Sketching Type I and Type II Regions

Type I and Type I regions are easily drawn parametrically, but must be done in three space to allow the use of the two parameters necessary. We draw the region in the plane z = 0, and set the orientation to look straight down on it, so that it looks like a two dimensional picture. To do this use the option, orientation = [-90,0] . Other useful options are axes = normal to draw in the coordinate axes, and scaling = constrained to draw the region using 1:1 scale.

The Type I region, 0 <= x <= 1, x <= y <= 2 - x, would be drawn as follows

> plot3d([x,y,0],x=0..1,y=x..(2-x),orientation=[-90,0],axes=normal);

To see the graph with the same units on both axes, click on the graph and then on the 1:1 button, or add the scaling = constrained option.

> plot3d([x,y,0],x=0..1,y=x..(2-x),orientation=[-90,0],axes=normal,scaling=constrained);

The Type II region, 1 <= y <= 2, y <= x <= y^3, would be drawn as follows. Note that unconstrained scaling gives a better, albeit somewhat distorted, view of the region.

> plot3d([x,y,0],x=y..y^3,y=1..2,orientation=[-90,0],axes=normal);

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