In my previous question 2D random walk within a bounded area, I asked how to implement a 2D random walk within a bounded area. In the provided solution, one can use Rectangle[{-10, -10}, {10, 10}] or Disk[{x, y}, r] to define the bounded region as a disk or rectangle. How can I define new bounded regions in Mathematica?
For example, how can I add these two Rectangle[{-10, -10}, {10, 10}] and Rectangle[{10, 0}, {15, 5}] to get a new region made of these two rectangles?
As Pickett's answer in the comment, if you are using v10 then you may try this:
r = RegionUnion[Rectangle[{-10, -10}, {10, 10}],
Rectangle[{10, 0}, {15, 5}]];
RegionPlot[r, BoundaryStyle -> Black, PlotStyle -> Black,
Frame -> False]
RegionUnion this question should be closed as "can easily be found in the documentation".
$\endgroup$
RegionUnion..
$\endgroup$
If you do not want to use RegionUnion[], it is easy to produce a Polygon[] corresponding to the desired shape: this hinges on the use of the undocumented functions Graphics`PolygonUtils`PolygonUnion[] and Graphics`PolygonUtils`PolygonCombine[]. (In much older versions, they were in the Graphics`Mesh` context.) In your case, you will need the additional step of needing to convert Rectangle[] into an explicit Polygon[].
r1 = Rectangle[{-10, -10}, {10, 10}]; r2 = Rectangle[{10, 0}, {15, 5}];
new = Composition[Graphics`PolygonUtils`PolygonCombine,
Graphics`PolygonUtils`PolygonUnion][{r1, r2} /.
Rectangle[pmin_, pmax_] :> Polygon[{#1, #2, #4, #3} & @@
Tuples[Transpose[{pmin, pmax}]]]];
{Graphics[new], Graphics[Line @@ new]} // GraphicsRow
Polygonon earlier versions. $\endgroup$Element[position + randomStep, region]is the line that determines if the new step is valid or not. If you use an earlier version than 10, you don't have access toRegionUnionso you can't combine arbitrary shapes. Instead you have to writeElement[position + randomStep, rectangel1] || Element[position+randomStep, rectangle2]to indicate that both areas are valid. $\endgroup$