BIMBase之python建模宝典:三通管的诞生

BIMBase自从2021年发布以来获得了众多关心国产BIM和业务数字化转型的圈内老法师的关注，除了是国内首款完全自主知识产权的的BIMBase系统，实现建筑信息模型（BIM）关键核心技术自主研发安全可控。

同时开创了BIM X PYthon的技术跨界混搭风，得以让建模可以通过快速编程实现。

So！

BIMBase团队为了在功能和场景上

帮助大家了解BIMBase

学习建模小技巧

开设了技术专栏

【BIMBase之python建模宝典】

今日分享第二弹

三通管作为管道连接件的一种，是给排水工程中的常见构件之一。今天我们就来教教大家如何用Python参数化建模方法创建三通管。废话不多说，咱直接上干货！

三通管构件

建模方法

BIMBase三通管建模

①引用pyp3d和numpy,定义参数，变量赋值

from pyp3d import *

import numpy as np

class 三通管2(Component):

def __init__(self):

Component.__init__(self)

self['三通管2'] = Attr(None, show = True)

self['管口内径'] = Attr(20, obvious = True, group = '管口')

self['管壁厚'] = Attr(1, obvious = True, group = '管口')

self['管口长'] = Attr(25, obvious = True, group = '管口')

self['接口内径'] = Attr(28, obvious = True, group = '接口')

self['接口长'] = Attr(8, obvious = True, group = '接口')

self.replace()

@export

def replace(self):

pipe_InR = self['管口内径']

pipe_T = self['管壁厚']

pipe_H = self['管口长']

way_InR = self['接口内径']

way_H = self['接口长']

D = 100 # 管口距中心长度

pipe_exR = pipe_InR+pipe_T# 管口外径

way_exR = way_InR+pipe_T # 接口外径

②管口：通过两个Cone之间布尔减创建管壁；三次旋转阵列创建全部管口

# 管口

bpipe_1st = (Cone(Vec3(0, 0, 0), Vec3(0, pipe_H, 0), pipe_exR, pipe_exR) - \

Cone(Vec3(0, 0, 0), Vec3(0, pipe_H, 0), pipe_InR, pipe_InR))

junction_1st = trans(0, pipe_H, 0)*\

(Cone(Vec3(0, 0, 0), Vec3(0, way_H, 0), way_exR, way_exR) - \

Cone(Vec3(0, 0, 0), Vec3(0, way_H, 0), way_InR, way_InR))

crossing_1st = trans(0, pipe_H-pipe_T, 0)*\

(Cone(Vec3(0, 0, 0), Vec3(0, pipe_T, 0), way_exR, way_exR) - \

Cone(Vec3(0, 0, 0), Vec3(0, pipe_T, 0), pipe_exR, pipe_exR))

pipe_1st = trans(0, -D, 0)*Combine(bpipe_1st, junction_1st, crossing_1st)

pipe_2nd = rotz(2*pi/3)*pipe_1st

pipe_3rd = rotz(-2*pi/3)*pipe_1st

pipe = Combine(pipe_1st, pipe_2nd, pipe_3rd)

③连接段：

自定义函数MirrorPoint（Point1,Point2,Point3）返回平面上某点关于直线的对称点；自定义函数vectorialAngle（vector1, vector2）返回空间中两向量夹角；确定放样截面和路径，放样；旋转。

此处的自定义函数MirrorPoint和vectorialAngle主要用于空间几何运算，在三通管中用于确定连接段放样路径，即用计算出来的三个点来三点绘弧，以此弧线作为放样路径。

自定义函数MirrorPoint

## 求平面上一点关于直线的对称点。

def MirrorPoint(P1, P2, P):

k = (P2.y-P1.y) / (P2.x-P1.x)

c = (k*P1.x-P1.y) / k

b = -c / (P1.y-k*P1.x)

a = -b*k

sqr = a*a + b*b

x = (b*b*P.x-a*b*P.y-a*c) / sqr

y = (a*a*P.y-a*b*P.x-b*c) / sqr

return Vec3(2*x-P.x, 2*y-P.y, 0)

自定义函数vectorialAngle

## 求空间中两向量夹角。

def vectorialAngle(V1, V2):

normal1 = np.array([V1.x, V1.y, V1.z]).reshape(1, -1)

normal2 = np.array([V2.x, V2.y, V2.z]).reshape(1, -1)

data_M = np.sqrt(np.sum(normal1*normal1, axis = 1))

data_N = np.sqrt(np.sum(normal2*normal2, axis = 1))

cos_theta = np.sum(normal1*normal2, axis = 1)/(data_M*data_N)

theta = np.degrees(acos(cos_theta))/180*pi

return theta

连接段代码

# 连接段

P1 = Vec3(way_InR, pipe_H+way_H-D, 0)

P2 = rotz(2*pi/3)*roty(pi)*P1

P = Vec3(0, 0, 0)

P_mir = MirrorPoint(P1, P2, P)

V1 = P1-P_mir

V2 = P2-P_mir

P3 = arbitrary_rotate(P_mir, Vec3(0, 0, 1), -vectorialAngle(V1, V2)/2)*P1

sec = Section(Line(rotz(-pi/2)*scale(way_InR)*Arc(pi),

rotz(pi/2)*scale(way_exR)*Arc(-pi),))

unitShell_1st = Sweep(trans(0, pipe_H+way_H-D, 0)*rotx(pi/2)*sec, Line(Arc(P1, P3, P2)))

unitShell_2nd = rotz(2*pi/3)*unitShell_1st

unitShell_3rd = rotz(-2*pi/3)*unitShell_1st

shell = Combine(unitShell_1st, unitShell_2nd, unitShell_3rd)

④顶面和底面：

计算点绘制弧线，首先确定三维点topPoint，再通过自定义函数vectorialAngle、内置函数arbitrary_rotate和rotz得到其他两个三维点，通过三个三维点确定弧线capLine_1st，分别顺时针和逆时针旋转120°得到另两段弧线，通过get_intersect_point_of_two_arcs函数确定两弧线交点，通过to_vec2函数将三维点转化为二维点，再由得到的点三点画弧，将弧分别顺时针和逆时针旋转120°得到所需的三段弧线；由弧线绘制截面；

截面移动trans镜像mirror得到顶面和底面

# 顶面和底面

topPoint = Vec3(0, pipe_H+way_H-D, way_exR)

MidPoint = arbitrary_rotate(P_mir, Vec3(0, 0, 1), -vectorialAngle(V1, V2)/2)*topPoint

endPoint = rotz(2*pi/3)*topPoint

capLine_1st = Arc(topPoint, MidPoint, endPoint)

capLine_2nd = rotz(2*pi/3)*capLine_1st

capLine_3rd = rotz(-2*pi/3)*capLine_1st

node_2nd = get_intersect_point_of_two_arcs(capLine_1st, capLine_2nd)

capLine_1st = Arc(to_vec2(rotz(-2*pi/3)*node_2nd[0]), to_vec2(MidPoint), to_vec2(node_2nd[0]))

capLine_2nd = rotz(2*pi/3)*capLine_1st

capLine_3rd = rotz(-2*pi/3)*capLine_1st

capSec = Section(Line(capLine_1st, capLine_2nd, capLine_3rd))

capTop = trans(0, 0, way_exR)*Sweep(scale(1.1)*capSec, Line(Vec3(0, 0, 0), Vec3(0, 0, -pipe_T)))

capBottom = mirror("xy")*capTop

cap1 = Combine(capTop, capBottom)

函数总结

BIMBase三通管建模

1. Cone：圆柱

2. Sweep：扫掠

3. rotx\roty\rotz\arbitrary_rotate：绕X轴旋转、绕Y轴旋转、绕Z轴旋转、绕任意轴旋转

4. Trans：平移

5. mirror：镜像

6. to_vec2：三维点、向量转化为二维点、向量

7. get_intersect_point_of_two_arcs：求两段圆弧交点坐标

是不是很简单呢，大家快动手试试吧！