3D Visualization

Rotate and zoom a three-dimensional object.

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Question

How can matrices rotate, resize, move, and display a three-dimensional object?

Matrix multiplication carries each 3D point from the model to the screen.
Matrix multiplication carries each 3D point from the model to the screen.

Goals

  • Build matrix transformations for a 3D model.
  • Create interactive rotation and zoom with a screen projection.

Method

Store the object as coordinates and transform every point with matrices.

  • Represent vertices and edges in homogeneous coordinates.
  • Multiply by rotation, scaling, translation, camera, and projection matrices.
  • Render the transformed points and connect controls for rotation and zoom.

Try an example

Rotate!

Source code ↗ Open full screen ↗

A playable example that applies rotation matrices and scaling to a wireframe torus.

Controls: Press Enter. Use W/S, Q/E, and A/D for the three rotation axes; use Up/Down to zoom.