OpenCASCADE and the Invisible Sun of Tao

The best traveler who leaves no traces

The best leader who inspires without speech

The plan is perfect, if there is no plan at all

And if a wise man closes the door,

you will never solve the secret.

The Great Book of Tao - Verse 27 (Translation by Y. Polezhaeva)

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#initMode = 'screen','web','stl'
def ScInit(initMode, decoration, precision, exportDir):
  pass

#default styles
#'stInfo' - for service objects
#'stMain' - for main object of drawing
#'stFocus' - for important details
def ScStyle(styleVal):
  pass

#draw objects
def ScPoint(pnt, style):
  pass
def ScLine(pnt1, pnt2, style):
  pass
def ScCircle(pnt1, pnt2, pnt3, style):
  pass
def ScShape(shape, style):
  pass
def ScLabel(pnt, text, style):
  pass

#start render
def ScStart()    

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def getPntsBase(r):
    
    r2 = r/2
    
    gpPntMinC = gp_Pnt(0,r2,0)
    
    p0 = gp_Pnt(0,0,0)      
    p1 = getPntRotate(gpPntMinC , p0, -pi/4)      
    p2 = gp_Pnt(-r2,r2,0)      
    p3 = getPntRotate(gpPntMinC , p0, -pi/4*3)      
    p4 = gp_Pnt(0,r,0)      
    p5 = gp_Pnt(r,0,0)      
    p6 = gp_Pnt(0,-r,0)      
    p7 = gp_Pnt(r2,-r2,0)      
    
    return p0, p1, p2, p3, p4, p5, p6, p7
  
def getWireDaoClassic(ppBase):
    
    p0, p1, p2, p3, p4, p5, p6, p7  = ppBase
    
    arc1 =  GC_MakeArcOfCircle(p0,p1,p2).Value()
    arc2 =  GC_MakeArcOfCircle(p2,p3,p4).Value()
    arc3 =  GC_MakeArcOfCircle(p4,p5,p6).Value()
    arc4 =  GC_MakeArcOfCircle(p6,p7,p0).Value()
 
    edge1 = BRepBuilderAPI_MakeEdge(arc1).Edge()
    edge2 = BRepBuilderAPI_MakeEdge(arc2).Edge()
    edge3 = BRepBuilderAPI_MakeEdge(arc3).Edge()
    edge4 = BRepBuilderAPI_MakeEdge(arc4).Edge()
  
    shape =  BRepBuilderAPI_MakeWire(edge1, edge2, edge3, edge4).Wire()
    
    return shape
 
def slide_01_DaoClassic(r):
    
    drawCircle(r, 'stInfo')
    pntsBase = getPntsBase(r)
    drawPoints(pntsBase, 'stFocus', 'b')
    shapeDaoClassic = getWireDaoClassic(pntsBase)
    ScShape(shapeDaoClassic, 'stMain')

WebGL-: 01

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def getShapeOffset(shape, offset):
    tool = BRepOffsetAPI_MakeOffset()
    tool.AddWire(shape)
    tool.Perform(offset)
    shape = tool.Shape()  
    return shape

def slide_02_DaoConcept(r, offset):
    
    drawCircle(r + offset, 'stInfo')
    pntsBase = getPntsBase(r)
    wireDaoClassic = getWireDaoClassic(pntsBase)
    wireDao0 = getShapeOffset(wireDaoClassic, -offset)
    ScShape(wireDao0, 'stMain')
  
    pntsDao0 = getPntsOfShape(wireDao0)
    drawPoints(pntsDao0, 'stFocus', 'd')
  
    wireDao1 = getShapeOZRotate(wireDao0, pi)
    ScShape(wireDao1, 'stInfo')

WebGL-: 02

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def getPntDaoFocus(r):
    return gp_Pnt(0,-r/4,0)


def getPntsForDaoSec(pntDaoStart, pntUpLimit, pntDaoEnd, pntDownLimit, pntFocus, k):
    angleLimit = 0
    pntLimit = getPntScale(pntFocus, pntUpLimit, 1.2)
    angleStart = getAngle(pntFocus, pntLimit, pntDaoStart)
    angleEnd = getAngle(pntFocus, pntLimit, pntDaoEnd)
    kLimit = (angleLimit - angleStart)/(angleEnd - angleStart)
    if k < kLimit: #head
        kHead = (k - 0) / (kLimit- 0)
        xStart = pntUpLimit.X()
        xEnd = pntDaoStart.X()
        dx = (xEnd-xStart)*(1 - kHead)
        pnt0 = getPntTranslate(pntFocus, dx, 0, 0)
        pnt1 = getPntTranslate(pntLimit, dx, 0, 0)
    else: #tail    
        kTail = (k - kLimit) / (1 - kLimit)
        angle = -angleEnd*kTail
        pnt0 = pntFocus
        pnt1 = getPntRotate(pntFocus, pntLimit, angle)
    return pnt0, pnt1


def getWireDaoSec(shapeDao, pntFocus, k):
    
    pntsDao = getPntsOfShape(shapeDao)
    pntDownLimit, pntDaoStart, pntUpLimit, pntDaoEnd = pntsDao
    
    p1, p2 = getPntsForDaoSec(pntDaoStart, pntUpLimit, pntDaoEnd, pntDownLimit, 
                              pntFocus, k)
    sectionPlane = getFacePlane(p1, p2, 3)
    
    pnt0, pnt1 =  getPntsEdgesFacesIntersect(shapeDao, sectionPlane)
    pntUp = getPntSectionUp(pnt0, pnt1)
    circle = GC_MakeCircle(pnt0, pntUp, pnt1).Value()
    edge = BRepBuilderAPI_MakeEdge(circle).Edge()
    wire =  BRepBuilderAPI_MakeWire(edge).Wire()
    return wire

   
def slide_03_DaoSecPrincipe(r, offset, k, h):
    
    drawCircle(r + offset,  'stInfo')
    pntsBase = getPntsBase(r)
    wireDaoClassic = getWireDaoClassic(pntsBase)
    wireDao0 = getShapeOffset(wireDaoClassic, -offset)
    ScShape(wireDao0, 'stMain')
    
    # for oure goal we need divide Dao on Head and Tail
    # Head sections is parallell
    # Tail sections is focused on focus point
    pntsDao0 = getPntsOfShape(wireDao0)
    pntDownLimit, pntDaoStart, pntUpLimit, pntDaoEnd  = pntsDao0
    
    # we need focus to determine tail sections 
    pntFocus = getPntDaoFocus(r)
    ScPoint(pntFocus, 'stMain')
    ScLabel(pntFocus, 'F' ,'stMain')
    
    # we need two points to determine section
    pnt1, pnt2 = getPntsForDaoSec(pntDaoStart, pntUpLimit, pntDaoEnd, 
                                  pntDownLimit, pntFocus, k)
    ScLine(pnt1, pnt2, 'stFocus')
    
    # !!! we need use plane to detect intercsect (not line) becouse 3D
    planeSec = getFacePlane(pnt1, pnt2, h)
    ScShape(planeSec, 'stFocus')

    pntsSec =  getPntsEdgesFacesIntersect(wireDao0, planeSec)
    drawPoints(pntsSec, 'stFocus')
    
    wireSec = getWireDaoSec(wireDao0, pntFocus, k)
    ScShape(wireSec, 'stFocus') 

WebGL-: 03

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def slide_04_DaoManySec(r, offset, kStart, kEnd, cnt):
    
    drawCircle(r + offset, 'stInfo')
    pntsBase = getPntsBase(r)
    wireDaoClassic = getWireDaoClassic(pntsBase)
    wireDao0 = getShapeOffset(wireDaoClassic, -offset)
    ScShape(wireDao0, 'stMain')
    
    pntsDao0 = getPntsOfShape(wireDao0)
    pntDownLimit, pntDaoStart, pntUpLimit, pntDaoEnd  = pntsDao0
    
    pntFocus = getPntDaoFocus(r)
    
    for i in range(cnt+1):
        k = i/cnt
        kkScale = kEnd - kStart
        kk = kStart + k* kkScale
        p0,p1 = getPntsForDaoSec(pntDaoStart, pntUpLimit, pntDaoEnd, 
        pntDownLimit, pntFocus, kk)
        ScLine(p0, p1, 'stFocus')
        wireSec = getWireDaoSec(wireDao0, pntFocus, kk)
        ScShape(wireSec, 'stMain') 

WebGL-: 04

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def slide_05_DaoSkinning (r, offset):
    
    drawCircle(r + offset,  'stInfo')
    pntsBase = getPntsBase(r)
    wireDaoClassic = getWireDaoClassic(pntsBase)
    wireDao0 = getShapeOffset(wireDaoClassic, -offset)
    ScShape(wireDao0, 'stMain')
    
    pntsDao0 = getPntsOfShape(wireDao0)
    pntDownLimit, pntDaoStart, pntUpLimit, pntDaoEnd  = pntsDao0
    
    pntFocus = getPntDaoFocus(r)
    drawPoints(pntFocus, 'stMain')
  
    ks = [ 3, 9 , 16, 24, 35, 50, 70, 85] 
    wiresSec = []
 
    for k in  ks:
       wireSec = getWireDaoSec(wireDao0, pntFocus, k/100)
       ScShape(wireSec, 'stMain')
       wiresSec += [wireSec]    
    
    solidDao0 = getShapeSkin(pntDaoStart, wiresSec, pntDaoEnd)
    ScShape(solidDao0, 'stFocus')

WebGL-: 05

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def getSolidDao(r, offset):
    
    pntsBase = getPntsBase(r)
    wireDaoClassic = getWireDaoClassic(pntsBase)
    wireDao = getShapeOffset(wireDaoClassic, -offset)
    
    pntsDao = getPntsOfShape(wireDao)
    pntDownLimit, pntDaoStart, pntUpLimit, pntDaoEnd  = pntsDao
    
    pntFocus = getPntDaoFocus(r)
   
    ks = [ 3, 9 , 16, 24, 35, 50, 70, 85] 
    wiresSec = []
 
    for k in  ks:
       wireSec = getWireDaoSec(wireDao, pntFocus, k/100)
       wiresSec += [wireSec]    
    
    solidDao = getShapeSkin(pntDaoStart, wiresSec, pntDaoEnd)
    solidDao = getShapeZScale(solidDao, 0.7)
    return solidDao
   
def slide_06_DaoComplete (r, offset):
    
    solidDao0 = getSolidDao(r, offset)
    ScShape(solidDao0, stDao0)
    solidDao1  = getShapeOZRotate(solidDao0, pi)
    ScShape(solidDao1, stDao1)

WebGL-: 06

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def getDaoCase(r, offset, h):
    r2 = r*2                                    
    h2 = h/2
    rTop = r + offset
    rSphere = gp_Vec(0,rTop,h2).Magnitude()
    sphere = BRepPrimAPI_MakeSphere(rSphere).Shape()
    limit = BRepPrimAPI_MakeBox( gp_Pnt(-r2, -r2, -h2), gp_Pnt(r2, r2, h2) ).Shape()
    case = BRepAlgoAPI_Common(sphere, limit).Shape()
    case = getShapeTranslate(case, 0,0,-h2)
 
    
    solidDao0 = getSolidDao(r, offset)
    solidDao1  = getShapeOZRotate(solidDao0, pi)
   
    case = BRepAlgoAPI_Cut(case, solidDao0).Shape()
    case = BRepAlgoAPI_Cut(case, solidDao1).Shape()
  
    return case
    
def slide_07_DaoWithCase (r, offset, caseH, caseZMove ,gap):
    
    solidDao0 = getSolidDao(r, offset+gap)
    ScShape(solidDao0, stDao0)
    solidDao1  = getShapeOZRotate(solidDao0, pi)
    ScShape(solidDao1, stDao1)
    
    case = getDaoCase(r, offset, caseH)
    
    case = getShapeTranslate(case, 0,0, caseZMove)
    ScShape(case, stCase)

WebGL-: 07

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We need to know when to stop The

vessel cannot be overfilled

Great values ​​are more difficult to guard

And a sword that is too sharp will dull faster With a

good rank too proud

To call

your house to your house Your work is over, so be able to leave

This is the meaning of strength, life and path.

The Great Book of Tao - Verse 9 (Translation by Y. Polezhaeva)