49 | 50 | maze.js 51 | 52 |
53 | Given a surface, defined as collection of cells divided 54 | by walls, we can generated a simple maze by finding a 55 | spanning tree of the graph whose nodes are the cells and 56 | whose edges are the walls. Here we use Kruskal's algorithm 57 | to build up the spanning tree: pick walls randomly to 58 | include or exclude from the tree; include if the cells on 59 | either side are already connected, otherwise exclude 60 | (so as to connect the cells on either side in the 61 | resulting tree). Repeat until all walls have been 62 | considered. 63 |
64 | We can describe a 3-dimensional surface by a set of points 65 | and a set of faces, with each face having a list of 66 | points as its boundary. A wall is then just a pair of 67 | points that are adjacent in one or two cell boundaries and 68 | we can then apply our maze generating algorithm as above. 69 |
70 | Having determined the set of walls in the maze, we can 71 | then use the coordinates of the points to 72 | construct a 3-dimensional model. All we need is a base 73 | model to start with, and this is conveniently given by an 74 | OFF file as generated by a tool such as 75 | Antiprism, used here 76 | to generate models for a (dual) geodesic sphere, a torus 77 | and a Möbius strip. 78 |
Click on a pane for an expanded, more interactive 79 | view. Controls for the expanded view are:
80 |91 | 92 | maze3.js 93 | 94 |
95 | Alternatively, we can construct a true 3d maze. Here we 96 | generate the underlying geometry directly with some Javascript: 97 |
98 | 109 |This is all using a framework I've been experimenting with, 111 | based on Three.js, for 112 | drawing polyhedra and other geometric objects: 113 |