import numpy as np import pyrr from collections import defaultdict def getRay(x, y): direc = [y[0] - x[0], y[1] - x[1], y[2] - x[2]] return np.array([x, direc]) def getDist(pos1, pos2): return np.sqrt(sum([(pos1[0] - pos2[0]) ** 2, (pos1[1] - pos2[1]) ** 2, (pos1[2] - pos2[2]) ** 2])) def getManDist(pos1, pos2): return sum([abs(pos1[0] - pos2[0]), abs(pos1[1] - pos2[1]), abs(pos1[2] - pos2[2])]) def getNearest(Space, pt): '''get the nearest point on the grid''' mindis, minpt = 1000, None for pts in Space: dis = getDist(pts, pt) if dis < mindis: mindis, minpt = dis, pts return minpt def Heuristic(Space, t): '''Max norm distance''' h = {} for k in Space.keys(): h[k] = max([abs(t[0] - k[0]), abs(t[1] - k[1]), abs(t[2] - k[2])]) return h def heuristic_fun(initparams, k, t=None): if t is None: t = initparams.goal return max([abs(t[0] - k[0]), abs(t[1] - k[1]), abs(t[2] - k[2])]) def isinbound(i, x): if i[0] <= x[0] < i[3] and i[1] <= x[1] < i[4] and i[2] <= x[2] < i[5]: return True return False def isinball(i, x): if getDist(i[0:3], x) <= i[3]: return True return False def lineSphere(p0, p1, ball): # https://cseweb.ucsd.edu/classes/sp19/cse291-d/Files/CSE291_13_CollisionDetection.pdf c, r = ball[0:3], ball[-1] line = [p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2]] d1 = [c[0] - p0[0], c[1] - p0[1], c[2] - p0[2]] t = (1 / (line[0] * line[0] + line[1] * line[1] + line[2] * line[2])) * ( line[0] * d1[0] + line[1] * d1[1] + line[2] * d1[2]) if t <= 0: if (d1[0] * d1[0] + d1[1] * d1[1] + d1[2] * d1[2]) <= r ** 2: return True elif t >= 1: d2 = [c[0] - p1[0], c[1] - p1[1], c[2] - p1[2]] if (d2[0] * d2[0] + d2[1] * d2[1] + d2[2] * d2[2]) <= r ** 2: return True elif 0 < t < 1: x = [p0[0] + t * line[0], p0[1] + t * line[1], p0[2] + t * line[2]] k = [c[0] - x[0], c[1] - x[1], c[2] - x[2]] if (k[0] * k[0] + k[1] * k[1] + k[2] * k[2]) <= r ** 2: return True return False def lineAABB(p0, p1, dist, aabb): # https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php?print=1 mid = [(p0[0] + p1[0]) / 2, (p0[1] + p1[1]) / 2, (p0[2] + p1[2]) / 2] # mid point I = [(p1[0] - p0[0]) / dist, (p1[1] - p0[1]) / dist, (p1[2] - p0[2]) / dist] # unit direction hl = dist / 2 # radius P = aabb.P # center of the AABB E = aabb.E # extents of AABB T = [P[0] - mid[0], P[1] - mid[1], P[2] - mid[2]] # do any of the principal axis form a separting axis? if abs(T[0]) > (E[0] + hl * abs(I[0])): return False if abs(T[1]) > (E[1] + hl * abs(I[1])): return False if abs(T[2]) > (E[2] + hl * abs(I[2])): return False # I.cross(x axis) ? r = E[1] * abs(I[2]) + E[2] * abs(I[1]) if abs(T[1] * I[2] - T[2] * I[1]) > r: return False # I.cross(y axis) ? r = E[0] * abs(I[2]) + E[2] * abs(I[0]) if abs(T[2] * I[0] - T[0] * I[2]) > r: return False # I.cross(z axis) ? r = E[0] * abs(I[1]) + E[1] * abs(I[0]) if abs(T[0] * I[1] - T[1] * I[0]) > r: return False return True def StateSpace(env, factor=0): boundary = env.boundary resolution = env.resolution xmin, xmax = boundary[0] + factor * resolution, boundary[3] - factor * resolution ymin, ymax = boundary[1] + factor * resolution, boundary[4] - factor * resolution zmin, zmax = boundary[2] + factor * resolution, boundary[5] - factor * resolution xarr = np.arange(xmin, xmax, resolution).astype(float) yarr = np.arange(ymin, ymax, resolution).astype(float) zarr = np.arange(zmin, zmax, resolution).astype(float) Space = set() for x in xarr: for y in yarr: for z in zarr: Space.add((x, y, z)) return Space def g_Space(initparams): '''This function is used to get nodes and discretize the space. State space is by x*y*z,3 where each 3 is a point in 3D.''' g = {} Space = StateSpace(initparams.env) for v in Space: g[v] = np.inf # this hashmap initialize all g values at inf return g def isCollide(initparams, x, child, dist): '''see if line intersects obstacle''' '''specified for expansion in A* 3D lookup table''' if dist==None: dist = getDist(x, child) if not isinbound(initparams.env.boundary, child): return True, dist for i in range(len(initparams.env.AABB)): # if isinbound(initparams.env.blocks[i], child): # return True, dist if lineAABB(x, child, dist, initparams.env.AABB[i]): return True, dist for i in initparams.env.balls: # if isinball(i, child): # return True, dist if lineSphere(x, child, i): return True, dist return False, dist def children(initparams, x): # get the neighbor of a specific state allchild = [] resolution = initparams.env.resolution for direc in initparams.Alldirec: child = tuple(map(np.add, x, np.multiply(direc, resolution))) if any([isinball(i ,child) for i in initparams.env.balls]): continue if any([isinbound(i ,child) for i in initparams.env.blocks]): continue if isinbound(initparams.env.boundary, child): allchild.append(child) # initparams.Alldirec[direc]*resolution return allchild def obstacleFree(initparams, x): for i in initparams.env.blocks: if isinbound(i, x): return False for i in initparams.env.balls: if isinball(i, x): return False return True def cost(initparams, i, j, dist=None, settings=0): collide, dist = isCollide(initparams, i, j, dist) # collide, dist= False, getDist(i, j) if settings == 0: if collide: return np.inf else: return dist if settings == 1: if collide: return np.inf else: return getManDist(i, j) def initcost(initparams): # initialize cost dictionary, could be modifed lateron c = defaultdict(lambda: defaultdict(dict)) # two key dicionary for xi in initparams.X: cdren = children(initparams, xi) for child in cdren: c[xi][child] = cost(initparams, xi, child) return c if __name__ == "__main__": a = '()' print(list(a))