namespace nilrider { ld f_heisenberg0(hyperpoint h) { return 0; } ld rot_plane(hyperpoint h) { return h[0] * h[1] / 2; } ld f_rot_well(hyperpoint h) { return h[0] * h[1] / 2 + h[0] * h[0] + h[1] * h[1]; } ld long_x(hyperpoint h) { return h[0] * h[1]; } ld geodesics_0(hyperpoint h) { ld r = hypot_d(2, h); ld phi = atan2(h[1], h[0]); ld z = (phi / 2 / M_PI) * (M_PI * r * r + 2 * M_PI); return z + rot_plane(h); } ld geodesics_at_4(hyperpoint h) { ld r = 4; ld phi = atan2(h[1], h[0]); ld z = (phi / 2 / M_PI) * (M_PI * r * r + 2 * M_PI); return z + rot_plane(h); } map bcols = { {' ', 0xFF101010}, {'W', 0xFFFFFFFF}, {'g', 0xFF008000}, {'h', 0xFF20A020}, {'r', 0xFFFF4040}, {'u', 0xFF4040FF}, {'b', 0xFF804000}, {'l', 0xFF0000C0}, {'f', 0xFF603000}, {'F', 0xFF804000}, {'2', 0xFF404040}, {'4', 0xFF808080}, {'6', 0xFFC0C0C0}, }; map > submaps = { {'o', { "WWWWWWWWWWWWWWWW", "W22222222222222W", "W22222666622222W", "W22266222266222W", "W22622222222622W", "W22622222222622W", "W26222222222262W", "W262222WW222262W", "W262222WW222262W", "W26222222222262W", "W22622222222622W", "W22622222222622W", "W22266222266222W", "W22222666622222W", "W22222222222222W", "WWWWWWWWWWWWWWWW" }}, {'x', { "WWWWWWWWWWWWWWWW", "W22222222222222W", "W22222222222222W", "W22222222222222W", "W22222222222222W", "W22222222222222W", "W22222622622222W", "W222222rW222222W", "W222222Wr222222W", "W22222622622222W", "W22222222222222W", "W22222222222222W", "W22222222222222W", "W22222222222222W", "W22222222222222W", "WWWWWWWWWWWWWWWW" }}, {'b', { " ", " rrr rrr rrr rrr", " ", "rr rrr rrr rrr r", " ", " rrr rrr rrr rrr", " ", "rr rrr rrr rrr r", " ", " rrr rrr rrr rrr", " ", "rr rrr rrr rrr r", " ", " rrr rrr rrr rrr", " ", "rr rrr rrr rrr r", }}, {'f', { "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", "FfFfFfFfFfFfFfFf", "fFfFfFfFfFfFfFfF", }}, {'l', { "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", "llllllllllllllll", }}, {'g', { "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", }}, {'G', { "ghghghghghghghgh", "hghghghghghWhghg", "ghghrhghghWlWhgh", "hghrWrhghghWhghg", "ghghrhghghghghgh", "hghghghghghghghg", "ghghghghghghghgh", "hghghghlhghghghg", "ghghghlWlhghghgh", "hghghghlhghghghg", "ghghghghghghgrgh", "hghglghghghgrWrg", "ghglWlghghghgrgh", "hghglghghghghghg", "ghghghghghghghgh", "hghghghghghghghg", }}, {'r', { "rrrrrrrrrrrrrrru", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "ubbbbbbbbbbbbbbu", "urrrrrrrrrrrrrrr", }}, {'*', { "WWWWWW WW WWWWWW", "W W", "W W", "W W", "W W", "W rr W", " rr ", "W r r W", "W r r W", " r r ", "W r r W", "W rrrrrrrr W", "W W", "W W", "W W", "WWWWWW WW WWWWWW", }}, {'+', { "gh WW gh", "hg WW hg", " WW ", " ", " ", " WW ", " WW ", "WWW WWWWWW WWW", "WWW WWWWWW WWW", " WW ", " WW ", " ", " ", " WW ", "gh WW gh", "hg WW hg", }}, {'-', { "ghghghghghghghgh", "hghghghghghghghg", " ", " ", " ", " ", " ", "WWW WWWWWW WWW", "WWW WWWWWW WWW", " ", " ", " ", " ", " ", "ghghghghghghghgh", "hghghghghghghghg", }}, {'|', { "gh WW gh", "hg WW hg", "gh WW gh", "hg hg", "gh gh", "hg WW hg", "gh WW gh", "hg WW hg", "gh WW gh", "hg WW hg", "gh WW gh", "hg hg", "gh gh", "hg WW hg", "gh WW gh", "hg WW hg", }}, }; level rotplane( "Trying to be horizontal", 'r', 0, "All the lines going through the center are horizontal.", -7.5*dft_block, 7.5*dft_block, 8.5*dft_block, -8.5*dft_block, { "ggggggggggggggg!", "ggggggfffgggggg!", "ggggggfffgggggg!", "gggg|ggggg|gggg!", "ggg-*-----*-ggg!", "gggg|ggggf|gggg!", "ggGg|g+ggg|grgG!", "gGgg|g|xgo|gggg!", "ggGg|g|ggg|grgg!", "gggg|g|ggg|gggg!", "gg--*-+---*--gg!", "gggg|ggggg|gggg!", "gggggggGGgggggg!", "ggggggggggggggg!", "ggggggggggggggg!", "!!!!!!!!!!!!!!!!" }, 6, 6, rot_plane ); level longtrack( "A Long Track", 'l', 0, "The main street is horizontal, as well as the lines orthogonal to it.", 0*dft_block, +6.5*dft_block, 64*dft_block, -1.5*dft_block, { "Ggggggggr!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!", "Ggggggggr!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!", "Ggggggggr!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!x!", "Ggggxgggr!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!", "gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg", "ggggggggrggggggrggggggggrGggggggggGGggggGGGgggggGGGGggggggggggGG", "g+------------------------------------------------------------*G", "gggggfffffggggggggggggggggggggggggggggggggggggggggggggggggggggGG" }, 0, 5, long_x ); level geodesical( "Roads are Geodesics", 'g', nrlPolar, "All the roads here are helical geodesics.", -45*degree, 3*dft_block, 225*degree, 0, // -8*dft_block, +8*dft_block, +8*dft_block, 0, { "ffffffffffffffff", "----------------", "----------------", "----------------", "----------------", "----------------", "----------------", "bbbbbbbbbbbbbbbb", }, 0, 6, geodesics_0 ); level geodesical4( "Helical Geodesic", 's', nrlPolar, "The main road here is a helical geodesic. Orthogonal lines are horizontal.", -80*degree, 8.5*dft_block, 260*degree, 0.5*dft_block, // -8*dft_block, +8*dft_block, +8*dft_block, 0, { "!!!!!!!!!!!!!!!!", "ffffffffffffffff", "gggggggggggggggg", "ggGggggggggGgggg", "+--------------*", "gggggGggggGggggg", "gggGgggggGgggggg", "ffffffffffffffff", }, 0, 5, geodesics_at_4 ); level heisenberg0( "Heisenberg Zero", 'z', 0, "This is the plane z=0 in the Heisenberg group model of Nil. The roads are x=0, y=0 axes.", -7.5*dft_block, 7.5*dft_block, 8.5*dft_block, -8.5*dft_block, { "ggggggg|ggggggg!", "grggggg|gggggrg!", "ggggggg|ggggggg!", "gggffgg|ggggggg!", "gggffgg|ggfrggg!", "ggggggg|gggggGg!", "ggggggg|ggggggg!", "-------+-------!", "ggggggg|ggggggg!", "gggGgog|ggggggg!", "ggggggg|ggrgrgg!", "gggGgGg|ggggggg!", "ggggggg|ggggggg!", "grggggg|gggggrg!", "ggggggg|ggggggg!", "!!!!!!!!!!!!!!!!" }, 8, 8, f_heisenberg0 ); level rotwell( "Deep Well", 'd', 0, "Can you escape this well?", -7.5*dft_block, 7.5*dft_block, 8.5*dft_block, -8.5*dft_block, { "ggggggggggggggg!", "gogggggggggggog!", "ggggg--*--ggggg!", "gggg*ggggg*gggg!", "ggg*ggGfGgg*ggg!", "gg|ggfgggfgg|gg!", "gg|gGgggggGg|gg!", "gg*gfggxggfg*gg!", "gg|gGgggggGg|gg!", "gg|ggfgggfgg|gg!", "ggg*ggGfGgg*ggg!", "gggg*ggggg*gggg!", "ggggg--*--ggggg!", "gogggggggggggog!", "ggggggggggggggg!", "!!!!!!!!!!!!!!!!" }, 8, 8, f_rot_well ); level labyrinth( "Labyrinth", 'l', 0, "Go clockwise. The squares of this level have half of their usual length.", -7.5*dft_block/2, 7.5*dft_block/2, 8.5*dft_block/2, -8.5*dft_block/2, { "ogggrfffffffffo!", "g*ggrgggggggggg!", "ggggrgggggggggg!", "ggggrgggggggggg!", "ggggrgggrrggggg!", "ggggrgGGGrrgggg!", "ggggrGgggGrgggg!", "ggggrGgxgGrgggg!", "ggggrGgggGrgggg!", "ggggrrGGGrrgggg!", "gggggrrrrrggggg!", "ggggggggggggggg!", "ggggggggggggggg!", "ggggggggggggggg!", "offfffffffffffo!", "!!!!!!!!!!!!!!!!" }, 8, 8, rot_plane ); level *curlev = &rotplane; vector all_levels = { &rotplane, &longtrack, &geodesical, &geodesical4, &heisenberg0, &rotwell, &labyrinth }; }