Twelve lessons

SeenGeometry

Twelve pictures. Each one is a matrix acting on a shape.

  1. 01

    Instanced field

    One box. Many matrices. Every copy is drawn in one pass.

    Games, cities, and repeated parts

  2. 02

    Morph targets

    Spike and squash. Two weights move the same points.

    Faces, speech, and product shapes

  3. 03

    Order of transforms

    Same translate, rotate, and scale. Three products. Three pictures.

    Robots, bones, and assemblies

  4. 04

    Point vs direction

    w = 1 moves. w = 0 stays. Same translation.

    Normals, maps, and physics

  5. 05

    Shear

    The area stays 1. The corner angle changes.

    Type, drawings, and scans

  6. 06

    Determinant and reflection

    A negative determinant flips the shape. Zero flattens it.

    Area, mirrors, and warnings

  7. 07

    Fold

    A crease reflects the sheet. The mark flips.

    Symmetric parts and folded sheets

  8. 08

    Rotation

    A point on the circle. Two folds make one turn.

    Cameras, joints, and sensors

  9. 09

    Projection

    A house drops onto a plane. Top, front, and side. det = 0.

    Plans, elevations, and drawings

  10. 10

    Perspective

    Move the eye. Divide by w. Depth lines meet on the horizon.

    Cameras, drawings, and phones

  11. 11

    Inverse

    Apply a matrix, then its inverse. The product is the identity.

    CAD, cameras, and a teaching cipher

  12. 12

    Eigenvectors

    Most arrows turn. The red ones stay on a line and stretch by λ.

    Search, data, and structures