What is a 3D model?
A 3D model is a description of a shape in three directions: width (x), height (y) and depth (z). The computer stores it as numbers.
- Vertex (plural vertices): a point with x, y, z coordinates.
- Edge: a straight line joining two vertices.
- Face (polygon): a flat surface closed by edges, usually a triangle or a four-sided “quad”.
- Mesh: all the vertices, edges and faces together.
A cube has 8 vertices, 12 edges and 6 faces. For any closed simple solid, V − E + F = 2 (Euler’s rule). Check: 8 − 12 + 6 = 2.
Kinds of 3D modelling
- Polygon (mesh) modelling: for games, films, VR.
- Solid modelling in CAD: exact sizes in mm for engineering and products.
- Sculpting: push and pull a surface like clay, for characters.
- 3D scanning: copying a real object into a mesh.
Building a model: primitives, transforms and extrude
Most models start from primitives: cube, sphere, cylinder, cone, plane.
Transforms
- Move (translate): change position along x, y or z.
- Rotate: turn by an angle about an axis.
- Scale: make bigger or smaller (×2 doubles every length).
Box modelling
Start with a box, then:
- Extrude a face: pull it out to make a new part (arms, a handle).
- Inset/loop cut: add more edges where you need detail.
- Subdivide/smooth: split faces into smaller ones so the shape looks rounder.
In CAD, you often draw a 2D sketch with exact sizes and then extrude or revolve it into a solid. Other tools: Boolean (join, subtract or intersect two shapes), fillet (round an edge) and mirror (copy to the other side).
Mock-ups and prototypes
Designers check ideas with quick card or foam mock-ups, then a 3D model, then a printed prototype to test size and fit.
Materials, lights, cameras and rendering
A mesh alone is just grey shape. To make a picture we add:
- Material: colour, shininess, roughness, see-through or not.
- Texture: an image wrapped on the surface (wood grain, skin). The flat layout used for wrapping is called a UV map.
- Lights: sun, point, spot lights make shading and shadows.
- Camera: chooses the view, like a real camera.
Rendering is when the computer calculates the colour of every pixel from these. Games render in real time (about 60 pictures a second). Films use slower, more realistic rendering that can take minutes per frame. Models can also be animated or shown in VR and AR.
3D printing (additive manufacturing)
Additive means building by adding material, layer by layer. (Cutting material away, like on a lathe, is subtractive.)
- Design the model and export it (often as an STL or 3MF file).
- A slicer program cuts it into thin horizontal layers and plans the nozzle path.
- The printer builds from the bottom up. In FDM printing, a hot nozzle melts plastic filament (like PLA) and draws each layer.
Layer height is often 0.1–0.3 mm. Thinner layers look smoother but take longer. Number of layers = height ÷ layer height. A 24 mm tall model at 0.2 mm per layer needs 24 ÷ 0.2 = 120 layers.
Overhangs need supports. Infill (for example 20%) fills the inside with a light pattern to save plastic. Uses: prototypes, spare parts, medical models, prosthetic hands, even houses printed in concrete.
Key formulas and definitions
- Vertex = point (x, y, z); Edge = line between 2 vertices; Face = flat surface
- V − E + F = 2 (simple closed solid)
- Transform = move (translate) + rotate + scale
- Extrude = pull a face or sketch out into 3D
- Rendering = computing the final picture from model + materials + lights + camera
- Number of layers = model height ÷ layer height
- Additive = add material layer by layer; subtractive = cut material away
Worked examples
1. A cube has one face extruded. How many vertices, edges and faces now? Check with Euler’s rule.
Extruding one face adds 4 vertices, 8 edges and 4 faces: V = 12, E = 20, F = 10. Check: 12 − 20 + 10 = 2 ✓.
2. A 4 cm tall box is scaled by 1.5. How tall is it now?
Scale multiplies every length: 4 × 1.5 = 6 cm.
3. A model 30 mm tall is printed with 0.2 mm layers. How many layers? If one layer takes 20 s, how long in minutes?
Layers = 30 ÷ 0.2 = 150. Time = 150 × 20 = 3000 s = 50 minutes.
4. You want a mug. Which operations would you use in box modelling?
Start with a cylinder, inset the top face and extrude it downwards to hollow the inside, extrude a small box on the side into a handle, then subdivide/smooth.
Common mistakes
- Thinking a 3D model is a picture. It is data (vertices, edges, faces); the picture comes from rendering.
- Mixing extrude and scale. Extrude adds new geometry; scale only resizes what is there.
- Forgetting units: CAD for printing needs real sizes in mm.
- Thinking thinner print layers are always better. They are smoother but take much longer.