3D printing or a game).
Try it
At home, look for objects made of primitives: a can is a cylinder, a funnel is a cone, a ball is a sphere. Draw a mug: what is the profile you would revolve? (A rectangle for the wall, and a small handle added as another part.) In the 3D, set Extrude depth to 3.0 and the angle to 180 degrees. Predict first, then check.
Key formulas and definitions
- Box: V − E + F = 8 − 12 + 6 = 2
- Extrude volume = profile area × depth
- Cylinder from a revolved rectangle: V = π r² h
- Assembly = parts + mates (constraints)
- Exploded view = parts moved along their assembly axes
Worked examples
1. How many primitives does the chair in the 3D use, and which kinds?
6 primitives: 1 box (seat), 4 cylinders (legs) and 1 box (back).
2. A rectangular profile 4 cm by 3 cm is extruded 5 cm. Find the volume of the solid.
Area = 4 × 3 = 12 cm². Volume = 12 × 5 = 60 cm³.
3. A rectangle 2 cm wide and 5 cm tall is revolved 360 degrees around its tall edge. What solid is made and what is its volume (π = 3.14)?
A cylinder with radius 2 cm and height 5 cm. V = 3.14 × 2² × 5 = 3.14 × 20 = 62.8 cm³.
4. An L-shaped profile is made of a 6 × 2 rectangle and a 2 × 4 rectangle that do not overlap. Extrude it 3 cm. Find the volume.
Area = 12 + 8 = 20 cm². Volume = 20 × 3 = 60 cm³.
5. Why does the stool need a ring in an exploded view when you hardly see it assembled?
The ring braces the legs and is inside the stool. An exploded view pulls the parts apart so hidden parts like the ring become visible.
Common mistakes
- Making the whole model as one lump. Build separate named parts so you can change or reuse them.
- Revolving a profile that crosses the axis. It makes a messy, self-crossing solid. Draw it on one side only.
- Moving exploded parts in random directions. Move each along the line it would slide in when assembling.
- Forgetting units. Keep sizes in centimetres or millimetres from the start.