Parametric Equations

Parametric curves

A parametric curve is a point that is a function of a parameter t. Points are vectors, so a parametric is written with the same mat notation as any other vector (see Matrices, vectors and points), with components that use t:

Start 2 by 1 matrix, Row 1: cos ( 3 "t" ) ; Row 2: sin ( 2 "t" ) , End matrix

The color, thickness, and visibility of a parametric curve can be adjusted using the settings panel accessed by right clicking the graphs color swatch, the same way as it would in be in any other graph.

Parametric bounds

The parameter runs from 0 to 1 by default. A parametric box shows a small t: 0 to 1 row underneath it; edit the two numbers to change the range.

Recording of the calculator performing the steps described above

Parametrics from matrix math

A parametric curve does not have to be written as a literal vector. Anything that evaluates to a point and depends on t is drawn the same way, which means you can build a parametric out of matrix operations. Here a 3D helix is rotated using a rotation matrix, and then flattened onto the screen with a 2 by 3 projection matrix (the same idea as the torus graph on the home page). Since the final expresion is a 2x1 vector, and it depends on t, it is drawn as a 2d parametric curve.