def offset(mesh,offset=1,doclose=True): newMesh=Mesh() # calculate vertex normals for vertex in mesh.vertices: vertex.vertex = Vertex(0,0,0) vertex.nfaces = 0 for face in mesh.faces: normal = utils_face.face_normal(face) for vertex in face.vertices: vertex.vertex.add(normal) vertex.nfaces += 1 for vertex in mesh.vertices: vertex.vertex.scale(offset / vertex.nfaces) vertex.vertex.add(vertex) # create faces for face in mesh.faces: offsetVertices = [] for vertex in face.vertices: offsetVertices.append(vertex.vertex) offsetVertices.reverse() newFace = Face(offsetVertices) newMesh.faces.append(newFace) newMesh.faces.append(face) # create sides if doclose: for edge in mesh.edges: if edge.face1 == None or edge.face2 == None: offsetVertices = [edge.v1, edge.v2, edge.v2.vertex, edge.v1.vertex] if edge.face2 == None: offsetVertices.reverse() newFace = Face(offsetVertices) newMesh.faces.append(newFace) newMesh.update_topology() return newMesh
def construct_cone(z1, z2, radius1, radius2, nSegments, capBottom=True, capTop=True): """ Creates and returns a conic cylinder. Arguments: ---------- z1, z2 : float<br> The bottom and top z-level.<br> radius1, radius2 : float<br> The radii at the bottom and at the top respectively<br> nSegments : int<br> The number of segments along the circumference<br> capBottom, capTop : bool<br> Toggle whether or not to close the cylinder at the bottom and the top """ delaAngle = math.radians(360.0 / nSegments) angle = 0 verticesBottom = [] verticesTop = [] for i in range(nSegments): x1 = radius1 * math.cos(angle) y1 = radius1 * math.sin(angle) verticesBottom.append(Vertex(x1, y1, z1)) x2 = radius2 * math.cos(angle) y2 = radius2 * math.sin(angle) verticesTop.append(Vertex(x2, y2, z2)) angle += delaAngle mesh = Mesh() mesh.vertices.extend(verticesBottom) mesh.vertices.extend(verticesTop) for i in range(nSegments): i2 = (i + 1) % nSegments mesh.faces.append( Face([ verticesBottom[i], verticesBottom[i2], verticesTop[i2], verticesTop[i] ])) if capBottom: # centerBottom = Vertex(0, 0, z1) # mesh.vertices.append(centerBottom) # for i in range(nSegments): # i2=(i+1)%nSegments # mesh.faces.append(Face([verticesBottom[i2],verticesBottom[i],centerBottom])) mesh.faces.append(Face(list(reversed(verticesBottom)))) if capTop: # centerTop=Vertex(0,0,z2) # mesh.vertices.append(centerTop) # for i in range(nSegments): # i2=(i+1)%nSegments # mesh.faces.append(Face([verticesTop[i],verticesTop[i2],centerTop])) mesh.faces.append(Face(verticesTop)) mesh.update_topology() return mesh
def subdivide_face_split_rel_multiple(face, direction, splits): sA = [] sA.append(face.vertices[direction]) lA = face.vertices[direction + 1] sB = [] sB.append(face.vertices[direction + 3]) lB = face.vertices[(direction + 2) % len(face.vertices)] for i in range(len(splits)): sA.append(utils_vertex.vertex_between_rel(sA[0], lA,splits[i])) sB.append(utils_vertex.vertex_between_rel(sB[0], lB,splits[i])) sA.append(lA) sB.append(lB) result = [] for i in range(len(splits) + 1): if(dir == 1): f = Face([sB[i], sA[i], sA[i+1], sB[i+1]]) utils_face.face_copy_properties(face, f) result.append(f) else: f = Face([sB[i], sB[i+1], sA[i+1], sA[i]]) utils_face.face_copy_properties(face, f) result.append(f) return result
def construct_tetrahedron(size=1, cx=0, cy=0, cz=0): """ Constructs a tetrahedron mesh. Optional Arguments: ---------- side : float<br> The edge length of the tetrahedron<br> cx,cy,cz : float<br> The coordinates of the center point. """ mesh = Mesh() coord = 1 / math.sqrt(2) mesh.vertices = [ Vertex(+1, 0, -coord), Vertex(-1, 0, -coord), Vertex(0, +1, +coord), Vertex(0, -1, +coord) ] for i in range(len(mesh.vertices)): mesh.vertices[i] = utils_vertex.vertex_scale(mesh.vertices[i], size / 2) mesh.vertices[i] = utils_vertex.vertex_add(mesh.vertices[i], Vertex(cx, cy, cz)) f1 = Face([mesh.vertices[0], mesh.vertices[1], mesh.vertices[2]]) f2 = Face([mesh.vertices[1], mesh.vertices[0], mesh.vertices[3]]) f3 = Face([mesh.vertices[2], mesh.vertices[3], mesh.vertices[0]]) f4 = Face([mesh.vertices[3], mesh.vertices[2], mesh.vertices[1]]) mesh.faces = [f1, f2, f3, f4] mesh.update_topology() return mesh
def construct_octahedron(edgeLen=1, cx=0, cy=0, cz=0): mesh = Mesh() #make vertices mesh.vertices = [ Vertex(0, 0, edgeLen / 2), Vertex(-edgeLen / 2, 0, 0), Vertex(0, -edgeLen / 2, 0), Vertex(edgeLen / 2, 0, 0), Vertex(0, edgeLen / 2, 0), Vertex(0, 0, -edgeLen / 2) ] #move center to desired coordinates center = Vertex(cx, cy, cz) for v in mesh.vertices: v.add(center) #construct triangular faces f1 = Face([mesh.vertices[0], mesh.vertices[1], mesh.vertices[2]]) f2 = Face([mesh.vertices[0], mesh.vertices[2], mesh.vertices[3]]) f3 = Face([mesh.vertices[0], mesh.vertices[3], mesh.vertices[4]]) f4 = Face([mesh.vertices[0], mesh.vertices[4], mesh.vertices[1]]) f5 = Face([mesh.vertices[5], mesh.vertices[2], mesh.vertices[1]]) f6 = Face([mesh.vertices[5], mesh.vertices[3], mesh.vertices[2]]) f7 = Face([mesh.vertices[5], mesh.vertices[4], mesh.vertices[3]]) f8 = Face([mesh.vertices[5], mesh.vertices[1], mesh.vertices[4]]) mesh.faces = [f1, f2, f3, f4, f5, f6, f7, f8] mesh.update_topology() return mesh
def subdivide_face_extrude_tapered(face, height=0.0, fraction=0.5,doCap=True): """ Extrudes the face tapered like a window by creating an offset face and quads between every original edge and the corresponding new edge. Arguments: ---------- face : mola.core.Face The face to be extruded height : float The distance of the new face to the original face, default 0 fraction : float The relative offset distance, 0: original vertex, 1: center point default 0.5 (halfway) """ center_vertex = utils_face.face_center(face) normal = utils_face.face_normal(face) scaled_normal = utils_vertex.vertex_scale(normal, height) # calculate new vertex positions new_vertices = [] for i in range(len(face.vertices)): n1 = face.vertices[i] betw = utils_vertex.vertex_subtract(center_vertex, n1) betw = utils_vertex.vertex_scale(betw, fraction) nn = utils_vertex.vertex_add(n1, betw) nn = utils_vertex.vertex_add(nn, scaled_normal) new_vertices.append(nn) new_faces = [] # create the quads along the edges num = len(face.vertices) for i in range(num): n1 = face.vertices[i] n2 = face.vertices[(i + 1) % num] n3 = new_vertices[(i + 1) % num] n4 = new_vertices[i] new_face = Face([n1,n2,n3,n4]) new_faces.append(new_face) # create the closing cap face if doCap: cap_face = Face(new_vertices) new_faces.append(cap_face) for new_face in new_faces: utils_face.face_copy_properties(face,new_face) return new_faces
def subdivide_face_split_grid(face,nU,nV): """ splits a triangle, quad or a rectangle into a regular grid """ if len(face.vertices) > 4: print('too many vertices') return face if len(face.vertices) == 4: vsU1 = _vertices_between(face.vertices[0], face.vertices[1], nU) vsU2 = _vertices_between(face.vertices[3], face.vertices[2], nU) gridVertices = [] for u in range(len(vsU1)): gridVertices.append(_vertices_between(vsU1[u], vsU2[u], nV)) faces = [] for u in range(len(vsU1) - 1): vs1 = gridVertices[u] vs2 = gridVertices[u + 1] for v in range(len(vs1) - 1): #f = Face([vs1[v], vs1[v + 1], vs2[v + 1], vs2[v]]) f = Face([vs1[v], vs2[v], vs2[v + 1], vs1[v + 1]]) utils_face.face_copy_properties(face, f) faces.append(f) return faces if len(face.vertices) == 3: vsU1 = _vertices_between(face.vertices[0], face.vertices[1], nU) vsU2 = _vertices_between(face.vertices[0], face.vertices[2], nU) gridVertices = [] for u in range(1, len(vsU1)): gridVertices.append(_vertices_between(vsU1[u], vsU2[u], nV)) faces = [] # triangles v0 = face.vertices[0] vs1 = gridVertices[0] for v in range(len(vs1) - 1): f = Face([v0,vs1[v],vs1[v + 1]]) utils_face.face_copy_properties(face, f) faces.append(f) for u in range(len(gridVertices) - 1): vs1 = gridVertices[u] vs2 = gridVertices[u + 1] for v in range(len(vs1) - 1): f = Face([vs1[v],vs1[v + 1], vs2[v + 1], vs2[v]]) utils_face.face_copy_properties(face, f) faces.append(f) return faces
def marching_cubes(nX,nY,nZ,values,iso, scale_to_canvas=False): mesh = Mesh() nYZ = nY * nZ index = 0 n =[0]*8 switcher = { 0:lambda: Vertex(x + _v(n[0], n[1], iso), y + 1, z), 1:lambda: Vertex(x + 1, y + _v(n[2], n[1], iso), z), 2:lambda: Vertex(x + _v(n[3], n[2], iso), y, z), 3:lambda: Vertex(x, y + _v(n[3], n[0], iso), z), 4:lambda: Vertex(x + _v(n[4], n[5], iso), y + 1, z + 1), 5:lambda: Vertex(x + 1, y + _v(n[6], n[5], iso), z + 1), 6:lambda: Vertex(x + _v(n[7], n[6], iso), y, z + 1), 7:lambda: Vertex(x, y + _v(n[7], n[4], iso), z + 1), 8:lambda: Vertex(x, y + 1, z + _v(n[0], n[4], iso)), 9:lambda: Vertex(x + 1, y + 1, z + _v(n[1], n[5], iso)), 10:lambda: Vertex(x, y, z + _v(n[3], n[7], iso)), 11:lambda: Vertex(x + 1, y, z + _v(n[2], n[6], iso)) } for x in range(nX - 1): for y in range(nY - 1): for z in range(nZ - 1): caseNumber = 0 index = z + y * nZ + x * nYZ # collecting the values n[0] = values[index + nZ]# 0,1,0 n[1] = values[index + nYZ + nZ]#1,1,0 n[2] = values[index + nYZ]# 1,0,0 n[3] = values[index]# 0,0,0 n[4] = values[index + nZ + 1]# 0,1,1 n[5] = values[index + nYZ + nZ + 1]# 1,1,1 n[6] = values[index + nYZ + 1]# 1,0,1 n[7] = values[index + 1]# 0,0,1 for i in range(7,-1,-1): if n[i] > iso: caseNumber+=1 if i > 0: caseNumber = caseNumber << 1 # collecting the faces offset = caseNumber * 15 for i in range(offset,offset + 15,3): if _faces[i] > -1: vs=[] for j in range(i,i+3): v = switcher[_faces[j]]() mesh.vertices.append(v) vs.append(v) if len(vs) == 3: mesh.faces.append(Face(vs)) mesh.update_topology() if(scale_to_canvas): mesh.translate(-nX/2.0,-nY/2.0,-nZ/2.0) sc = 20.0/max(nX,nY) mesh.scale(sc,sc,sc) return mesh
def construct_dodecahedron(radius=1, cx=0, cy=0, cz=0): """ Constructs a dodecaheron mesh. Optional Arguments: ---------- radius : float<br> The radius of the containing sphere<br> cx,cy,cz : float<br> The coordinates of the center point. """ mesh = Mesh() phi = (1 + 5**0.5) / 2 mesh.vertices = [ Vertex(1, 1, 1), Vertex(1, 1, -1), Vertex(1, -1, 1), Vertex(1, -1, -1), Vertex(-1, 1, 1), Vertex(-1, 1, -1), Vertex(-1, -1, 1), Vertex(-1, -1, -1), Vertex(0, -phi, -1 / phi), Vertex(0, -phi, 1 / phi), Vertex(0, phi, -1 / phi), Vertex(0, phi, 1 / phi), Vertex(-phi, -1 / phi, 0), Vertex(-phi, 1 / phi, 0), Vertex(phi, -1 / phi, 0), Vertex(phi, 1 / phi, 0), Vertex(-1 / phi, 0, -phi), Vertex(1 / phi, 0, -phi), Vertex(-1 / phi, 0, phi), Vertex(1 / phi, 0, phi) ] for i in range(len(mesh.vertices)): mesh.vertices[i] = utils_vertex.vertex_scale(mesh.vertices[i], radius) mesh.vertices[i] = utils_vertex.vertex_add(mesh.vertices[i], Vertex(cx, cy, cz)) indices = [ 2, 9, 6, 18, 19, 4, 11, 0, 19, 18, 18, 6, 12, 13, 4, 19, 0, 15, 14, 2, 4, 13, 5, 10, 11, 14, 15, 1, 17, 3, 1, 15, 0, 11, 10, 3, 17, 16, 7, 8, 2, 14, 3, 8, 9, 6, 9, 8, 7, 12, 1, 10, 5, 16, 17, 12, 7, 16, 5, 13 ] for i in range(0, len(indices), 5): f = Face([ mesh.vertices[indices[i]], mesh.vertices[indices[i + 1]], mesh.vertices[indices[i + 2]], mesh.vertices[indices[i + 3]], mesh.vertices[indices[i + 4]] ]) mesh.faces.append(f) mesh.update_topology() return mesh
def subdivide_face_split_frame(face, w): """ Creates an offset frame with quad corners. Works only with convex shapes. Arguments: ---------- face : mola.core.Face The face to be split w : float The width of the offset frame """ faces = [] innerVertices = [] for i in range(len(face.vertices)): if (i == 0): vp = face.vertices[len(face.vertices) - 1] else: vp = face.vertices[i - 1] v = face.vertices[i] vn = face.vertices[(i + 1) % len(face.vertices)] vnn = face.vertices[(i + 2) % len(face.vertices)] th1 = utils_vertex.vertex_angle_triangle(vp, v, vn) th2 = utils_vertex.vertex_angle_triangle(v, vn, vnn) w1 = w / math.sin(th1) w2 = w / math.sin(th2) vs1 = _vertices_frame(v, vn, w1, w2) vs2 = _vertices_frame( _vertices_frame(vp, v, w1, w1)[2], _vertices_frame(vn, vnn, w2, w2)[1], w1, w2) innerVertices.append(vs2[1]) f1 = Face([vs1[0], vs2[0], vs2[1], vs1[1]]) utils_face.face_copy_properties(face, f1) f2 = Face([vs1[1], vs2[1], vs2[2], vs1[2]]) utils_face.face_copy_properties(face, f2) faces.extend([f1, f2]) fInner = Face(innerVertices) utils_face.face_copy_properties(face, fInner) faces.append(fInner) return faces
def subdivide_face_split_rel_free_quad(face, indexEdge, split1, split2): """ Splits a quad in two new quads through the points specified by relative position along the edge. Arguments: ---------- face : mola.core.Face The face to be extruded indexEdge : int direction of split, 0: 0->2, 1: 1->3 split1, split2 : float relative position of split on each edge (0..1) """ # only works with quads, therefore return original face if triangular if len(face.vertices) != 4: return face # constrain indexEdge to be either 0 or 1 indexEdge = indexEdge % 2 indexEdge1 = (indexEdge + 1) % len(face.vertices) indexEdge2 = (indexEdge + 2) % len(face.vertices) indexEdge3 = (indexEdge + 3) % len(face.vertices) p1 = utils_vertex.vertex_between_rel(face.vertices[indexEdge], face.vertices[indexEdge1], split1) p2 = utils_vertex.vertex_between_rel(face.vertices[indexEdge2], face.vertices[indexEdge3], split2) faces = [] if indexEdge == 0: f1 = Face([face.vertices[0], p1, p2, face.vertices[3]]) f2 = Face([p1, face.vertices[1], face.vertices[2], p2]) utils_face.face_copy_properties(face, f1) utils_face.face_copy_properties(face, f2) faces.extend([f1, f2]) elif indexEdge == 1: f1 = Face([face.vertices[0], face.vertices[1], p1, p2]) f2 = Face([p2, p1, face.vertices[2], face.vertices[3]]) utils_face.face_copy_properties(face, f1) utils_face.face_copy_properties(face, f2) faces.extend([f1, f2]) return faces
def mesh_from_rhino_mesh(obj): mesh = Mesh() vertices = rs.MeshVertices(obj) for v in vertices: mesh.vertices.append(Vertex(v[0], v[1], v[2])) faceVerts = rs.MeshFaceVertices(obj) for face in faceVerts: if face[2] == face[3]: mesh.faces.append( Face([ mesh.vertices[face[0]], mesh.vertices[face[1]], mesh.vertices[face[2]] ])) else: mesh.faces.append( Face([ mesh.vertices[face[0]], mesh.vertices[face[1]], mesh.vertices[face[2]], mesh.vertices[face[3]] ])) return mesh
def mesh_offset(mesh, offset=1, doclose=True): """ Creates an offset of a mesh. If `doclose` is `True`, it will create quad faces along the naked edges of an open input mesh. """ newMesh = Mesh() # calculate vertex normals for vertex in mesh.vertices: vertex.vertex = Vertex(0, 0, 0) vertex.nfaces = 0 for face in mesh.faces: normal = utils_face.face_normal(face) for vertex in face.vertices: vertex.vertex.add(normal) vertex.nfaces += 1 for vertex in mesh.vertices: vertex.vertex.scale(offset / vertex.nfaces) vertex.vertex.add(vertex) # create faces for face in mesh.faces: offsetVertices = [] for vertex in face.vertices: offsetVertices.append(vertex.vertex) offsetVertices.reverse() newFace = Face(offsetVertices) newMesh.faces.append(newFace) newMesh.faces.append(face) # create sides if doclose: for edge in mesh.edges: if edge.face1 == None or edge.face2 == None: offsetVertices = [ edge.v1, edge.v2, edge.v2.vertex, edge.v1.vertex ] if edge.face2 == None: offsetVertices.reverse() newFace = Face(offsetVertices) newMesh.faces.append(newFace) newMesh.update_topology() return newMesh
def construct_box(x1, y1, z1, x2, y2, z2): """ Creates and returns a mesh box with six quad faces. Arguments: ---------- x1,y1,z1 : float<br> The coordinates of the bottom left front corner<br> x2,y2,z2 : float<br> The coordinates of the top right back corner """ mesh = Mesh() v1 = Vertex(x1, y1, z1) v2 = Vertex(x1, y2, z1) v3 = Vertex(x2, y2, z1) v4 = Vertex(x2, y1, z1) v5 = Vertex(x1, y1, z2) v6 = Vertex(x1, y2, z2) v7 = Vertex(x2, y2, z2) v8 = Vertex(x2, y1, z2) mesh.vertices = [v1, v2, v3, v4, v5, v6, v7, v8] f1 = Face([v1, v2, v3, v4]) f2 = Face([v8, v7, v6, v5]) f3 = Face([v4, v3, v7, v8]) f4 = Face([v3, v2, v6, v7]) f5 = Face([v2, v1, v5, v6]) f6 = Face([v1, v4, v8, v5]) mesh.faces = [f1, f2, f3, f4, f5, f6] mesh.update_topology() return mesh
def subdivide_face_extrude(face, height=0.0, capBottom=False, capTop=True): """ Extrudes the face straight by distance height. Arguments: ---------- face : mola.core.Face The face to be extruded height : float The extrusion distance, default 0 capBottom : bool Toggle if bottom face (original face) should be created, default False capTop : bool Toggle if top face (extrusion face) should be created, default True """ normal=utils_face.face_normal(face) normal=utils_vertex.vertex_scale(normal,height) # calculate vertices new_vertices=[] for i in range(len(face.vertices)): new_vertices.append(utils_vertex.vertex_add(face.vertices[i], normal)) # faces new_faces=[] if capBottom: new_faces.append(face) for i in range(len(face.vertices)): i2=i+1 if i2>=len(face.vertices): i2=0 v0=face.vertices[i] v1=face.vertices[i2] v2=new_vertices[i2] v3=new_vertices[i] new_faces.append(Face([v0,v1,v2,v3])) if capTop: new_faces.append(Face(new_vertices)) for new_face in new_faces: utils_face.face_copy_properties(face,new_face) return new_faces
def construct_icosahedron(radius=1, cx=0, cy=0, cz=0): """ Creates and returns a mesh in the form of an icosahedron. Optional Arguments: ---------- radius : float<br> The radius of the containing sphere.<br> cx,cy,cz : float<br> The coordinates of the center point. """ mesh = Mesh() phi = (1 + 5**0.5) / 2 coordA = 1 / (2 * math.sin(2 * math.pi / 5)) coordB = phi / (2 * math.sin(2 * math.pi / 5)) mesh.vertices = [ Vertex(0, -coordA, coordB), Vertex(coordB, 0, coordA), Vertex(coordB, 0, -coordA), Vertex(-coordB, 0, -coordA), Vertex(-coordB, 0, coordA), Vertex(-coordA, coordB, 0), Vertex(coordA, coordB, 0), Vertex(coordA, -coordB, 0), Vertex(-coordA, -coordB, 0), Vertex(0, -coordA, -coordB), Vertex(0, coordA, -coordB), Vertex(0, coordA, coordB) ] for i in range(len(mesh.vertices)): mesh.vertices[i] = utils_vertex.vertex_scale(mesh.vertices[i], radius) mesh.vertices[i] = utils_vertex.vertex_add(mesh.vertices[i], Vertex(cx, cy, cz)) indices = [ 1, 2, 6, 1, 7, 2, 3, 4, 5, 4, 3, 8, 6, 5, 11, 5, 6, 10, 9, 10, 2, 10, 9, 3, 7, 8, 9, 8, 7, 0, 11, 0, 1, 0, 11, 4, 6, 2, 10, 1, 6, 11, 3, 5, 10, 5, 4, 11, 2, 7, 9, 7, 1, 0, 3, 9, 8, 4, 8, 0 ] faces = [] for i in range(0, len(indices), 3): f = Face([ mesh.vertices[indices[i]], mesh.vertices[indices[i + 1]], mesh.vertices[indices[i + 2]] ]) faces.append(f) mesh.faces = faces mesh.update_topology() return mesh
def quad_mesh(self, functionIn, functionOut): faces = [] for x in range(self.nx): for y in range(self.ny): for z in range(self.nz): index = self.get_index(x, y, z) if functionIn(self.values[index]): # (x,y) (x1,y) (x1,y1) (x,y1) if x == self.nx - 1 or functionOut( self.get_value_at_xyz(x + 1, y, z)): v1 = Vertex(x + 1, y, z) v2 = Vertex(x + 1, y + 1, z) v3 = Vertex(x + 1, y + 1, z + 1) v4 = Vertex(x + 1, y, z + 1) faces.append(Face([v1, v2, v3, v4])) if x == 0 or functionOut( self.get_value_at_xyz(x - 1, y, z)): v1 = Vertex(x, y + 1, z) v2 = Vertex(x, y, z) v3 = Vertex(x, y, z + 1) v4 = Vertex(x, y + 1, z + 1) faces.append(Face([v1, v2, v3, v4])) if y == self.ny - 1 or functionOut( self.get_value_at_xyz(x, y + 1, z)): v1 = Vertex(x + 1, y + 1, z) v2 = Vertex(x, y + 1, z) v3 = Vertex(x, y + 1, z + 1) v4 = Vertex(x + 1, y + 1, z + 1) faces.append(Face([v1, v2, v3, v4])) if y == 0 or functionOut( self.get_value_at_xyz(x, y - 1, z)): v1 = Vertex(x, y, z) v2 = Vertex(x + 1, y, z) v3 = Vertex(x + 1, y, z + 1) v4 = Vertex(x, y, z + 1) faces.append(Face([v1, v2, v3, v4])) if z == self.nz - 1 or functionOut( self.get_value_at_xyz(x, y, z + 1)): v1 = Vertex(x, y, z + 1) v2 = Vertex(x + 1, y, z + 1) v3 = Vertex(x + 1, y + 1, z + 1) v4 = Vertex(x, y + 1, z + 1) faces.append(Face([v1, v2, v3, v4])) if z == 0 or functionOut( self.get_value_at_xyz(x, y, z - 1)): v1 = Vertex(x, y + 1, z) v2 = Vertex(x + 1, y + 1, z) v3 = Vertex(x + 1, y, z) v4 = Vertex(x, y, z) faces.append(Face([v1, v2, v3, v4])) mesh = Mesh() mesh.faces = faces mesh.update_topology() if (self.scale_to_canvas): mesh.translate(-self.nx / 2.0, -self.ny / 2.0, -self.nz / 2.0) sc = 20.0 / max(self.nx, self.ny) mesh.scale(sc, sc, sc) return mesh
def construct_single_face(vertices): """ Creates and returns a single face mesh from the vertices. Arguments: ---------- vertices : list of mola.core.Vertex<br> The vertices describing the face """ mesh = Mesh() mesh.vertices = vertices mesh.faces = [Face(vertices)] mesh.update_topology() return mesh
def subdivide_face_offset_planar(face,offsets): newPts = [] for i in range(len(face.vertices)): iP = i - 1 if(iP < 0): iP = len(face.vertices)-1 iN = (i + 1) % len(face.vertices) v0 = face.vertices[iP] v1 = face.vertices[i] v2 = face.vertices[iN] newPts.append(utils_vertex.vertex_offset_point(v0, v1, v2, offsets[iP], offsets[i])) f = Face(newPts) utils_face.face_copy_properties(face, f) return f
def subdivide_face_split_roof(face, height): """ Extrudes a pitched roof Arguments: ---------- face : mola.core.Face The face to be extruded height : mola.core.Vertex Th height of the roof """ faces = [] normal = utils_face.face_normal(face) normal = utils_vertex.vertex_scale(normal,height) if len(face.vertices) == 4: ev1 = utils_vertex.vertex_center(face.vertices[0], face.vertices[1]) ev1 = utils_vertex.vertex_add(ev1, normal) ev2 = utils_vertex.vertex_center(face.vertices[2], face.vertices[3]) ev2 = utils_vertex.vertex_add(ev2, normal) faces.append(Face([face.vertices[0], face.vertices[1], ev1])) faces.append(Face([face.vertices[1], face.vertices[2], ev2, ev1])) faces.append(Face([face.vertices[2], face.vertices[3], ev2])) faces.append(Face([face.vertices[3], face.vertices[0], ev1, ev2])) for f in faces: utils_face.face_copy_properties(face,f) return faces elif len(face.vertices) == 3: ev1 = utils_vertex.vertex_center(face.vertices[0], face.vertices[1]) ev1 = utils_vertex.vertex_add(ev1, normal) ev2 = utils_vertex.vertex_center(face.vertices[1], face.vertices[2]) ev2 = utils_vertex.vertex_add(ev2, normal) faces.append(Face([face.vertices[0], face.vertices[1], ev1])) faces.append(Face([face.vertices[1], ev2, ev1])) faces.append(Face([face.vertices[1], face.vertices[2], ev2])) faces.append(Face([face.vertices[2], face.vertices[0], ev1, ev2])) for f in faces: utils_face.face_copy_properties(face, f) return faces return [face]
def _collect_new_faces(mesh): newMesh=Mesh() for face in mesh.faces: v1 = face.vertices[-2] v2 = face.vertices[-1] for v3 in face.vertices: edge1 = mesh.edge_adjacent_to_vertices(v1,v2) edge2 = mesh.edge_adjacent_to_vertices(v2,v3) if (edge1 != None) and (edge2!= None): newFace = Face([edge1.vertex, v2.vertex, edge2.vertex, face.vertex]) newFace.color = face.color newFace.group = face.group newMesh.faces.append(newFace) v1 = v2 v2 = v3 newMesh.update_topology() return newMesh
def subdivide_face_split_offsets(face,offsets): offsetFace = subdivide_face_offset_planar(face,offsets) nOffsetFaces = 0 for o in offsets: if(abs(o) > 0): nOffsetFaces += 1 faces = [] for i in range(len(face.vertices)): if(abs(offsets[i]) > 0): i2 = (i + 1) % len(face.vertices) f = Face([face.vertices[i], face.vertices[i2], offsetFace.vertices[i2], offsetFace.vertices[i]]) utils_face.face_copy_properties(face, f) faces.append(f) faces.append(offsetFace) for f in faces: if(utils_face.face_area(f) < 0): f.vertices.reverse() return faces
def subdivide_face_extrude_to_point(face, point): """ Extrudes the face to a point by creating a triangular face from each edge to the point. Arguments: ---------- face : mola.core.Face The face to be extruded point : mola.core.Vertex The point to extrude to """ numV = len(face.vertices) faces = [] for i in range(numV): v1 = face.vertices[i] v2 = face.vertices[(i + 1) % numV] f = Face([v1, v2, point]) utils_face.face_copy_properties(face, f) faces.append(f) return faces
def quad_mesh(self, functionIn, functionOut): faces = [] for x in range(self.nx): for y in range(self.ny): for z in range(self.nz): index=self.get_index(x,y,z) if functionIn(self.values[index]): # (x,y) (x1,y) (x1,y1) (x,y1) if x == self.nx - 1 or functionOut(self.get_value_at_xyz(x + 1, y, z)): v1 = Vertex(x + 1, y, z) v2 = Vertex(x + 1, y + 1, z) v3 = Vertex(x + 1, y + 1, z + 1) v4 = Vertex(x + 1, y, z + 1) faces.append(Face([v1, v2, v3, v4])) if x == 0 or functionOut(self.get_value_at_xyz(x-1,y,z)): v1 = Vertex(x, y + 1, z) v2 = Vertex(x, y, z) v3 = Vertex(x, y, z + 1) v4 = Vertex(x, y + 1, z + 1) faces.append(Face([v1, v2, v3, v4])) if y == self.ny - 1 or functionOut(self.get_value_at_xyz(x, y + 1, z)): v1 = Vertex(x + 1, y + 1, z) v2 = Vertex(x, y + 1, z) v3 = Vertex(x, y + 1, z + 1) v4 = Vertex(x + 1, y + 1, z + 1) faces.append(Face([v1, v2, v3, v4])) if y == 0 or functionOut(self.get_value_at_xyz(x, y - 1, z)): v1 = Vertex(x, y, z) v2 = Vertex(x + 1, y, z) v3 = Vertex(x + 1, y, z + 1) v4 = Vertex(x, y, z + 1) faces.append(Face([v1, v2, v3, v4])) if z==self.nz-1 or functionOut(self.get_value_at_xyz(x, y, z + 1)): v1 = Vertex(x, y, z + 1) v2 = Vertex(x + 1, y, z + 1) v3 = Vertex(x + 1, y + 1, z + 1) v4 = Vertex(x, y + 1, z + 1) faces.append(Face([v1, v2, v3, v4])) if z == 0 or functionOut(self.get_value_at_xyz(x, y, z - 1)): v1 = Vertex(x, y + 1, z) v2 = Vertex(x + 1, y + 1, z) v3 = Vertex(x + 1, y, z) v4 = Vertex(x, y, z) faces.append(Face([v1, v2, v3, v4])) mesh = Mesh() mesh.faces = faces mesh.update_topology() return mesh
def construct_torus(ringRadius, tubeRadius, ringN=16, tubeN=16): """ Constructs a torus mesh. Arguments: ---------- ringRadius : float<br> the big radius of the axis<br> tubeRadius : float<br> radius of the the tube along the axis<br> Optional Arguments: ---------- ringN : int<br> resolution along the ring<br> tubeN : int<br> resolution along the tube """ mesh = Mesh() theta = 2 * math.pi / ringN phi = 2 * math.pi / tubeN for i in range(ringN): for j in range(tubeN): mesh.vertices.append( _torus_vertex(ringRadius, tubeRadius, phi * j, theta * i)) for i in range(ringN): ii = (i + 1) % ringN for j in range(tubeN): jj = (j + 1) % tubeN a = i * tubeN + j b = ii * tubeN + j c = ii * tubeN + jj d = i * tubeN + jj f = Face([mesh.vertices[k] for k in [a, b, c, d]]) mesh.faces.append(f) mesh.update_topology() return mesh
def import_obj(filename): """Loads a Wavefront OBJ file. """ mesh = Mesh() group = "" for line in open(filename, "r"): if line.startswith('#'): continue values = line.split() if not values: continue if values[0] == 'g': group=values[1] elif values[0] == 'v': v = [float(c) for c in values[1 : 4]] #v = map(float, values[1:4]) mesh.vertices.append(Vertex(v[0],v[1],v[2])) elif values[0] == 'f': face = Face([]) face.group = group for v in values[1:]: w = v.split('/') vertex = mesh.vertices[int(w[0]) - 1] face.vertices.append(vertex) mesh.faces.append(face) return mesh
def subdivide_custom_triface_extrude_tapered_nonU(face, height=0.0, fraction=0.5, doCap=True): """ Extrudes a triangular face tapered like a window by creating an offset face and quads between every original edge and the corresponding new edge. The vertices of the new edge which corresponds to the shortest edge of the triangle are moved closer to the later, while preserving the offset from its other edges Arguments: ---------- face : mola.core.Face The face to be extruded height : float The distance of the new face to the original face, default 0 fraction : float The relative offset distance, 0: original vertex, 1: center point default 0.5 (halfway) """ center_vertex = utils_face.face_center(face) normal = utils_face.face_normal(face) scaled_normal = utils_vertex.vertex_scale(normal, height) minD = 9999999999999999 for i in range(len(face.vertices) - 1): n1 = face.vertices[i] for j in range(i + 1, len(face.vertices)): n2 = face.vertices[j] d = (n2.x - n1.x)**2.0 + (n2.y - n1.y)**2.0 + (n2.z - n1.z)**2.0 if d < minD: minD = d shortF_st = i shortF_end = j other = 3 - shortF_st - shortF_end n_other = face.vertices[other] betw_other = utils_vertex.vertex_subtract(center_vertex, n_other) betw_other = utils_vertex.vertex_scale(betw_other, fraction) nn_other = utils_vertex.vertex_add(n_other, betw_other) nn_other = utils_vertex.vertex_add(nn_other, scaled_normal) # calculate new vertex positions new_vertices = [] for i in range(len(face.vertices)): n1 = face.vertices[i] betw = utils_vertex.vertex_subtract(center_vertex, n1) betw = utils_vertex.vertex_scale(betw, fraction) nn = utils_vertex.vertex_add(n1, betw) nn = utils_vertex.vertex_add(nn, scaled_normal) if i == shortF_st or i == shortF_end: vec = utils_vertex.vertex_subtract(n1, nn_other) vec = utils_vertex.vertex_scale(vec, 0.25) nn = utils_vertex.vertex_add(nn, vec) new_vertices.append(nn) new_faces = [] # create the quads along the edges num = len(face.vertices) for i in range(num): n1 = face.vertices[i] n2 = face.vertices[(i + 1) % num] n3 = new_vertices[(i + 1) % num] n4 = new_vertices[i] new_face = Face([n1, n2, n3, n4]) new_faces.append(new_face) # create the closing cap face if doCap: cap_face = Face(new_vertices) new_faces.append(cap_face) for new_face in new_faces: utils_face.face_copy_properties(face, new_face) return new_faces
def construct_rhombic_dodecahedron(edge_length=1, cx=0, cy=0, cz=0): mesh = Mesh() #make vertices mesh.vertices = [ Vertex(0, 0, 2 * edge_length), Vertex(-edge_length, edge_length, edge_length), Vertex(-edge_length, -edge_length, edge_length), Vertex(edge_length, -edge_length, edge_length), Vertex(edge_length, edge_length, edge_length), Vertex(-2 * edge_length, 0, 0), Vertex(0, -2 * edge_length, 0), Vertex(2 * edge_length, 0, 0), Vertex(0, 2 * edge_length, 0), Vertex(-edge_length, edge_length, -edge_length), Vertex(-edge_length, -edge_length, -edge_length), Vertex(edge_length, -edge_length, -edge_length), Vertex(edge_length, edge_length, -edge_length), Vertex(0, 0, -2 * edge_length) ] #move center to desired coordinates center = Vertex(cx, cy, cz) for v in mesh.vertices: v.add(center) #construct quad faces f1 = Face([ mesh.vertices[0], mesh.vertices[2], mesh.vertices[5], mesh.vertices[1] ]) f2 = Face([ mesh.vertices[0], mesh.vertices[3], mesh.vertices[6], mesh.vertices[2] ]) f3 = Face([ mesh.vertices[0], mesh.vertices[4], mesh.vertices[7], mesh.vertices[3] ]) f4 = Face([ mesh.vertices[0], mesh.vertices[1], mesh.vertices[8], mesh.vertices[4] ]) f5 = Face([ mesh.vertices[2], mesh.vertices[6], mesh.vertices[10], mesh.vertices[5] ]) f6 = Face([ mesh.vertices[3], mesh.vertices[7], mesh.vertices[11], mesh.vertices[6] ]) f7 = Face([ mesh.vertices[4], mesh.vertices[8], mesh.vertices[12], mesh.vertices[7] ]) f8 = Face([ mesh.vertices[1], mesh.vertices[5], mesh.vertices[9], mesh.vertices[8] ]) f9 = Face([ mesh.vertices[10], mesh.vertices[13], mesh.vertices[9], mesh.vertices[5] ]) f10 = Face([ mesh.vertices[11], mesh.vertices[13], mesh.vertices[10], mesh.vertices[6] ]) f11 = Face([ mesh.vertices[12], mesh.vertices[13], mesh.vertices[11], mesh.vertices[7] ]) f12 = Face([ mesh.vertices[9], mesh.vertices[13], mesh.vertices[12], mesh.vertices[8] ]) mesh.faces = [f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12] mesh.update_topology() return mesh
def add_face(self, vertices): f = Face(vertices) self.faces.append(f) return f