def TrefoilKnot(): from math import cos,sin,pi pts = [[0,0,0],[10,0,0],[10,10,0],[0,10,0]] doc1 = g.Cn(len(pts)) doc1['pts'] = pts t = 0 dt = .04 path = [] while t <= 2*pi + dt: # https://en.wikipedia.org/wiki/Trefoil_knot x = sin(t) + 2*sin(2*t) y = cos(t) - 2*cos(2*t) z = -sin(3*t) pt = [x,y,z] path.append(pt) t = t + dt C = aff.Center(path) degrees = 30 axis = [0,0,1] q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2]) s = [20,20,20] # the same scale as previous for caps t = [20,0,0] pts = aff.Translate(path,-C[0],-C[1],-C[2],align=False) pts = aff.Rotate(pts,q,align=False) pts = aff.Scale(pts, s[0],s[1],s[2],align=False) pts = aff.Translate(pts,t[0],t[1],t[2],align=False) path = pts #path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]] H = Extrusion(doc1,path) return H
def RevolveCurve(curve, t, q, s, n=20, bcap=True, ecap=True): # Assume curve has symmetry y-axis x0 = curve[0][0] x_min = min([pt[0] - x0 for pt in curve]) x_max = max([pt[0] - x0 for pt in curve]) y_min = min([pt[1] for pt in curve]) y_max = max([pt[1] for pt in curve]) poly_wb = deepcopy(curve) pts = [[0, pt[1], 0] for pt in poly_wb] y_min = min([pt[1] for pt in poly_wb]) y_max = max([pt[1] for pt in poly_wb]) doc = g.Cn(n) cx, cy, cz = [0, 0, 0] r0 = 1. doc1 = CreateCircleGeometry(doc, cx, cy, cz, r0) spath = [] path = [] pti = poly_wb[0] xi, yi = pti yi_last = yi dx = x_max - x_min dy = y_max - y_min epsilon = 1e-4 if abs(dx) > epsilon: aspect = 1. * dy / dx else: aspect = 1. * dx / dy for i in range(len(poly_wb)): pti = poly_wb[i] xi, yi = pti r = abs(xi - x0) dy = yi - yi_last epsilon = .1 if abs(dy) > epsilon: spath.append(r) path.append([yi, 0, 0]) yi_last = yi degrees = 90 axis = [0, 1, 0] q0 = aff.HH.rotation_quaternion(degrees, axis[0], axis[1], axis[2]) q = q * q0 C = aff.Center(path) pts = aff.Translate(path, -C[0], -C[1], -C[2], align=False) pts = aff.Rotate(pts, q, align=False) pts = aff.Scale(pts, s[0], s[1], s[2], align=False) pts = aff.Translate(pts, t[0], t[1], t[2], align=False) path = pts #path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]] H = ext.Extrusion0(doc1, path, spath, bcap, ecap) return H
def Parabola(): pts = [[0,0,0],[10,0,0],[10,10,0],[0,10,0]] doc1 = g.Cn(len(pts)) doc1['pts'] = pts x = 0 dx = .1 path = [] while x <= 10: pt = [10*x,x**2,0] path.append(pt) x = x + dx #path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]] H = Extrusion(doc1,path) return H
def Wire0(r, ppath, m=10, n=40): assert (len(ppath) >= 2) C = [0, 0, 0] H1 = gra.Cn(m) H1 = gra.CreateCircleGeometry(H1, C[0], C[1], C[2], r) t = 0 dt = 1. / n path = [] while t <= 1: pt = B(t, ppath) path.append(pt) t = t + dt H = ext.Extrusion(H1, path, bcap=True, ecap=True, closed=True) return H
def Cube(ww,hh,dd,mass=1e8): G1 = g.Cn(4) G2 = g.Pn(2) # graph G G = g.GraphProduct(G1,G2) # points to G pts = [[0,0,0],[0,0,dd],[ww,0,0],[ww,0,dd], [ww,hh,0],[ww,hh,dd],[0,hh,0],[0,hh,dd]] G['pts'] = pts # faces to G sorted by normals x,-x,y,-y,z,-z F = [[0,1,7,6],[4,5,3,2],[2,3,1,0], [6,7,5,4],[2,0,6,4],[1,3,5,7]] G['F'] = F G['N'] = map(lambda v: FaceNormal(G,v), range(len(F))) return G
def Torus0(r1,r2,m=10,n=40): C = [0,0,0] H1 = gra.Cn(m) H1 = gra.CreateCircleGeometry(H1,C[0],C[1],C[2],r1) t = 0 dt = 2*pi/n path = [] while t <= 2*pi + dt: x = r2*sin(t) y = r2*cos(t) z = 0 pt = [x,y,z] path.append(pt) t = t + dt H = ext.Extrusion(H1,path,bcap=False,ecap=False,closed=True) return H
def Helix0(r, a, b, m=10, n=40, N=1): C = [0, 0, 0] H1 = gra.Cn(m) H1 = gra.CreateCircleGeometry(H1, C[0], C[1], C[2], r) t = 0 dt = 2 * pi / n path = [] while t <= 2 * pi * N + dt: # https://en.wikipedia.org/wiki/Helix x = a * sin(t) y = a * cos(t) z = b * t pt = [x, y, z] path.append(pt) t = t + dt H = ext.Extrusion(H1, path, bcap=True, ecap=True, closed=True) return H
def WaterBottle(): global poly_wb pts = [[0, pt[1], 0] for pt in poly_wb] y_min = min([pt[1] for pt in poly_wb]) y_max = max([pt[1] for pt in poly_wb]) n = 10 doc = g.Cn(n) cx, cy, cz = [0, 0, 0] r = 1. doc1 = CreateCircleGeometry(doc, cx, cy, cz, r) spath = [] path = [] pti = poly_wb[0] xi, yi = pti yi_last = yi sy = 33. / (y_max - y_min) for i in range(len(poly_wb)): pti = poly_wb[i] xi, yi = pti r = abs(xi - x0) dy = yi - yi_last epsilon = .1 if abs(dy) > epsilon: spath.append(r) path.append([yi * sy, 0, 0]) yi_last = yi C = aff.Center(path) degrees = 90 axis = [0, 1, 0] q = aff.HH.rotation_quaternion(degrees, axis[0], axis[1], axis[2]) s = [20, 20, 20] # the same scale as previous for caps t = [20, 0, 0] pts = aff.Translate(path, -C[0], -C[1], -C[2], align=False) pts = aff.Rotate(pts, q, align=False) pts = aff.Scale(pts, s[0], s[1], s[2], align=False) pts = aff.Translate(pts, t[0], t[1], t[2], align=False) path = pts #path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]] H = ext.Extrusion0(doc1, path, spath) return H
def TableLeg(height,radius1,radius2,n=10,m=10): h = height r1 = radius1 r2 = radius2 curve = [] x0 = 0 for i in range(1,m-1): r = mapto.MapTo(0,r1,m-1,r2,i) xi = r yi = mapto.MapTo(0,0,m-1,h,i) pt = [xi,yi] curve.append(pt) yi = mapto.MapTo(0,0,m-1,h,.1) curve = [[0,yi]]+curve+[[0,height]] # Assume curve has symmetry y-axis x0 = curve[0][0] x_min = min(map(lambda pt: pt[0]-x0,curve)) x_max = max(map(lambda pt: pt[0]-x0,curve)) y_min = min(map(lambda pt: pt[1],curve)) y_max = max(map(lambda pt: pt[1],curve)) poly_wb = deepcopy(curve) pts = map(lambda pt: [0,pt[1],0], poly_wb) y_min = min(map(lambda pt: pt[1],poly_wb)) y_max = max(map(lambda pt: pt[1],poly_wb)) doc = g.Cn(n) cx,cy,cz = [0,0,0] r0 = 1. doc1 = rc.CreateCircleGeometry(doc,cx,cy,cz,r0) spath = [] path = [] pti = poly_wb[0] xi,yi = pti yi_last = yi dx = x_max-x_min dy = y_max-y_min epsilon = 1e-4 if abs(dx) > epsilon: aspect = 1.*dy/dx else: aspect = 1.*dx/dy for i in range(len(poly_wb)): pti = poly_wb[i] xi,yi = pti r = abs(xi - x0) dy = yi-yi_last epsilon = .1 if abs(dy) > epsilon: spath.append(r) path.append([yi,0,0]) yi_last = yi degrees = 90+180 axis = [0,1,0] q0 = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2]) q = q0 t = [0,0,-height*.4] s = [1,1,1] C = aff.Center(path) pts = aff.Translate(path,-C[0],-C[1],-C[2],align=False) pts = aff.Rotate(pts,q,align=False) pts = aff.Scale(pts, s[0],s[1],s[2],align=False) pts = aff.Translate(pts,t[0],t[1],t[2],align=False) path = pts #path = [[0,0,0],[10,1,0],[20,4,0],[30,9,0]] H = ext.Extrusion0(doc1,path,spath) return H
def CoffeeCup0(n=30,m=20,r0=20.): flag_cup = True flag_handle = True H1 = {} H1['V'] = [] H1['E'] = [] H1['pts'] = [] H1['F'] = [] H1['N'] = [] H2 = {} H2['V'] = [] H2['E'] = [] H2['pts'] = [] H2['F'] = [] H2['N'] = [] if flag_cup: # polygon curve of surface of revolution # Create Cup. At present, its imperfect recreating # a cover to coffee cup. curve1a = [[406, 388], [441, 384], [469, 378], [489, 363], [506, 347], [518, 330], [520, 314], [522, 297], [525, 276], [528, 258], [530, 228], [528, 182], [528, 150], [527, 113], [527, 91], [532, 73], [540, 68]] curve1b = [[554, 70], [554, 86], [549, 108], [550, 136], [546, 181], [547, 214], [544, 249], [544, 268], [538, 281], [540, 288], [539, 300], [531, 312], [532, 329], [526, 350], [513, 362], [502, 378], [482, 393], [446, 406], [417, 409]] curve1 = curve1a + curve1b x0 = curve1[0][0] x_min = min(map(lambda pt: pt[0]-x0,curve1)) x_max = max(map(lambda pt: pt[0]-x0,curve1)) y_min = min(map(lambda pt: pt[1],curve1)) y_max = max(map(lambda pt: pt[1],curve1)) degrees = 0 axis = [0,1,0] q = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2]) scale = 1. s = [scale,scale,scale] # the same scale as previous for caps t = [0,0,0] H1 = rc.RevolveCurve(curve1,t,q,s, n, bcap=False, ecap=False) if flag_handle: # Create Handle curve2 = [[203, 130], [189, 114], [165, 102], [149, 100], [132, 101], [116, 106], [106, 113], [107, 128], [112, 152], [118, 169], [127, 184], [138, 201], [149, 208], [165, 209], [186, 214], [207, 213]] # Assume curve has symmetry y-axis x0 = curve2[0][0] x_min = min(map(lambda pt: pt[0]-x0,curve2)) x_max = max(map(lambda pt: pt[0]-x0,curve2)) y_min = min(map(lambda pt: pt[1],curve2)) y_max = max(map(lambda pt: pt[1],curve2)) poly_wb = deepcopy(curve2) pts = map(lambda pt: [0,pt[1],0], poly_wb) y_min = min(map(lambda pt: pt[1],poly_wb)) y_max = max(map(lambda pt: pt[1],poly_wb)) doc = g.Cn(m) cx,cy,cz = [0,0,0] doc1 = rc.CreateCircleGeometry(doc,cx,cy,cz,r0) spath = [] path = [] pti = poly_wb[0] xi,yi = pti yi_last = yi dx = x_max-x_min dy = y_max-y_min for i in range(len(poly_wb)): pti = poly_wb[i] xi,yi = pti r = abs(xi - x0) dy = yi-yi_last epsilon = .1 if abs(dy) > epsilon: spath.append(1.) path.append([xi,yi,0]) degrees = 90+180 axis = [1,0,0] q0 = aff.HH.rotation_quaternion(degrees,axis[0],axis[1],axis[2]) q = q0 t = [-184,0,100] s = [1,1,1] C = aff.Center(path) pts = aff.Translate(path,-C[0],-C[1],-C[2],align=False) pts = aff.Rotate(pts,q,align=False) pts = aff.Scale(pts, s[0],s[1],s[2],align=False) pts = aff.Translate(pts,t[0],t[1],t[2],align=False) path = pts H2 = ext.Extrusion0(doc1,path,spath) H = ext.GraphUnionS(H1,H2) return H
if event == cv2.EVENT_MOUSEMOVE and (len(pts) > 0): pt_move = [x,y] return return pts = [] pt_move = [0,0] print("Select the two points on 2D plane") cv2.namedWindow("result") cv2.setMouseCallback("result",getxy) doc = {} doc["V"] = list(range(2)) doc["E"] = [[0,1]] doc["pts"] = [[119, 304],[480, 53]] doc = graph.Cn(4) w = 400 h = 400 cx,cy,cz = (w/2,h/2,0) r = 0.75*w/2 doc = graph.CreateCircleGeometry(doc,cx,cy,cz,r) doc['_id'] = 1 w = 600 h = 600 gr = racg.Graphics(w=w,h=h) def PlotGraph(gr,G,color): black = [0,0,0] for e in G['E']: A,B = [G['pts'][v] for v in e]
def Circle(r, k): G = graph.Cn(k) C = [0, 0, 0] G = graph.CreateCircleGeometry(G, C[0], C[1], C[2], r) return G