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/*
* Wrapper module for libqhull, providing Delaunay triangulation.
*
* This module's methods should not be accessed directly. To obtain a Delaunay
* triangulation, construct an instance of the matplotlib.tri.Triangulation
* class without specifying a triangles array.
*/
#
include
<
pybind11/pybind11.h
>
#
include
<
pybind11/numpy.h
>
#
ifdef
_MSC_VER
/*
The Qhull header does not declare this as extern "C", but only MSVC seems to
* do name mangling on global variables. We thus need to declare this before
* the header so that it treats it correctly, and doesn't mangle the name.
*/
extern
"
C
"
{
extern
const
char
qh_version[];
}
#
endif
#
include
"
libqhull_r/qhull_ra.h
"
#
include
<
cstdio
>
#
include
<
vector
>
#
ifndef
MPL_DEVNULL
#
error
"MPL_DEVNULL must be defined as the OS-equivalent of /dev/null"
#
endif
#
define
STRINGIFY
(
x
)
STR
(x)
#
define
STR
(
x
) #x
namespace
py
=
pybind11;
using
namespace
pybind11
::literals
;
//
Input numpy array class.
typedef
py::
array_t
<
double
, py::array::c_style | py::array::forcecast> CoordArray;
//
Output numpy array class.
typedef
py::
array_t
<
int
> IndexArray;
static
const
char
* qhull_error_msg[
6
] = {
"
"
,
/*
0 = qh_ERRnone
*/
"
input inconsistency
"
,
/*
1 = qh_ERRinput
*/
"
singular input data
"
,
/*
2 = qh_ERRsingular
*/
"
precision error
"
,
/*
3 = qh_ERRprec
*/
"
insufficient memory
"
,
/*
4 = qh_ERRmem
*/
"
internal error
"
};
/*
5 = qh_ERRqhull
*/
/*
Return the indices of the 3 vertices that comprise the specified facet (i.e.
* triangle).
*/
static
void
get_facet_vertices
(qhT* qh,
const
facetT* facet,
int
indices[
3
])
{
vertexT *vertex, **vertexp;
FOREACHvertex_
(facet->
vertices
) {
*indices++ =
qh_pointid
(qh, vertex->
point
);
}
}
/*
Return the indices of the 3 triangles that are neighbors of the specified
* facet (triangle).
*/
static
void
get_facet_neighbours
(
const
facetT* facet, std::vector<
int
>& tri_indices,
int
indices[
3
])
{
facetT *neighbor, **neighborp;
FOREACHneighbor_
(facet) {
*indices++ = (neighbor->
upperdelaunay
? -
1
: tri_indices[neighbor->
id
]);
}
}
/*
Return true if the specified points arrays contain at least 3 unique points,
* or false otherwise.
*/
static
bool
at_least_3_unique_points
(py::
ssize_t
npoints,
const
double
* x,
const
double
* y)
{
const
py::
ssize_t
unique1 =
0
;
/*
First unique point has index 0.
*/
py::
ssize_t
unique2 =
0
;
/*
Second unique point index is 0 until set.
*/
if
(npoints <
3
) {
return
false
;
}
for
(py::
ssize_t
i =
1
; i < npoints; ++i) {
if
(unique2 ==
0
) {
/*
Looking for second unique point.
*/
if
(x[i] != x[unique1] || y[i] != y[unique1]) {
unique2 = i;
}
}
else
{
/*
Looking for third unique point.
*/
if
( (x[i] != x[unique1] || y[i] != y[unique1]) &&
(x[i] != x[unique2] || y[i] != y[unique2]) ) {
/*
3 unique points found, with indices 0, unique2 and i.
*/
return
true
;
}
}
}
/*
Run out of points before 3 unique points found.
*/
return
false
;
}
/*
Holds on to info from Qhull so that it can be destructed automatically.
*/
class
QhullInfo
{
public:
QhullInfo
(
FILE
*error_file, qhT* qh) {
this
->
error_file
= error_file;
this
->
qh
= qh;
}
~QhullInfo
() {
qh_freeqhull
(
this
->
qh
, !qh_ALL);
int
curlong, totlong;
/*
Memory remaining.
*/
qh_memfreeshort
(
this
->
qh
, &curlong, &totlong);
if
(curlong || totlong) {
PyErr_WarnEx
(PyExc_RuntimeWarning,
"
Qhull could not free all allocated memory
"
,
1
);
}
if
(
this
->
error_file
!= stderr) {
fclose
(error_file);
}
}
private:
FILE
* error_file;
qhT* qh;
};
/*
Delaunay implementation method.
* If hide_qhull_errors is true then qhull error messages are discarded;
* if it is false then they are written to stderr.
*/
static
py::tuple
delaunay_impl
(py::
ssize_t
npoints,
const
double
* x,
const
double
* y,
bool
hide_qhull_errors)
{
qhT qh_qh;
/*
qh variable type and name must be like
*/
qhT* qh = &qh_qh;
/*
this for Qhull macros to work correctly.
*/
facetT* facet;
int
i, ntri, max_facet_id;
int
exitcode;
/*
Value returned from qh_new_qhull().
*/
const
int
ndim =
2
;
double
x_mean =
0.0
;
double
y_mean =
0.0
;
QHULL_LIB_CHECK
/*
Allocate points.
*/
std::vector<coordT>
points
(npoints * ndim);
/*
Determine mean x, y coordinates.
*/
for
(i =
0
; i < npoints; ++i) {
x_mean += x[i];
y_mean += y[i];
}
x_mean /= npoints;
y_mean /= npoints;
/*
Prepare points array to pass to qhull.
*/
for
(i =
0
; i < npoints; ++i) {
points[
2
*i ] = x[i] - x_mean;
points[
2
*i+
1
] = y[i] - y_mean;
}
/*
qhull expects a FILE* to write errors to.
*/
FILE
* error_file =
nullptr
;
if
(hide_qhull_errors) {
/*
qhull errors are ignored by writing to OS-equivalent of /dev/null.
* Rather than have OS-specific code here, instead it is determined by
* meson.build and passed in via the macro MPL_DEVNULL.
*/
error_file =
fopen
(
STRINGIFY
(
MPL_DEVNULL
),
"
w
"
);
if
(error_file ==
nullptr
) {
throw
std::runtime_error
(
"
Could not open devnull
"
);
}
}
else
{
/*
qhull errors written to stderr.
*/
error_file = stderr;
}
/*
Perform Delaunay triangulation.
*/
QhullInfo
info
(error_file, qh);
qh_zero
(qh, error_file);
exitcode =
qh_new_qhull
(qh, ndim, (
int
)npoints, points.
data
(), False,
(
char
*)
"
qhull d Qt Qbb Qc Qz
"
,
nullptr
, error_file);
if
(exitcode != qh_ERRnone) {
std::string msg =
py::str
(
"
Error in qhull Delaunay triangulation calculation: {} (exitcode={})
"
)
.
format
(qhull_error_msg[exitcode], exitcode).
cast
<std::string>();
if
(hide_qhull_errors) {
msg +=
"
; use python verbose option (-v) to see original qhull error.
"
;
}
throw
std::runtime_error
(msg);
}
/*
Split facets so that they only have 3 points each.
*/
qh_triangulate
(qh);
/*
Determine ntri and max_facet_id.
Note that libqhull uses macros to iterate through collections.
*/
ntri =
0
;
FORALLfacets {
if
(!facet->
upperdelaunay
) {
++ntri;
}
}
max_facet_id = qh->
facet_id
-
1
;
/*
Create array to map facet id to triangle index.
*/
std::vector<
int
>
tri_indices
(max_facet_id+
1
);
/*
Allocate Python arrays to return.
*/
int
dims[
2
] = {ntri,
3
};
IndexArray
triangles
(dims);
int
* triangles_ptr = triangles.
mutable_data
();
IndexArray
neighbors
(dims);
int
* neighbors_ptr = neighbors.
mutable_data
();
/*
Determine triangles array and set tri_indices array.
*/
i =
0
;
FORALLfacets {
if
(!facet->
upperdelaunay
) {
int
indices[
3
];
tri_indices[facet->
id
] = i++;
get_facet_vertices
(qh, facet, indices);
*triangles_ptr++ = (facet->
toporient
? indices[
0
] : indices[
2
]);
*triangles_ptr++ = indices[
1
];
*triangles_ptr++ = (facet->
toporient
? indices[
2
] : indices[
0
]);
}
else
{
tri_indices[facet->
id
] = -
1
;
}
}
/*
Determine neighbors array.
*/
FORALLfacets {
if
(!facet->
upperdelaunay
) {
int
indices[
3
];
get_facet_neighbours
(facet, tri_indices, indices);
*neighbors_ptr++ = (facet->
toporient
? indices[
2
] : indices[
0
]);
*neighbors_ptr++ = (facet->
toporient
? indices[
0
] : indices[
2
]);
*neighbors_ptr++ = indices[
1
];
}
}
return
py::make_tuple
(triangles, neighbors);
}
/*
Process Python arguments and call Delaunay implementation method.
*/
static
py::tuple
delaunay
(
const
CoordArray& x,
const
CoordArray& y,
int
verbose)
{
if
(x.
ndim
() !=
1
|| y.
ndim
() !=
1
) {
throw
std::invalid_argument
(
"
x and y must be 1D arrays
"
);
}
auto
npoints = x.
shape
(
0
);
if
(npoints != y.
shape
(
0
)) {
throw
std::invalid_argument
(
"
x and y must be 1D arrays of the same length
"
);
}
if
(npoints <
3
) {
throw
std::invalid_argument
(
"
x and y arrays must have a length of at least 3
"
);
}
if
(!
at_least_3_unique_points
(npoints, x.
data
(), y.
data
())) {
throw
std::invalid_argument
(
"
x and y arrays must consist of at least 3 unique points
"
);
}
return
delaunay_impl
(npoints, x.
data
(), y.
data
(), verbose ==
0
);
}
PYBIND11_MODULE
(_qhull, m, py::mod_gil_not_used())
{
m.
doc
() =
"
Computing Delaunay triangulations.
\n
"
;
m.
def
(
"
delaunay
"
, &delaunay,
"
x
"
_a,
"
y
"
_a,
"
verbose
"
_a,
"
--
\n\n
"
"
Compute a Delaunay triangulation.
\n
"
"
\n
"
"
Parameters
\n
"
"
----------
\n
"
"
x, y : 1d arrays
\n
"
"
The coordinates of the point set, which must consist of at least
\n
"
"
three unique points.
\n
"
"
verbose : int
\n
"
"
Python's verbosity level.
\n
"
"
\n
"
"
Returns
\n
"
"
-------
\n
"
"
triangles, neighbors : int arrays, shape (ntri, 3)
\n
"
"
Indices of triangle vertices and indices of triangle neighbors.
\n
"
);
m.
def
(
"
version
"
, []() {
return
qh_version; },
"
version()
\n
--
\n\n
"
"
Return the qhull version string.
"
);
}
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