# program a wall in which an object can not pass

This is the code we have created so far for a Pacman type game:

DynamicModule[{diskPosition = {250, 450}, diskRadius = 15,
pacman = {9, 4}},
EventHandler[

PlotRange -> {{0, 460}, {0, 590}}, Background -> Black],

{
"LeftArrowKeyDown" :> {(pacman = {9, 4}), (diskPosition[[
1]] += -10)},

"RightArrowKeyDown" :> {(pacman = {1, 6}), (diskPosition[[1]] +=
10)},

"UpArrowKeyDown" :> {(pacman = {2, 7}), (diskPosition[[2]] += 10)},

"DownArrowKeyDown" :> {(pacman = {-2, -7}), (diskPosition[[
2]] += -10)}

}]]

We want to create a grid which the pacman cannot pass through the barriers, creating a maze it must go through.

• It might be easier to build a path along which the pacman can move (rather than a wall that it cannot cross). – bill s Nov 29 '16 at 18:46
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• How would would I build a path that the pacman can only move on? – pacman Nov 29 '16 at 20:59

Before making a move, test if the new position is a valid position. A valid position is one where Pac-Man does not touch the walls. Mathematica has convenient functions that deal with regions, so we might consider creating a region and then using those functions. Regions can be built using Graphics primitives and then converted into regions with DiscretizeGraphics, therefore we will first create a graphics object of the map. I decided to start from this image:

I used some image processing functions to turn the map into a region, but note that you can create your map by hand using Rectangle, Line, Polygon or whatever you may want.

img = ImageCrop@Binarize@Import["http://wallpapercave.com/wp/6SKGas2.png"];
components = MorphologicalComponents[Thinning[img]];
indices = DeleteCases[DeleteDuplicates@Flatten[components], 0];
curvePathPlots = ListCurvePathPlot[Position[components, #]] & /@ indices;
lines = Cases[Show[curvePathPlots, PlotRange -> All], _Line, Infinity];

lines now contains Line objects corresponding to all the lines. We now create the map, for displaying as a background, and the region, for collision checking.

map = Graphics[{Thickness[0.004], White, lines}, Background -> Black];
region = DiscretizeGraphics[map];

Evaluate map to see what it looks like, put a white disk of radius 20 in as well for scale:

Show[
map,
Graphics[{White, Disk[{420, 425}, 20]}]
]

Because of a change of coordinate system we've rotated the image, but it doesn't matter. The one who cares about it, may fix it.

Now we need a function that will tell us if a Pac-Man, represented as a disk of radius 20, collides with the walls, if it is positioned at a certain position. Since it is a disk it is equivalent to checking whether the distance to the wall is larger than 20:

freeQ[{x_, y_}] := RegionDistance[region, {x, y}] > 20

Now, an event in the EventHandler may look like this:

"LeftArrowKeyDown" :> If[freeQ[diskPosition - {10, 0}],
pacman = {9, 4};
diskPosition[[1]] += -10
]

This says "if the new position will not cause Pac-Man to collide with any wall, make the move." Here is your updated code:

DynamicModule[
{
diskPosition = {510, 470},
pacman = {9, 4}
},
EventHandler[Show[
map,
Graphics[
PlotRange -> {{0, 460}, {0, 590}}
]
],
{
"LeftArrowKeyDown" :> If[freeQ[diskPosition - {10, 0}],
pacman = {9, 4};
diskPosition[[1]] += -10
],
"RightArrowKeyDown" :> If[freeQ[diskPosition + {10, 0}],
pacman = {1, 6};
diskPosition[[1]] += 10;
],
"UpArrowKeyDown" :> If[freeQ[diskPosition + {0, 10}],
pacman = {2, 7};
diskPosition[[2]] += 10
],
"DownArrowKeyDown" :> If[freeQ[diskPosition - {0, 10}],
pacman = {-2, -7};
diskPosition[[2]] += -10
]
}]]

• This code is great except our pacman will only move along the center box. Any idea why our pacman can't move around the entire map? – pacman Dec 1 '16 at 16:24
• @pacman I think I demonstrate in my animation that the Pac-Man can in fact move around the entire map? – C. E. Dec 1 '16 at 20:38
• I tried it out but for some reason it only goes around the center box. – pacman Dec 1 '16 at 21:01
• @pacman I just tried it too. There was a slight change of image size when I uploaded the image, so I had to adjust the starting position (I've now incorporated this into answer), but other than that it runs fine... I'm using version 11, but I expect it to work in Mathematica 10 as well. – C. E. Dec 1 '16 at 21:17

Here's a maze for the pacman to operate in (which is taken from here)

style = {Background -> GrayLevel[0],
BaseStyle -> {Directive[White, EdgeForm[], Opacity[1]]},
VertexShapeFunction -> (Rectangle[#1 + .16, #1 - .16] &),
EdgeShapeFunction -> (Rectangle[#1[[1]] + .16, #1[[2]] - .16] &)};
embedding = GraphEmbedding[GridGraph[{20, 30}]];
g = GridGraph[{20, 30}, EdgeWeight -> RandomReal[10, 1150]];
tree = FindSpanningTree[{g, 1}];
maze = Binarize[Image[Rasterize[Graph[tree, VertexCoordinates->embedding, style],
RasterSize -> 1000], ImageSize -> 1000]];
m = 5;

Now the pac man in-the-maze, constrained with the If[] statements to the white portions of the maze.

DynamicModule[{diskPosition = {250, 450}, diskRadius = 15, pacman = {9, 4}},
EventHandler[
PlotRange -> {{0, 200}, {0, 300}}]],
{"RightArrowKeyDown" :>
If[PixelValue[maze, {diskPosition[[1]] + m, diskPosition[[2]]}] == 1,
pacman = {1, 6}; diskPosition[[1]] += m],
"LeftArrowKeyDown" :>
If[PixelValue[maze, {diskPosition[[1]] - m, diskPosition[[2]]}] == 1,
pacman = {9, 4}; diskPosition[[1]] += -m],
"UpArrowKeyDown" :>
If[PixelValue[maze, {diskPosition[[1]], diskPosition[[2]] + m}] == 1,
pacman = {2, 7}; diskPosition[[2]] += m],
"DownArrowKeyDown" :>
If[PixelValue[maze, {diskPosition[[1]], diskPosition[[2]] - m}] == 1,
pacman = {-2, -7}; diskPosition[[2]] += -m]}]]

here is an idea..crude but may show how to proceed.

box = {{50, 200}, {300, 200}, {300, 400}, {50, 400}, {50, 200}};
up[p_] :=
Module[ {t = p + {0, 10}},
If[ 200 - 15 < t[[2]] < 400 + 15 && 50 < t[[1]] < 300 , 0, 10]]
left[p_] :=
Module[ {t = p - {10, 0}},
If[ 200 < t[[2]] < 400 && 50 - 15 < t[[1]] < 300 + 15, 0, -10]]
right[p_] :=
Module[ {t = p + {10, 0}},
If[ 200 < t[[2]] < 400 && 50 - 15 < t[[1]] < 300 + 15, 0, 10]]
down[p_] :=
Module[ {t = p - {0, 10}},
If[ 200 - 15 < t[[2]] < 400 + 15 && 50 < t[[1]] < 300 , 0, -10]]
DynamicModule[
{diskPosition = {250, 450}, diskRadius = 15, pacman = {9, 4}},
EventHandler[
Thick, White, Line[box]}, PlotRange -> {{0, 460}, {0, 590}},
Background -> Black], {
"LeftArrowKeyDown" :> {(pacman = {9, 4}), (diskPosition[[1]] +=
left[diskPosition])},
"RightArrowKeyDown" :> {(pacman = {1, 6}), (diskPosition[[1]] +=
right[diskPosition])},
"UpArrowKeyDown" :> {(pacman = {2, 7}), (diskPosition[[2]] +=
up[diskPosition])},
"DownArrowKeyDown" :> {(pacman = {-2, -7}), (diskPosition[[2]] +=
down[diskPosition])}}]]

as noted in comment it may be better to define a permissible path, which would amount to a list of permissible positions on a 10x10 grid. Then as you do each update you check if the updated position is in the permissible list ( MemberQ maybe. )

grid = Table[ {i, 450}, {i, 100, 400, 10}]~Join~
Table[ {100, j}, {j, 100, 500, 10}];
up[p_] := Module[ {t = p + {0, 10}}, If[ MemberQ[grid, t] , 10, 0]]
left[p_] := Module[ {t = p - {10, 0}}, If[ MemberQ[grid, t] , -10, 0]]
right[p_] := Module[ {t = p + {10, 0}}, If[ MemberQ[grid, t] , 10, 0]]
down[p_] := Module[ {t = p - {0, 10}}, If[ MemberQ[grid, t] , -10, 0]]
DynamicModule[
{diskPosition = {250, 450}, diskRadius = 15, pacman = {9, 4}},
EventHandler[