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Welcome to the Parametric Lab

Learn the foundations of parametric and generative design — from Grasshopper primitives like points, planes, and data trees, through attractor fields, Voronoi diagrams, recursion, and pathfinding — all animated with sliders you control. Then build your own algorithm graphs in the visual node sandbox.

16 animated modulesGH Foundations (points, domains, lists, data trees), parametric geometry (attractors, Voronoi, subdivision), and algorithm fundamentals (sorting, pathfinding, recursion) — each interactive with live controls.

Visual node sandboxWire together algorithm nodes on a canvas. Build your own generative patterns and save them to share or revisit later.

No code requiredEvery concept is explained visually first. The guided lessons walk you through what to look for and what to tweak.

Guided Path0/16 done

Geometry · Foundations

Points, Planes & Vectors

The three primitives every Grasshopper definition is built on: a point is a location [x,y,z], a vector is a direction with magnitude, and a plane is a local coordinate system.

Point grid density11

Vector scale %80

Show plane axes (0=off 1=on)1

ELI5

Think of a city map. A point is a specific address. A vector is a set of walking directions: '3 blocks east, 2 north' — it has length and direction but no fixed start. A plane is a building floor: it has an origin corner, a front direction (X), a side direction (Y), and a direction pointing straight up (Z) out of it.

How it works

A point stores [x, y, z]. A vector has the same structure but means 'go this far in this direction.' A plane is an origin point plus three perpendicular unit vectors labelled X, Y, Z. Move your cursor to see a vector from the world origin to your cursor point.

Glossary

Point: A location in 3D space defined by three numbers [x, y, z]. The most basic data type in any geometry system.
Vector: A direction and magnitude — visualised as an arrow. Same data as a point but relative: describes 'which way and how far' rather than 'where.' Has no fixed position.
Plane: A local coordinate system: an origin point, an X axis, a Y axis, and a Z normal perpendicular to both. Everything you orient in Grasshopper — circles, boxes, extrusions — references a plane.
World Origin: The fixed reference point [0, 0, 0] where world axes meet. All points and vectors are measured relative to this.

Where this shows up

🪑
Orienting joints
A mortise-and-tenon joint is placed and oriented using a plane — the plane says where the joint sits and which way it faces.
🏢
Facade panels
Each panel on a curved facade has its own plane telling Grasshopper 'this panel is here and faces outward at this angle.'
💡
Light direction
A directional light in rendering is a vector: it has direction but no single source position.
🌀
Sweep paths
Sweeping a profile along a curve: at each curve point, Grasshopper places a plane using the tangent vector and the profile is drawn in that plane.

Furniture takeaway

Every bracket, hinge, or leg attachment is placed at a point with a specific orientation — that's a plane. Grasshopper designers use planes to orient joints, handles, and fastener holes across complex surfaces without repositioning each one by hand.

Code (Python + GH)

⬡ Grasshopper node graph

Construct Point [x,y,z]→Unit Vector→Plane Normal→XY / YZ / XZ Plane

Use Construct Point with Number sliders for x, y, z to place any point in space.
Unit Vector normalises any direction to length 1 — always safe for orientation input.
Plane Normal takes an origin + normal vector → returns a plane oriented to that normal.
Feed that plane into Circle, Box, or Extrude — geometry sits at your point, facing your direction.

🐍 Python — paste-readyIronPython 2.7 / CPython 3

# ============================================================
# Build a point, a vector, and a plane
# ------------------------------------------------------------
# COMPONENT: GhPython (R6/7) or Script > Python 3 (R8)
# INPUTS to create on the component (right-click > add input):
#   x — type hint: float, access: Item
#   y — type hint: float, access: Item
#   z — type hint: float, access: Item
# OUTPUTS: pt — Point3d, vec — Vector3d (unit), pl — Plane
# NOTE: Pure Rhino.Geometry, no extras needed.
# ============================================================
import Rhino.Geometry as rg

# A point — a location
pt = rg.Point3d(x, y, z)

# A vector — a direction (auto-unitised to length 1)
vec = rg.Vector3d(x, y, z)
vec.Unitize()

# A plane — origin + normal direction
# (X and Y axes are auto-computed perpendicular to normal)
pl = rg.Plane(pt, vec)

# Access the axes:
# pl.XAxis  pl.YAxis  pl.ZAxis (the normal)

Feed pl into a Circle or Box Plane input — geometry now sits at your point facing your direction, not the default world XY.

Grasshopper analogue: Construct Point, Unit Vector, XY Plane — the first components in almost any definition. Nearly every geometry operation needs a plane to know where and how to orient itself.