\( \usepackage{euler} % must be loaded before fontspec for the whole doc (below); this must be kept for pngmath, however \usepackage{hyperref} \usepackage{amsmath} \usepackage{amsbsy} %\usepackage{mathabx} \usepackage{underscore} \usepackage[all]{xy} % Metadata of the pdf output \hypersetup{pdftitle={Yade Documentation}} \hypersetup{pdfauthor={Smilauer, V., et al.}} \hypersetup{pdfkeywords={Discrete element method, granular materials, contact law, hydromechanical coupling}} % symbols \renewcommand{\mat}{\boldsymbol} \renewcommand{\vec}{\boldsymbol} \renewcommand{\tens}{\boldsymbol} %normalized and locfram here \def\normalized#1{\widehat{#1}} \def\locframe#1{\widetilde{#1}} % timestep \def\Dt{\Delta t} \def\Dtcr{\Dt_{\rm cr}} % algorithm complexity \def\bigO#1{{\mathcal{O}(#1)}} % variants for greek symbols \let\epsilon\varepsilon \let\theta\vartheta \let\phi\varphi % shorthands \let\sig\sigma \let\eps\epsilon % variables at different points of time \def\prev#1{#1^-} \def\pprev#1{#1^\ominus} \def\curr#1{#1^{\circ}} \def\nnext#1{#1^\oplus} \def\next#1{#1^+} % shorthands for geometry \def\currn{\curr{\vec{n}}} \def\currC{\curr{\vec{C}}} \def\uT{\vec{u}_T} \def\curruT{\curr{\vec{u}}_T} \def\prevuT{\prev{\vec{u}}_T} \def\currn{\curr{\vec{n}}} \def\prevn{\prev{\vec{n}}} % motion \def\pprevvel{\pprev{\dot{\vec{u}}}} \def\nnextvel{\nnext{\dot{\vec{u}}}} \def\curraccel{\curr{\ddot{\vec{u}}}} \def\prevpos{\prev{\vec{u}}} \def\currpos{\curr{\vec{u}}} \def\nextpos{\next{\vec{u}}} \def\curraaccel{\curr{\dot{\vec{\omega}}}} \def\pprevangvel{\pprev{\vec{\omega}}} \def\nnextangvel{\nnext{\vec{\omega}}} \def\loccurr#1{\curr{\locframe{#1}}} \def\numCPU{n_{\rm cpu}} \DeclareMathOperator{\Align}{Align} \DeclareMathOperator{\sign}{sgn} % sorting algorithms \def\isleq#1{\currelem{#1}\ar@/^/[ll]^{\leq}} \def\isnleq#1{\currelem{#1}\ar@/^/[ll]^{\not\leq}} \def\currelem#1{\fbox{$#1$}} \def\sortSep{||} \def\sortInv{\hbox{\phantom{||}}} \def\sortlines#1{\xymatrix@=3pt{#1}} \def\crossBound{||\mkern-18mu<} \)

# Source code for yade.bodiesHandling

    # encoding: utf-8
    """
    Miscellaneous functions, which are useful for handling bodies.
    """

    from yade.wrapper import *
    import utils, math, numpy

    from yade.minieigenHP import *

    #spheresPackDimensions==================================================

    def spheresPackDimensions(idSpheres=[], mask=-1):
       """The function accepts the list of spheres id's or list of bodies and calculates max and min dimensions, geometrical center.

       :param list idSpheres: list of spheres
       :param int mask: :yref:`Body.mask` for the checked bodies

       :return: dictionary with keys ``min`` (minimal dimension, Vector3), ``max`` (maximal dimension, Vector3), ``minId`` (minimal dimension sphere Id, Vector3), ``maxId`` (maximal dimension sphere Id, Vector3), ``center`` (central point of bounding box, Vector3), ``extends`` (sizes of bounding box, Vector3), ``volume`` (volume of spheres, Real), ``mass`` (mass of spheres, Real), ``number`` (number of spheres, int),

       """
       idSpheresIter = []

       if (len(idSpheres) < 1):
          #check mask
          ifSpherMask = []
          if (mask > -1):  #The case, when only the mask was given, without list of ids
             for i in O.bodies:
                if ((i.mask & mask) != 0):
                   ifSpherMask.append(i.id)
             if (len(ifSpherMask) < 2):
                raise RuntimeWarning("Not enough bodies to analyze with given mask")
             else:
                idSpheresIter = ifSpherMask
          else:
             raise RuntimeWarning("Only a list of particles with length > 1 can be analyzed")
       else:
          idSpheresIter = idSpheres

       minVal = Vector3.Zero
       maxVal = Vector3.Zero

       minId = Vector3.Zero
       maxId = Vector3.Zero

       counter = 0
       volume = 0.0
       mass = 0.0

       for i in idSpheresIter:
          if (type(i).__name__ == 'int'):
             b = O.bodies[i]  #We have received a list of ID's
          elif (type(i).__name__ == 'Body'):
             b = i  #We have recevied a list of bodies
          else:
             raise TypeError("Unknow type of data, should be list of int's or bodies's")

          if (b):
             spherePosition = b.state.pos  #skip non-existent spheres

             try:
                sphereRadius = b.shape.radius  #skip non-spheres
             except AttributeError:
                continue

             if (mask > -1) and ((mask & b.mask) == 0):
                continue  #skip bodies with wrong mask

             sphereRadiusVec3 = Vector3(sphereRadius, sphereRadius, sphereRadius)

             sphereMax = spherePosition + sphereRadiusVec3
             sphereMin = spherePosition - sphereRadiusVec3

             for dim in range(0, 3):
                if ((sphereMax[dim] > maxVal[dim]) or (counter == 0)):
                   maxVal[dim] = sphereMax[dim]
                   maxId[dim] = b.id
                if ((sphereMin[dim] < minVal[dim]) or (counter == 0)):
                   minVal[dim] = sphereMin[dim]
                   minId[dim] = b.id
             volume += 4.0 / 3.0 * math.pi * sphereRadius * sphereRadius * sphereRadius
             mass += b.state.mass
             counter += 1

       center = (maxVal - minVal) / 2.0 + minVal
       extends = maxVal - minVal

       dimensions = {
               'max': maxVal,
               'min': minVal,
               'maxId': maxId,
               'minId': minId,
               'center': center,
               'extends': extends,
               'volume': volume,
               'mass': mass,
               'number': counter
       }
       return dimensions

    #facetsDimensions==================================================

    def facetsDimensions(idFacets=[], mask=-1):
       """The function accepts the list of facet id's or list of facets and calculates max and min dimensions, geometrical center.

       :param list idFacets: list of spheres
       :param int mask: :yref:`Body.mask` for the checked bodies

       :return: dictionary with keys ``min`` (minimal dimension, Vector3), ``max`` (maximal dimension, Vector3), ``minId`` (minimal dimension facet Id, Vector3), ``maxId`` (maximal dimension facet Id, Vector3), ``center`` (central point of bounding box, Vector3), ``extends`` (sizes of bounding box, Vector3), ``number`` (number of facets, int),

       """
       idFacetsIter = []

       if (len(idFacets) < 1):
          #check mask
          ifFacetMask = []
          if (mask > -1):  #The case, when only the mask was given, without list of ids
             for i in O.bodies:
                if ((i.mask & mask) != 0):
                   ifFacetMask.append(i.id)
             if (len(ifFacetMask) < 2):
                raise RuntimeWarning("Not enough bodies to analyze with given mask")
             else:
                idFacetsIter = ifFacetMask
          else:
             raise RuntimeWarning("Only a list of particles with length > 1 can be analyzed")
       else:
          idFacetsIter = idFacets

       minVal = Vector3.Zero
       maxVal = Vector3.Zero

       minId = Vector3.Zero
       maxId = Vector3.Zero

       counter = 0

       for i in idFacetsIter:
          if (type(i).__name__ == 'int'):
             b = O.bodies[i]  #We have received a list of ID's
          elif (type(i).__name__ == 'Body'):
             b = i  #We have recevied a list of bodies
          else:
             raise TypeError("Unknow type of data, should be list of int's or bodies's")

          if (b):
             p = b.state.pos
             o = b.state.ori
             s = b.shape
             pt1 = p + o * s.vertices[0]
             pt2 = p + o * s.vertices[1]
             pt3 = p + o * s.vertices[2]

             if (mask > -1) and ((mask & b.mask) == 0):
                continue  #skip bodies with wrong mask

             facetMax = Vector3(max(pt1[0], pt2[0], pt3[0]), max(pt1[1], pt2[1], pt3[1]), max(pt1[2], pt2[2], pt3[2]))
             facetMin = Vector3(min(pt1[0], pt2[0], pt3[0]), min(pt1[1], pt2[1], pt3[1]), min(pt1[2], pt2[2], pt3[2]))

             for dim in range(0, 3):
                if ((facetMax[dim] > maxVal[dim]) or (counter == 0)):
                   maxVal[dim] = facetMax[dim]
                   maxId[dim] = b.id
                if ((facetMin[dim] < minVal[dim]) or (counter == 0)):
                   minVal[dim] = facetMin[dim]
                   minId[dim] = b.id
             counter += 1

       center = (maxVal - minVal) / 2.0 + minVal
       extends = maxVal - minVal

       dimensions = {'max': maxVal, 'min': minVal, 'maxId': maxId, 'minId': minId, 'center': center, 'extends': extends, 'number': counter}
       return dimensions

    #spheresPackDimensions==================================================

    def spheresModify(idSpheres=[], mask=-1, shift=Vector3.Zero, scale=1.0, orientation=Quaternion((0, 1, 0), 0.0), copy=False):
       """The function accepts the list of spheres id's or list of bodies and modifies them: rotating, scaling, shifting.
       if copy=True copies bodies and modifies them.
       Also the mask can be given. If idSpheres not empty, the function affects only bodies, where the mask passes.
       If idSpheres is empty, the function search for bodies, where the mask passes.

       :param Vector3 shift: Vector3(X,Y,Z) parameter moves spheres.
       :param float scale: factor scales given spheres.
       :param Quaternion orientation: orientation of spheres
       :param int mask: :yref:`Body.mask` for the checked bodies
       :returns: list of bodies if copy=True, and Boolean value if copy=False
       """

       idSpheresIter = []

       if (len(idSpheres) == 0):
          #check mask
          ifSpherMask = []
          if (mask > -1):  #The case, when only the mask was given, without list of ids
             for i in O.bodies:
                if ((i.mask & mask) != 0):
                   ifSpherMask.append(i.id)
             if (len(ifSpherMask) == 0):
                raise RuntimeWarning("No bodies to modify with given mask")
             else:
                idSpheresIter = ifSpherMask
          else:
             raise RuntimeWarning("No bodies to modify")
       else:
          idSpheresIter = idSpheres

       dims = spheresPackDimensions(idSpheresIter)

       ret = []
       for i in idSpheresIter:
          if (type(i).__name__ == 'int'):
             b = O.bodies[i]  #We have received a list of ID's
          elif (type(i).__name__ == 'Body'):
             b = i  #We have recevied a list of bodies
          else:
             raise TypeError("Unknown type of data, should be list of int's or bodies")

          try:
             sphereRadius = b.shape.radius  #skip non-spheres
          except AttributeError:
             continue

          if (mask > -1) and ((mask & b.mask) == 0):
             continue  #skip bodies with wrong mask

          if (copy):
             b = sphereDuplicate(b)

          b.state.pos = orientation * (b.state.pos - dims['center']) + dims['center']
          b.shape.radius *= scale
          b.state.mass *= pow(scale, 3)
          b.state.inertia *= pow(scale, 5)
          b.state.pos = (b.state.pos - dims['center']) * scale + dims['center']

          b.state.pos += shift

          if (copy):
             ret.append(b)

       if (copy):
          return ret
       else:
          return True

    #spheresDublicate=======================================================

    def sphereDuplicate(idSphere):
       """The functions makes a copy of sphere"""

       i = idSphere
       if (type(i).__name__ == 'int'):
          b = O.bodies[i]  #We have received a list of ID's
       elif (type(i).__name__ == 'Body'):
          b = i  #We have recevied a list of bodies
       else:
          raise TypeError("Unknown type of data, should be list of int's or bodies")

       try:
          sphereRadius = b.shape.radius  #skip non-spheres
       except AttributeError:
          return False

       addedBody = utils.sphere(
               center=b.state.pos,
               radius=b.shape.radius,
               fixed=not (b.dynamic),
               wire=b.shape.wire,
               color=b.shape.color,
               highlight=b.shape.highlight,
               material=b.material,
               mask=b.mask
       )

       return addedBody