NumPy Geometry
Working with geometry using numpy.
Maintained by Dan-Patterson
Geo array basics
Import npg and take a subsample of some featureclass (in_fc) geometry objects (g).
IFT refers to the feature id value, the from and to points.
To reduce numeric problems, the value of the lower left corner is subtracted from all coordinates moving coordinate space into quadrant I. You could also subtract the mean value of the points which would center the shapes about the x-y axis origin.
test2(g, kind=2) # a polygon featureclass with 3 shapes
Listing of Geo array properties and functions
npg.dirr(g)
----------------------------------------------------------------------
| dir(npg) ...
| <class 'npg.Geo'>
-------... Geo class ...
(001) Bit CL FT
(002) Fr H IDs
(003) IFT IFT_str IP
(004) Info K LL
(005) N PID SR
(006) SVG To U
(007) UR X XT
(008) XY Y Z
(009) __author__ __dict__ __module__
(010) __name__ all_parts all_shapes
(011) aoi_extent aoi_rectangle areas
(012) as_arrays as_lists bit_IFT
(013) bit_ids bit_pnt_cnt bit_seq
(014) bits boundary bounding_circles
(015) centers centroids change_indices
(016) close_polylines common_segments convex_hulls
(017) densify_by_distance densify_by_factor densify_by_percent
(018) dupl_pnts extent_centers extent_corner
(019) extent_pnts extent_rectangles extents
(020) facts fill_holes first_bit
(021) first_part fr_to_pnts geo_props
(022) geom_check get_shapes holes_to_shape
(023) inner_IFT inner_rings is_clockwise
(024) is_convex is_in is_multipart
(025) is_multipart_report lengths maxs
(026) means min_area_rect mins
(027) moveto multipart_to_singlepart od_pairs
(028) outer_IFT outer_rings part_IFT
(029) part_ids parts pnt_counts
(030) pnt_ids pnt_indices pnt_on_poly
(031) polygon_angles polygons_to_polylines polyline_angles
(032) polylines_to_polygons polys_to_points prn
(033) prn_arr prn_obj radial_sort
(034) roll_shapes rotate segment_angles
(035) segment_pnt_ids segment_polys shapes
(036) shift shp_IFT shp_ids
(037) shp_part_cnt shp_pnt_cnt shp_pnt_ids
(038) singleton_pnts sort_by_area sort_by_extent
(039) sort_by_length sort_coords split_by
(040) structure svg to_segments
(041) translate triangulate uniq_pnts
(042) unique_segments xy_id
Functions from modules ...
npg_geom ...
(043) CH Delaunay bin_pnts
(044) common_extent densify_by_distance densify_by_factor
(045) eucl_dist extent_to_poly find_closest
(046) in_hole_check mabr npGeo
(047) np_wn offset_buffer pnts_in_pnts
(048) pnts_on_poly pnts_to_extent polys_to_segments
(049) polys_to_unique_pnts repack_fields scale_by_area
(050) script segments_to_polys simplify_lines
(051) stu triangulate_pnts uts
npg_geom helpers ...
(052) _add_pnts_on_line_ _angles_3pnt_ _bit_area_
(053) _bit_min_max_ _ch_ _ch_scipy_
(054) _ch_simple_ _closest_pnt_on_poly_ _dist_along_
(055) _e_2d_ _get_base_ _in_extent_
(056) _is_pnt_on_line_ _percent_along_ _pnt_on_segment_
npg_helpers ...
(057) a_eq_b cartesian_product coerce2array
(058) common_pnts compare_geom del_seq_dups
(059) dist_angle_sort flat interweave
(060) keep_geom polyline_angles project_pnt_to_line
(061) radial_sort reclass_ids remove_geom
(062) segment_angles shape_finder sort_xy
(063) stride_2d uniq_1d uniq_2d
npg_helpers helpers ...
(064) _angles_3pnt_ _area_centroid_ _bit_area_
(065) _bit_check_ _bit_crossproduct_ _bit_length_
(066) _bit_min_max_ _bit_segment_angles_ _from_north_
(067) _from_to_pnts_ _get_base_ _in_LBRT_
(068) _in_extent_ _is_ccw_ _is_clockwise_
(069) _is_convex_ _is_right_side _isin_2d_
(070) _od_angles_dist_ _perp_ _pnts_in_extent_
(071) _rotate_ _scale_ _to_lists_
(072) _trans_rot_ _translate_ prn_tbl
npg_io ...
(073) dtype_info load_geo save_geo
(074) load_txt save_txt load_geojson
(075) geojson_Geo
npg_prn ...
(076) _svg prn_ prn_Geo_shapes
(077) prn_arrays prn_as_obj prn_geo
(078) prn_lists prn_q prn_tbl
Geo array creation
new(cls, g=None, IFT=None, Kind=2, Info="Geo array")
g : array_like
- A 2D array sequence of points with shape (N, 2).
IFT : array_like
- Defines, the I(d)F(rom)T(o) and other structural elements that are
present in polyline or polygon geometry that
arrrepresents. Shape (N, 6) required.
Kind : integer
- Points (0), polylines/lines (1) and polygons (2).
Info : text (optional)
- Optional information if needed.
Properties
g the ndarray of xy coordinates
g.T # ---- g.T shown
# ---- Geo[[Xs], [Ys]]
Geo([[ 10.0, 10.0, 1.5, 0.0, 10.0, 3.0, 3.0, 9.0, 9.0, 3.0, 2.0,
1.0, 2.0, 2.0, 2.0, 1.0, 1.0, 2.0, 8.0, 8.0, 4.0, 5.0, 8.0,
6.0, 5.0, 7.0, 6.0, 25.0, 25.0, 15.0, 15.0, 23.0, 23.0, 15.0,
15.0, 25.0, 20.0, 20.0, 12.0, 12.0, 20.0, 20.0, 10.0, 10.0,
14.0, 20.0, 11.0, 12.0, 12.0, 11.0, 10.5, 10.5, 11.5, 10.5,
10.5, 10.5, 11.5, 10.5, 14.0, 10.0, 15.0, 14.0],
[ 10.0, 0.0, 1.5, 10.0, 10.0, 9.0, 3.0, 3.0, 9.0, 9.0, 7.0,
7.0, 5.0, 7.0, 8.0, 9.0, 8.0, 8.0, 8.0, 4.0, 4.0, 7.0, 8.0,
7.0, 5.0, 5.0, 7.0, 14.0, 4.0, 4.0, 6.0, 6.0, 12.0, 12.0,
14.0, 14.0, 10.0, 8.0, 8.0, 2.0, 2.0, 0.0, 0.0, 10.0, 10.0,
10.0, 9.0, 8.5, 9.0, 9.0, 8.5, 7.0, 7.0, 8.5, 2.0, 0.5, 0.5,
2.0, 10.0, 10.0, 18.0, 10.0]])
The structure and relationships between the array elements is given in the IFT property.
g.IFT ==> Id, From, To - shape ID, from-to points in the shape
g.IFT
array([[ 1, 0, 5, 1, 1, 0],
[ 1, 5, 10, 0, 1, 1],
[ 1, 10, 14, 0, 1, 2],
[ 1, 14, 18, 0, 1, 3],
[ 1, 18, 23, 1, 2, 0],
[ 1, 23, 27, 0, 2, 1],
[ 2, 27, 36, 1, 1, 0],
[ 2, 36, 46, 1, 2, 0],
[ 2, 46, 50, 0, 2, 1],
[ 2, 50, 54, 0, 2, 2],
[ 2, 54, 58, 0, 2, 3],
[ 3, 58, 62, 1, 1, 0]], dtype=int64)
Geo array ==>
- shape identification (IDs)
- from (FR)
- to (To)
- clockwise (CW)
- part ids (PID)
- bit ids (Bit)
- from-to (FT)
- shape type (K)
- information string (Info)
g.IDs IFT[:, 0] shape identifier
[1 1 1 ... 2 2 3]
g.Fr IFT[:, 1] shape from point
[ 0 5 10 ... 50 54 58]
g.To IFT[:, 2] to point
[ 5 10 14 ... 54 58 62]
g.CW IFT[:, 3] shape orientation (C)lock(W)ise boolean result
[1 0 0 ... 0 0 1]
g.PID IFT[:, 4] part identifier within a shape
[1 1 1 ... 2 2 1]
g.Bit IFT[:, 5] bit identifier with a shape
[0 1 2 ... 2 3 0]
g.FT IFT[:, 1:3] from-to point pairs
[[ 0 5]
[ 5 10]
[10 14]
...
[50 54]
[54 58]
[58 62]]
g.K ... 2 ... shape kind 1, 2, 3 for points, polylines, polygons
g.Info ... test ... extra information string
g.H ... Help on Geo arrays
**Geo class**
-------------
Construction from an ndarray, IFT, Kind and optional Info.
Parameters
----------
**Required**
arr : array-like
A 2D array sequence of points with shape (N, 2).
IFT : array-like
Defines, the I(d)F(rom)T(o) and other structural elements that are
present in polyline or polygon geometry that `arr` represents .
Shape (N, 6) required.
Kind : integer
Points (0), polylines/lines (1) and polygons (2).
Info : string (optional)
Optional information if needed.
**Derived**
IDs : IFT[:, 0]
Shape ids, the id number will be repeated for each part and hole in
the shape
Fr : IFT[:, 1]
The ``from`` point in the point sequence.
To : IFT[:, 2]
The ``to`` point in the point sequence.
CW : IFT[:, 3]
A value of ``1`` for exterior rings, ``0`` for interior/holes.
PID : IFT[:, 4]
Part ids sequence by shape. A singlepart shape will have one (1) part.
Subsequent parts are numbered incrementally.
Bit : IFT[:, 5]
The bit sequence in a singlepart feature with holes and/or multipart
features with or without holes
FT : IFT[:, 1:3]
The from-to ids together (Fr, To).
IP : IFT[:, [0, 4]]
Shape and part ids together (IDs, PID)
N : integer
The number of unique shapes.
U : integer(s)
A sequence of integers indicating the feature ID value. There is no
requirement for these to be sequential.
SR : text
Spatial reference name.
X, Y, XY, Z: Derived from columns in the point array.
X = arr[:, 0], Y = arr[:, 0], XY = arr[:, :2],
Z = arr[:, 2] if defined
XT : array
An array/list of points identifying the lower-left and upper-right,
of full extent of all the geometry objects.
LL, UR : array
The extent points as defined in XT.
hlp : this
self.H or self.docs where self is a Geo array will recall this information.
A featureclass with 3 shapes. The first two are multipart with holes.
arr.IFT # ---- annotated ----
# IDs, Fr, To, CW, PID, Bit
array([[ 1, 0, 5, 1, 1, 0], # first shape, first part, outer ring
[ 1, 5, 10, 0, 1, 1], # hole 1
[ 1, 10, 14, 0, 1, 2], # hole 2
[ 1, 14, 18, 0, 1, 3], # hole 3
[ 1, 18, 23, 1, 2, 0], # first shape, second part, outer ring
[ 1, 23, 27, 0, 2, 1], # hole 1
[ 2, 27, 36, 1, 1, 0], # second shape, first part, outer ring
[ 2, 36, 46, 1, 2, 0], # second shape, second part, outer ring
[ 2, 46, 50, 0, 2, 1], # hole 1
[ 2, 50, 54, 0, 2, 2], # hole 2
[ 2, 54, 58, 0, 2, 3], # hole 3
[ 3, 58, 62, 1, 1, 0]], # third shape, first part, outer ring
dtype=int64)
Derived Properties
shape, part, and bit : N, part_cnt, bit_cnt
shape, part and bit ids : shp_ids, part_ids, bit_ids
shape, part and bit counts : shp_IFT, part_IFT, bit_IFT
x, y and XY coordinates : X, Y, XY)
- sample size, unique shapes
g.N ... 3 ... len(uni) # uni, idx = np.unique(arr.IDs, True)
g.U ... [1 2 3] ... g.IDs[idx]
- coordinate values
g.X g[:, 0]
[ 10.00 10.00 1.50 ... 10.00 15.00 14.00]
g.Y g[:, 1]
[ 10.00 0.00 1.50 ... 10.00 18.00 10.00]
g.XY g[:, :2]
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
g.g[ not implemented yet
- identifiers by shape, part, bit
g.shp_IFT
[[ 1 0 27 -1 -1 -1]
[ 2 27 58 -1 -1 -1]
[ 3 58 62 -1 -1 -1]]
g.part_IFT
[[ 1 0 18 1 1 0]
[ 1 18 27 1 2 0]
[ 2 27 36 1 1 0]
[ 2 36 58 1 2 0]
[ 3 58 62 1 1 0]]
g.bit_IFT
[[ 1 0 5 1 1 0]
[ 1 5 10 0 1 1]
[ 1 10 14 0 1 2]
...
[ 2 50 54 0 2 2]
[ 2 54 58 0 2 3]
[ 3 58 62 1 1 0]]
g.shp_ids :[1 2 3]
g.part_ids :[1 1 2 2 3]
g.bit_ids :[1 1 1 ... 2 2 3]
g.bit_seq :[0 1 2 ... 2 3 0]
g.pnt_ids :[1 1 1 ... 3 3 3]
g.shp_pnt_cnt
[[ 1 27]
[ 2 31]
[ 3 4]]
g.shp_part_cnt
[[1 2]
[2 2]
[3 1]]
g.bit_pnt_cnt
[[1 0 5]
[1 1 5]
[1 2 4]
...
[2 2 4]
[2 3 4]
[3 0 4]]
g.shapes
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 5.00 5.00]
[ 7.00 5.00]
[ 6.00 7.00]] ... snip
[[ 14.00 10.00]
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
g.parts
[ 10.00 10.00] ... snip
[[ 14.00 10.00]
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
g.bits
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
[ 0.00 10.00]
[ 10.00 10.00]] ... snip
[[ 14.00 10.00]
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
Methods.....
(1) g.first_bit(True) ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(2) g.first_bit(True).IFT ...
[[ 1 0 5 1 1 0]
[ 1 5 10 1 2 0]
[ 2 10 19 1 1 0]
[ 2 19 29 1 2 0]
[ 3 29 33 1 1 0]]
(3) g.first_part(True) ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(4) g.first_part(True).IFT ...
[[ 1 0 5 1 1 0]
[ 1 5 10 0 1 1]
[ 1 10 14 0 1 2]
[ 1 14 18 0 1 3]
[ 2 18 27 1 1 0]
[ 3 27 31 1 1 0]]
(5) g.get_shape(ID=3, asGeo=True) ...
[[ 14.00 10.00]
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(6) g.get_shape(ID=3, asGeo=True).IFT ...
[[3 0 4 1 1 0]]
(7) g.outer_rings(asGeo=True) ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(8) g.outer_rings(asGeo=True).IFT ...
[[ 1 0 5 1 1 0]
[ 1 5 10 1 2 0]
[ 2 10 19 1 1 0]
[ 2 19 29 1 2 0]
[ 3 29 33 1 1 0]]
(9) g.areas(True) ...
[ 57.50 102.25 16.00]
(10) g.areas(False) ...
[85.0, -36.0, -1.0, -0.5, 12.0, -2.0, 52.0, 52.0, -0.25, -0.75, -0.75, 16.0]
(11) g.lengths(True) ...
[ 90.71 123.22 21.50]
(12) g.lengths(False) ...
[37.26267650163207, 24.0, 5.23606797749979,... snip ..., 21.49623888035515]
(13) g.cent_shapes() ...
[[ 4.71 6.60]
[ 15.35 7.18]
[ 13.00 12.67]]
(14) g.cent_parts() ...
[[ 5.38 5.38]
[ 6.25 5.75]
[ 19.50 9.00]
[ 15.33 5.56]
[ 13.00 12.67]]
(15) g.centroids() ...
[[ 7.65 3.56]
[ 16.51 6.09]
[ 13.00 12.67]]
(16) g.aoi_extent() ...
[ 0.00 0.00 25.00 18.00]
(17) g.aoi_rectangle() ...
[[ 0.00 0.00]
[ 0.00 18.00]
[ 25.00 18.00]
[ 25.00 0.00]
[ 0.00 0.00]]
(18) g.extents(splitter="part") ...
[[ 0.00 0.00 10.00 10.00]
[ 4.00 4.00 8.00 8.00]
[ 15.00 4.00 25.00 14.00]
[ 10.00 0.00 20.00 10.00]
[ 10.00 10.00 15.00 18.00]]
(19) g.extents(splitter="shape") ...
[[ 0.00 0.00 10.00 10.00]
[ 10.00 0.00 25.00 14.00]
[ 10.00 10.00 15.00 18.00]]
(20) g.extent_centers(splitter="part") ...
[[ 5.00 5.00]
[ 6.00 6.00]
[ 20.00 9.00]
[ 15.00 5.00]
[ 12.50 14.00]]
(21) g.extent_centers(splitter="shape") ...
[[ 5.00 5.00]
[ 17.50 7.00]
[ 12.50 14.00]]
(22) g.extent_rectangles(splitter="shape") ...
[array([[ 300000.00, 5000000.00],
[ 300000.00, 5000010.00],
[ 300010.00, 5000010.00],
[ 300010.00, 5000000.00],
[ 300000.00, 5000000.00]]), array([[ 300010.00, 5000000.00],
[ 300010.00, 5000014.00],
[ 300025.00, 5000014.00],
[ 300025.00, 5000000.00],
[ 300010.00, 5000000.00]]), array([[ 300010.00, 5000010.00],
[ 300010.00, 5000018.00],
[ 300015.00, 5000018.00],
[ 300015.00, 5000010.00],
[ 300010.00, 5000010.00]])]
(23) g.extent_rectangles(splitter="part") ...
[array([[ 300000.00, 5000000.00],
[ 300000.00, 5000010.00],
[ 300010.00, 5000010.00],
[ 300010.00, 5000000.00],
[ 300000.00, 5000000.00]]), array([[ 300004.00, 5000004.00],
[ 300004.00, 5000008.00],
[ 300008.00, 5000008.00],
[ 300008.00, 5000004.00],
[ 300004.00, 5000004.00]]), array([[ 300015.00, 5000004.00],
[ 300015.00, 5000014.00],
[ 300025.00, 5000014.00],
[ 300025.00, 5000004.00],
[ 300015.00, 5000004.00]])]
(24) g.maxs(by_bit=False) ...
[[ 10.00 10.00]
[ 25.00 14.00]
[ 15.00 18.00]]
(25) g.maxs(by_bit=True) ...
[[ 10.00 10.00]
[ 8.00 8.00]
[ 25.00 14.00]
[ 20.00 10.00]
[ 15.00 18.00]]
(26) g.is_clockwise(is_closed_polyline=False) ...
[(1, 1) (1, 0) (1, 0) ... (2, 0) (2, 0) (3, 1)]
(27) g.is_convex() ...
[1 1 0 0 1]
(28) g.is_multipart(as_structured=False) ...
[[1 1]
[2 1]
[3 0]]
(29) g.polygon_angles(inside=True, in_deg=True) ...
[array([ 90.00, 79.99, 110.02, 79.99]),
array([ 71.57, 90.00, 71.57, 126.87]),
array([ 90.00, 90.00, 90.00, 90.00, 270.00, 270.00, 90.00, 90.00]),
array([ 90.00, 90.00, 270.00, 270.00, 90.00, 90.00, 90.00, 90.00, 180.00]),
array([ 97.13, 57.99, 24.88])
]
(30) g.bounding_circles(angle=5, return_xyr=False) ...
[[ 0.00 8.26]
[ 0.03 8.88]
[ 0.11 9.49]
...
[ 9.93 16.44]
[ 9.87 16.85]
[ 9.85 17.26]]
(31) g.min_area_rect(as_structured=False) ...
[[ 139.67 -1.41 -1.41 9.49 11.41]
[ 23.52 3.20 4.60 8.80 8.80]
[ 100.00 15.00 4.00 25.00 14.00]
[ 100.00 10.00 0.00 20.00 10.00]
[ 54.02 8.55 9.74 16.45 16.58]]
(32) g.triangulate(by_bit=False, as_polygon=True) ...
[[ 3.00 9.00]
[ 0.00 10.00]
[ 10.00 10.00]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(33) g.fill_holes() ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(34) g.holes_to_shape() ...
[[ 3.00 9.00]
[ 9.00 9.00]
[ 9.00 3.00]
...
[ 11.50 0.50]
[ 10.50 0.50]
[ 10.50 2.00]]
(35) g.multipart_to_singlepart(info="") ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(36) g.od_pairs() ...
[[ 10.00 10.00 10.00 0.00]
[ 10.00 0.00 1.50 1.50]
[ 1.50 1.50 0.00 10.00]
[ 0.00 10.00 10.00 10.00]]
(37) g.polygons_to_polylines() ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(38) g.boundary() ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.00 10.00]
[ 15.00 18.00]
[ 14.00 10.00]]
(39) g.polys_to_points(keep_order=True, as_structured=False) ...
[[ 10.00 10.00]
[ 10.00 0.00]
[ 1.50 1.50]
...
[ 10.50 0.50]
[ 11.50 0.50]
[ 15.00 18.00]]
(40) g.densify_by_distance(spacing=1)n ...
[[ 10.00 10.00]
[ 10.00 9.00]
[ 10.00 8.00]
...
[ 14.13 11.05]
[ 14.01 10.06]
[ 14.00 10.00]]
(41) g.densify_by_percent(percent=50) ...
[[ 10.00 10.00]
[ 10.00 4.63]
[ 10.00 0.00]
...
[ 15.00 18.00]
[ 14.25 12.00]
[ 14.00 10.00]]
Others of interest
A simplified informational table of a Geo array's IFT array with annotations. Useful for documentation purposes.
sq2.structure()
Geo array structure
-------------------
OID_ : self.Id shape id
Fr_pnt : self.Fr from point id
To_pnt : self.To to point id for a shape
CW_CCW : self.CW outer (1) inner/hole (0)
Part_ID : self.PID part id for each shape
Bit_ID : self.Bit sequence order of each part in a shape
----
... OID_ Fr_pnt To_pnt CW_CCW Part_ID Bit_ID
--------------------------------------------------------------
000 1 0 7 1 1 0
001 1 7 11 0 1 1
002 2 11 19 1 1 0
003 3 19 25 1 1 0
004 4 25 30 1 1 0