3D Graphing

Draw the surface defined by a two-variable function.

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Question

How can a two-variable formula be turned into a readable picture of a surface?

A surface appears when sampled function values are joined across a two-dimensional grid.
A surface appears when sampled function values are joined across a two-dimensional grid.
A wireframe surface made from the sine and cosine functions.
A surface generated by the graphing code in the original calculus materials.

Goals

  • Sample a function of two variables and represent its values as points in three-dimensional space.
  • Render a surface that can be rotated, scaled, and viewed from different directions.

Method

Treat the formula as a height above each point of a grid.

  • Evaluate the function on a rectangular mesh of input points.
  • Join neighbouring points to form a wireframe or shaded surface.
  • Apply projection and coordinate transformations to produce the final image.