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Plotting 2D slices of CylindricalDecomposition objects?

Colin Rowat
Posted 3 years ago

I want to plot 2D slices of eight objects, $K1,...,K8$, in $(x,y,z) \in \mathbb{R}^3_+$. I am happy for the slices to be parallel to the planes.

The objects are returned from CylindricalDecomposition. Currently, I am plotting

RegionPlot3D[{K1, K2, K3, K4, K5, K6, K7, K8},{x,0,4},{y,0,4},{z,0,4}]

I would like something like

RegionPlot[{K1, K2, K3, K4, K5, K6, K7, K8},{x,0,4},{y,0,4},{z=i}]

for different fixed values of $i$.

One way of doing this would be to add $z=i$ as a constraint to $K1,...,K8$, but this seems labour intensive.
POSTED BY: Colin Rowat
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Colin Rowat
Colin Rowat
Posted 3 years ago

In my original formulation, each $K[i]$ contains the result of a CylindricalDecomposition call with variables $\{x,y,z\}$.

Thus, the problem with my RegionPlot above is that fixing $z=i$ passes two variables ( $x$ and $y$) and a constant ( $z=i$) to a CylindricalDecomposition expecting three variables. This yields error messages like "1 is not a valid variable".

Here is a MWE for a solution:

arg1[x_, y_, z_] := {x >= y && y >= z && z >= 0}
RegionPlot3D[Evaluate[CylindricalDecomposition[arg1[x, y, z], {x, y, z}]], {x, 0, 2}, {y, 0, 2}, {z, 0, 2}]
RegionPlot[Evaluate[CylindricalDecomposition[arg1[x, y, 0], {x, y}]], {x, 0, 2}, {y, 0, 2}]
POSTED BY: Colin Rowat
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