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// 2009 © Václav Šmilauer <eudoxos@arcig.cz>
#include <lib/base/AliasNamespaces.hpp>
#include <lib/base/Logging.hpp>
#include <lib/base/Math.hpp>
#include <lib/pyutil/doc_opts.hpp>
CREATE_CPP_LOCAL_LOGGER("_packPredicates.cpp");
namespace yade { // Cannot have #include directive inside.
/*
This file contains various predicates that say whether a given point is within the solid,
or, not closer than "pad" to its boundary, if pad is nonzero
Besides the (point,pad) operator, each predicate defines aabb() method that returns
(min,max) tuple defining minimum and maximum point of axis-aligned bounding box
for the predicate.
These classes are primarily used for yade.pack.* functions creating packings.
See examples/regular-sphere-pack/regular-sphere-pack.py for an example.
*/
// aux functions
void ttuple2vvec(const py::tuple& t, Vector3r& v1, Vector3r& v2)
{
v1 = py::extract<Vector3r>(t[0])();
v2 = py::extract<Vector3r>(t[1])();
}
// do not use make_tuple directly on vector ops, since their type can be something like Eigen::CwiseBinaryOp<...>
py::tuple vvec2tuple(const Vector3r& a, const Vector3r& b) { return py::make_tuple(a, b); }
struct Predicate {
public:
virtual bool operator()(const Vector3r& pt, Real pad = 0.) const = 0;
virtual py::tuple aabb() const = 0;
Vector3r dim() const
{
Vector3r mn, mx;
ttuple2vvec(aabb(), mn, mx);
return (mx - mn).eval();
}
Vector3r center() const
{
Vector3r mn, mx;
ttuple2vvec(aabb(), mn, mx);
return .5 * (mn + mx);
}
virtual ~Predicate() { }
};
struct PredicateWrap : Predicate, py::wrapper<Predicate> {
bool operator()(const Vector3r& pt, Real pad = 0.) const override { return this->get_override("__call__")(pt, pad); }
py::tuple aabb() const override { return this->get_override("aabb")(); }
};
/*********************************************************************************
****************** Boolean operations on predicates ******************************
*********************************************************************************/
const Predicate& obj2pred(py::object obj) { return py::extract<const Predicate&>(obj)(); }
class PredicateBoolean : public Predicate {
protected:
const py::object A, B;
public:
PredicateBoolean(const py::object _A, const py::object _B)
: A(_A)
, B(_B)
{
}
const py::object getA() { return A; }
const py::object getB() { return B; }
};
// http://www.linuxtopia.org/online_books/programming_books/python_programming/python_ch16s03.html
class PredicateUnion : public PredicateBoolean {
public:
PredicateUnion(const py::object _A, const py::object _B)
: PredicateBoolean(_A, _B)
{
}
bool operator()(const Vector3r& pt, Real pad) const override { return obj2pred(A)(pt, pad) || obj2pred(B)(pt, pad); }
py::tuple aabb() const override
{
Vector3r minA, maxA, minB, maxB;
ttuple2vvec(obj2pred(A).aabb(), minA, maxA);
ttuple2vvec(obj2pred(B).aabb(), minB, maxB);
return vvec2tuple(minA.cwiseMin(minB), maxA.cwiseMax(maxB));
}
};
PredicateUnion makeUnion(const py::object& A, const py::object& B) { return PredicateUnion(A, B); }
class PredicateIntersection : public PredicateBoolean {
public:
PredicateIntersection(const py::object _A, const py::object _B)
: PredicateBoolean(_A, _B)
{
}
bool operator()(const Vector3r& pt, Real pad) const override { return obj2pred(A)(pt, pad) && obj2pred(B)(pt, pad); }
py::tuple aabb() const override
{
Vector3r minA, maxA, minB, maxB;
ttuple2vvec(obj2pred(A).aabb(), minA, maxA);
ttuple2vvec(obj2pred(B).aabb(), minB, maxB);
return vvec2tuple(minA.cwiseMax(minB), maxA.cwiseMin(maxB));
}
};
PredicateIntersection makeIntersection(const py::object& A, const py::object& B) { return PredicateIntersection(A, B); }
class PredicateDifference : public PredicateBoolean {
public:
PredicateDifference(const py::object _A, const py::object _B)
: PredicateBoolean(_A, _B)
{
}
bool operator()(const Vector3r& pt, Real pad) const override { return obj2pred(A)(pt, pad) && !obj2pred(B)(pt, -pad); }
py::tuple aabb() const override { return obj2pred(A).aabb(); }
};
PredicateDifference makeDifference(const py::object& A, const py::object& B) { return PredicateDifference(A, B); }
class PredicateSymmetricDifference : public PredicateBoolean {
public:
PredicateSymmetricDifference(const py::object _A, const py::object _B)
: PredicateBoolean(_A, _B)
{
}
bool operator()(const Vector3r& pt, Real pad) const override
{
bool inA = obj2pred(A)(pt, pad), inB = obj2pred(B)(pt, pad);
return (inA && !inB) || (!inA && inB);
}
py::tuple aabb() const override
{
Vector3r minA, maxA, minB, maxB;
ttuple2vvec(obj2pred(A).aabb(), minA, maxA);
ttuple2vvec(obj2pred(B).aabb(), minB, maxB);
return vvec2tuple(minA.cwiseMin(minB), maxA.cwiseMax(maxB));
}
};
PredicateSymmetricDifference makeSymmetricDifference(const py::object& A, const py::object& B) { return PredicateSymmetricDifference(A, B); }
/*********************************************************************************
****************************** Primitive predicates ******************************
*********************************************************************************/
/*! Sphere predicate */
class inSphere : public Predicate {
Vector3r center;
Real radius;
public:
inSphere(const Vector3r& _center, Real _radius)
{
center = _center;
radius = _radius;
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override { return ((pt - center).norm() <= radius - pad); }
py::tuple aabb() const override
{
return vvec2tuple(
Vector3r(center[0] - radius, center[1] - radius, center[2] - radius),
Vector3r(center[0] + radius, center[1] + radius, center[2] + radius));
}
};
/*! Axis-aligned box predicate */
class inAlignedBox : public Predicate {
Vector3r mn, mx;
public:
inAlignedBox(const Vector3r& _mn, const Vector3r& _mx)
: mn(_mn)
, mx(_mx)
{
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
return mn[0] + pad <= pt[0] && mx[0] - pad >= pt[0] && mn[1] + pad <= pt[1] && mx[1] - pad >= pt[1] && mn[2] + pad <= pt[2]
&& mx[2] - pad >= pt[2];
}
py::tuple aabb() const override { return vvec2tuple(mn, mx); }
};
class inParallelepiped : public Predicate {
Vector3r n[6]; // outer normals, for -x, +x, -y, +y, -z, +z
Vector3r pts[6]; // points on planes
Vector3r mn, mx;
public:
inParallelepiped(const Vector3r& o, const Vector3r& a, const Vector3r& b, const Vector3r& c)
{
Vector3r A(o), B(a), C(a + (b - o)), D(b), E(c), F(c + (a - o)), G(c + (a - o) + (b - o)), H(c + (b - o));
Vector3r x(B - A), y(D - A), z(E - A);
n[0] = -y.cross(z).normalized();
n[1] = -n[0];
pts[0] = A;
pts[1] = B;
n[2] = -z.cross(x).normalized();
n[3] = -n[2];
pts[2] = A;
pts[3] = D;
n[4] = -x.cross(y).normalized();
n[5] = -n[4];
pts[4] = A;
pts[5] = E;
// bounding box
Vector3r vertices[8] = { A, B, C, D, E, F, G, H };
mn = mx = vertices[0];
for (int i = 1; i < 8; i++) {
mn = mn.cwiseMin(vertices[i]);
mx = mx.cwiseMax(vertices[i]);
}
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
for (int i = 0; i < 6; i++)
if ((pt - pts[i]).dot(n[i]) > -pad) return false;
return true;
}
py::tuple aabb() const override { return vvec2tuple(mn, mx); }
};
/*! Arbitrarily oriented cylinder predicate */
class inCylinder : public Predicate {
Vector3r c1, c2, c12;
Real radius, ht;
public:
inCylinder(const Vector3r& _c1, const Vector3r& _c2, Real _radius)
{
c1 = _c1;
c2 = _c2;
c12 = c2 - c1;
radius = _radius;
ht = c12.norm();
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
Real u = (pt.dot(c12) - c1.dot(c12)) / (ht * ht); // normalized coordinate along the c1--c2 axis
if ((u * ht < 0 + pad) || (u * ht > ht - pad)) return false; // out of cylinder along the axis
Real axisDist = ((pt - c1).cross(pt - c2)).norm() / ht;
if (axisDist > radius - pad) return false;
return true;
}
py::tuple aabb() const override
{
// see http://www.gamedev.net/community/forums/topic.asp?topic_id=338522&forum_id=20&gforum_id=0 for the algorithm
const Vector3r& A(c1);
const Vector3r& B(c2);
Vector3r k(
sqrt((pow(A[1] - B[1], 2) + pow(A[2] - B[2], 2))) / ht,
sqrt((pow(A[0] - B[0], 2) + pow(A[2] - B[2], 2))) / ht,
sqrt((pow(A[0] - B[0], 2) + pow(A[1] - B[1], 2))) / ht);
Vector3r mn = A.cwiseMin(B), mx = A.cwiseMax(B);
return vvec2tuple((mn - radius * k).eval(), (mx + radius * k).eval());
}
};
/*! Oriented hyperboloid predicate (cylinder as special case).
See http://mathworld.wolfram.com/Hyperboloid.html for the parametrization and meaning of symbols
*/
class inHyperboloid : public Predicate {
Vector3r c1, c2, c12;
Real R, a, ht, c;
public:
inHyperboloid(const Vector3r& _c1, const Vector3r& _c2, Real _R, Real _r)
{
c1 = _c1;
c2 = _c2;
R = _R;
a = _r;
c12 = c2 - c1;
ht = c12.norm();
Real uMax = sqrt(pow(R / a, 2) - 1);
c = ht / (2 * uMax);
}
// WARN: this is not accurate, since padding is taken as perpendicular to the axis, not the the surface
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
Real v = (pt.dot(c12) - c1.dot(c12)) / (ht * ht); // normalized coordinate along the c1--c2 axis
if ((v * ht < 0 + pad) || (v * ht > ht - pad)) return false; // out of cylinder along the axis
Real u = (v - .5) * ht / c; // u from the wolfram parametrization; u is 0 in the center
Real rHere = a * sqrt(1 + u * u); // pad is taken perpendicular to the axis, not to the surface (inaccurate)
Real axisDist = ((pt - c1).cross(pt - c2)).norm() / ht;
if (axisDist > rHere - pad) return false;
return true;
}
py::tuple aabb() const override
{
// the lazy way
return inCylinder(c1, c2, R).aabb();
}
};
/*! Axis-aligned ellipsoid predicate */
class inEllipsoid : public Predicate {
Vector3r c, abc;
public:
inEllipsoid(const Vector3r& _c, const Vector3r& _abc)
{
c = _c;
abc = _abc;
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
//Define the ellipsoid X-coordinate of given Y and Z
Real x = sqrt((1 - pow((pt[1] - c[1]), 2) / ((abc[1] - pad) * (abc[1] - pad)) - pow((pt[2] - c[2]), 2) / ((abc[2] - pad) * (abc[2] - pad)))
* ((abc[0] - pad) * (abc[0] - pad)))
+ c[0];
Vector3r edgeEllipsoid(x, pt[1], pt[2]); // create a vector of these 3 coordinates
//check whether given coordinates lie inside ellipsoid or not
if ((pt - c).norm() <= (edgeEllipsoid - c).norm()) return true;
else
return false;
}
py::tuple aabb() const override
{
const Vector3r& center(c);
const Vector3r& ABC(abc);
return vvec2tuple(
Vector3r(center[0] - ABC[0], center[1] - ABC[1], center[2] - ABC[2]),
Vector3r(center[0] + ABC[0], center[1] + ABC[1], center[2] + ABC[2]));
}
};
/*! Negative notch predicate.
Use intersection (& operator) of another predicate with notInNotch to create notched solid.
geometry explanation:
c: the center
normalHalfHt (in constructor): A-C
inside: perpendicular to notch edge, points inside the notch (unit vector)
normal: perpendicular to inside, perpendicular to both notch planes
edge: unit vector in the direction of the edge
↑ distUp A
-------------------------
| C
inside(unit) ← * → distInPlane
|
-------------------------
↓ distDown B
*/
class notInNotch : public Predicate {
Vector3r c, edge, normal, inside;
Real aperture;
public:
notInNotch(const Vector3r& _c, const Vector3r& _edge, const Vector3r& _normal, Real _aperture)
{
c = _c;
edge = _edge;
edge.normalize();
normal = _normal;
normal -= edge * edge.dot(normal);
normal.normalize();
inside = edge.cross(normal);
aperture = _aperture;
// LOG_DEBUG("edge="<<edge<<", normal="<<normal<<", inside="<<inside<<", aperture="<<aperture);
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
Real distUp = normal.dot(pt - c) - aperture / 2, distDown = -normal.dot(pt - c) - aperture / 2, distInPlane = -inside.dot(pt - c);
// LOG_DEBUG("pt="<<pt<<", distUp="<<distUp<<", distDown="<<distDown<<", distInPlane="<<distInPlane);
if (distInPlane >= pad) return true;
if (distUp >= pad) return true;
if (distDown >= pad) return true;
if (distInPlane < 0) return false;
if (distUp > 0) return sqrt(pow(distInPlane, 2) + pow(distUp, 2)) >= pad;
if (distDown > 0) return sqrt(pow(distInPlane, 2) + pow(distUp, 2)) >= pad;
// between both notch planes, closer to the edge than pad (distInPlane<pad)
return false;
}
// This predicate is not bounded, return infinities
py::tuple aabb() const override
{
Real inf = std::numeric_limits<Real>::infinity();
return vvec2tuple(Vector3r(-inf, -inf, -inf), Vector3r(inf, inf, inf));
}
};
} // namespace yade
#ifdef YADE_GTS
#if PY_MAJOR_VERSION < 3
extern "C" {
#endif
// HACK
#include "../3rd-party/pygts-0.3.1/pygts.h"
#if PY_MAJOR_VERSION < 3
}
#endif
namespace yade { // Cannot have #include directive inside.
/* Helper function for inGtsSurface::aabb() */
static void vertex_aabb(GtsVertex* vertex, std::pair<Vector3r, Vector3r>* bb)
{
GtsPoint* _p = GTS_POINT(vertex);
Vector3r p(_p->x, _p->y, _p->z);
bb->first = bb->first.cwiseMin(p);
bb->second = bb->second.cwiseMax(p);
}
/*
This class plays tricks getting around pyGTS to get GTS objects and cache bb tree to speed
up point inclusion tests. For this reason, we have to link with _gts.so (see corresponding
SConscript file), which is at the same time the python module.
*/
class inGtsSurface : public Predicate {
py::object pySurf; // to hold the reference so that surf is valid
GtsSurface* surf;
bool is_open, noPad, noPadWarned;
GNode* tree;
public:
inGtsSurface(py::object _surf, bool _noPad = false)
: pySurf(_surf)
, noPad(_noPad)
, noPadWarned(false)
{
if (!pygts_surface_check(_surf.ptr())) throw std::invalid_argument("Ctor must receive a gts.Surface() instance.");
surf = PYGTS_SURFACE_AS_GTS_SURFACE(PYGTS_SURFACE(_surf.ptr()));
if (!gts_surface_is_closed(surf)) throw std::invalid_argument("Surface is not closed.");
is_open = gts_surface_volume(surf) < 0.;
if ((tree = gts_bb_tree_surface(surf)) == NULL) throw std::runtime_error("Could not create GTree.");
}
~inGtsSurface() { g_node_destroy(tree); }
py::tuple aabb() const override
{
Real inf = std::numeric_limits<Real>::infinity();
std::pair<Vector3r, Vector3r> bb;
bb.first = Vector3r(inf, inf, inf);
bb.second = Vector3r(-inf, -inf, -inf);
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpragmas"
#pragma GCC diagnostic ignored "-Wcast-function-type"
gts_surface_foreach_vertex(surf, (GtsFunc)vertex_aabb, &bb);
#pragma GCC diagnostic pop
return vvec2tuple(bb.first, bb.second);
}
bool ptCheck(const Vector3r& pt) const
{
GtsPoint gp;
gp.x = static_cast<gdouble>(pt[0]);
gp.y = static_cast<gdouble>(pt[1]);
gp.z = static_cast<gdouble>(pt[2]);
return (bool)gts_point_is_inside_surface(&gp, tree, is_open);
}
bool operator()(const Vector3r& pt, Real pad = 0.) const override
{
if (noPad) {
if (pad != 0. && noPadWarned) LOG_WARN("inGtsSurface constructed with noPad; requested non-zero pad set to zero.");
return ptCheck(pt);
}
return ptCheck(pt) && ptCheck(pt - Vector3r(pad, 0, 0)) && ptCheck(pt + Vector3r(pad, 0, 0)) && ptCheck(pt - Vector3r(0, pad, 0))
&& ptCheck(pt + Vector3r(0, pad, 0)) && ptCheck(pt - Vector3r(0, 0, pad)) && ptCheck(pt + Vector3r(0, 0, pad));
}
py::object surface() const { return pySurf; }
};
} // namespace yade
#endif
// BOOST_PYTHON_MODULE cannot be inside yade namespace, it has 'extern "C"' keyword, which strips it out of any namespaces.
BOOST_PYTHON_MODULE(_packPredicates)
try {
using namespace yade; // 'using namespace' inside function keeps namespace pollution under control. Alernatively I could add y:: in front of function names below and put 'namespace y = ::yade;' here.
namespace py = ::boost::python;
py::scope().attr("__doc__") = "Spatial predicates for volumes (defined analytically or by triangulation).";
YADE_SET_DOCSTRING_OPTS;
// base predicate class
py::class_<PredicateWrap, /* necessary, as methods are pure virtual*/ boost::noncopyable>(
"Predicate",
"Spatial predicate base class.\nPredicates support boolean operations as described in `user's manual "
"<user.html#boolean-operations-on-predicates>`_")
.def("__call__", py::pure_virtual(&Predicate::operator()), (py::args("pt"), py::args("pad") = 0))
.def("containsPoint",
py::pure_virtual(&Predicate::operator()),
(py::args("pt"), py::args("pad") = 0),
"if given point is inside the predicate or not. ``pred.containsPoint(pt,pad)`` is equivalent to directly calling predicate itself "
"``pred(pt,pad)``")
.def("aabb", py::pure_virtual(&Predicate::aabb), "lower and upper corner of predicate's axis aligned bounding box")
.def("dim", &Predicate::dim, "axis aligned dimensions of the predicate")
.def("center", &Predicate::center, "center of the predicate")
.def("__or__", makeUnion)
.def("__and__", makeIntersection)
.def("__sub__", makeDifference)
.def("__xor__", makeSymmetricDifference);
// boolean operations
py::class_<PredicateBoolean, py::bases<Predicate>, boost::noncopyable>(
"PredicateBoolean", "Boolean operation on 2 predicates (abstract class)", py::no_init)
.add_property("A", &PredicateBoolean::getA)
.add_property("B", &PredicateBoolean::getB);
py::class_<PredicateUnion, py::bases<PredicateBoolean>>(
"PredicateUnion",
"Union (non-exclusive disjunction) of 2 predicates. A point has to be inside any of the two predicates to be inside. Can be constructed using "
"the ``|`` operator on predicates: ``pred1 | pred2``.",
py::init<py::object, py::object>());
py::class_<PredicateIntersection, py::bases<PredicateBoolean>>(
"PredicateIntersection",
"Intersection (conjunction) of 2 predicates. A point has to be inside both predicates. Can be constructed using the ``&`` operator on "
"predicates: ``pred1 & pred2``.",
py::init<py::object, py::object>());
py::class_<PredicateDifference, py::bases<PredicateBoolean>>(
"PredicateDifference",
"Difference (conjunction with negative predicate) of 2 predicates. A point has to be inside the first and outside the second predicate. Can be "
"constructed using the ``-`` operator on predicates: ``pred1 - pred2``.",
py::init<py::object, py::object>());
py::class_<PredicateSymmetricDifference, py::bases<PredicateBoolean>>(
"PredicateSymmetricDifference",
"SymmetricDifference (exclusive disjunction) of 2 predicates. A point has to be in exactly one predicate of the two. Can be constructed using "
"the ``^`` operator on predicates: ``pred1 ^ pred2``.",
py::init<py::object, py::object>());
// primitive predicates
py::class_<inSphere, py::bases<Predicate>>(
"inSphere", "Sphere predicate.", py::init<const Vector3r&, Real>(py::args("center", "radius"), "Ctor taking center (as a 3-tuple) and radius"));
py::class_<inAlignedBox, py::bases<Predicate>>(
"inAlignedBox",
"Axis-aligned box predicate",
py::init<const Vector3r&, const Vector3r&>(py::args("minAABB", "maxAABB"), "Ctor taking minumum and maximum points of the box (as 3-tuples)."));
py::class_<inParallelepiped, py::bases<Predicate>>(
"inParallelepiped",
"Parallelepiped predicate",
py::init<const Vector3r&, const Vector3r&, const Vector3r&, const Vector3r&>(
py::args("o", "a", "b", "c"),
"Ctor taking four points: ``o`` (for origin) and then ``a``, ``b``, ``c`` which define endpoints of 3 respective edges from ``o``."));
py::class_<inCylinder, py::bases<Predicate>>(
"inCylinder",
"Cylinder predicate",
py::init<const Vector3r&, const Vector3r&, Real>(
py::args("centerBottom", "centerTop", "radius"), "Ctor taking centers of the lateral walls (as 3-tuples) and radius."));
py::class_<inHyperboloid, py::bases<Predicate>>(
"inHyperboloid",
"Hyperboloid predicate",
py::init<const Vector3r&, const Vector3r&, Real, Real>(
py::args("centerBottom", "centerTop", "radius", "skirt"),
"Ctor taking centers of the lateral walls (as 3-tuples), radius at bases and skirt (middle radius)."));
py::class_<inEllipsoid, py::bases<Predicate>>(
"inEllipsoid",
"Ellipsoid predicate",
py::init<const Vector3r&, const Vector3r&>(
py::args("centerPoint", "abc"), "Ctor taking center of the ellipsoid (3-tuple) and its 3 radii (3-tuple)."));
py::class_<notInNotch, py::bases<Predicate>>(
"notInNotch",
"Outside of infinite, rectangle-shaped notch predicate",
py::init<const Vector3r&, const Vector3r&, const Vector3r&, Real>(
py::args("centerPoint", "edge", "normal", "aperture"),
"Ctor taking point in the symmetry plane, vector pointing along the edge, plane normal and aperture size.\nThe side inside the notch "
"is edge×normal.\nNormal is made perpendicular to the edge.\nAll vectors are normalized at construction time."));
#ifdef YADE_GTS
py::class_<inGtsSurface, py::bases<Predicate>>(
"inGtsSurface",
"GTS surface predicate",
py::init<py::object, py::optional<bool>>(
py::args("surface", "noPad"),
"Ctor taking a gts.Surface() instance, which must not be modified during instance lifetime.\nThe optional noPad can disable padding "
"(if set to True), which speeds up calls several times.\nNote: padding checks inclusion of 6 points along +- cardinal directions in "
"the pad distance from given point, which is not exact."))
.add_property("surf", &inGtsSurface::surface, "The associated gts.Surface object.");
#endif
} catch (...) {
LOG_FATAL("Importing this module caused an exception and this module is in an inconsistent state now.");
PyErr_Print();
PyErr_SetString(PyExc_SystemError, __FILE__);
boost::python::handle_exception();
throw;
}
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