Degree and coordinate conversion

Sometimes working directly with coordinates in degrees is cumbersome. For example, you have no way to calculate easily distance between two points, or say “this coordinate 2 metres west”.

These routines and objects try to remedy that:

Please note that error introduced by this transformation is the more pronounced the closer you are to the Poles, so no flying over the Poles for you!

Basic structures

Note that you first need to set a satisfying epsilon:

geom3d.set_epsilon(new_epsilon: float)

Set a new value of epsilon.

Epsilon is used to compare two floats, and to determine the handness of the vector inside/outside the polygon

Parameters:new_epsilon – new value of epsilon
class geom3d.Vector(x: float, y: float, z: float = 0.0)

A 3D vector

cross_product(other: geom3d.basic.Vector) → geom3d.basic.Vector

Calculate the cross product between this vector and the other

dot_product(other: geom3d.basic.Vector) → float

Calculate the dot product between this vector and the other

unitize() → geom3d.basic.Vector

Return an unit vector having the same heading as current vector

classmethod zero() → geom3d.basic.Vector

Return a (0, 0, 0) point

zero_z() → geom3d.basic.Vector

Return self, but with z coordinate zeroed

class geom3d.Line(start: Vector, stop: Vector)

A line in 3D. It starts somewhere and ends somewhere.

Parameters:
  • start – where does the line start
  • stop – where does the line end
get_point(distance_from_start: float) → geom3d.basic.PointInLine

Get a point that lies on this line some distance from the start

Parameters:distance_from_start – the distance from the start
get_points_along(step: float, include_last_point: bool = False) → Iterator[geom3d.basic.Vector]

Return a list of vectors corresponding to equally-spaced points on this line

Parameters:
  • step – next vector will be distant by exactly this from the previous one
  • include_last_point – whether to include last point. Distance from the almost last to last might not be equal to step
length

Return the length of this line

unit_vector

Return a unit vector corresponding to the direction of this line.

class geom3d.PointInLine(line: geom3d.basic.Line, distance_from_start: float)

This class serves to compute points that lie a certain distance from the start, but still lie on this line.

length

The distance from the start of the line

to_vector() → geom3d.basic.Vector

Return the physical point given PointInLine corresponds to

class geom3d.Path(size: Optional[geom3d.basic.Vector] = None, points: Optional[List[geom3d.basic.Vector]] = None)
advance(delta: geom3d.basic.Vector)

Place next segment of the path at given difference from current head

classmethod from_to(source: geom3d.basic.Vector, destination: geom3d.basic.Vector, size: geom3d.basic.Vector, step: Optional[float] = None)

Get a path from a point to other point with particular _size

Points will be placed each _size/2 if a vector is given, otherwise each size_of_step distance.

get_intersecting_boxes(other: geom3d.paths.path.Path) → Generator[Tuple[geom3d.basic.Box, geom3d.basic.Box], None, None]

Return all intersections of these elements that collide.

head_towards(point: geom3d.basic.Vector, delta: float)

Place next pieces of the path at delta distances going towards the point. The last segment may be shorter

Parameters:
  • point – point to advance towards
  • delta – size of step to use in constructing the path

Polygons

class geom3d.polygons.Polygon2D(points: List[geom3d.basic.Vector])

A polygon that disregards the z axis

centroid

Return the center of mass for this polygon

downscale(step: float) → geom3d.polygons.twodimensional.Polygon2D

Make a smaller polygon by moving each vertex by step inside the polygon.

Parameters:step – distance to which move each vertex
Raises:ValueError – polygon cannot be shrunk further
get_next_segment(segment: geom3d.basic.Line) → geom3d.basic.Line

Return the next segment in regards to the one currently passed

get_nth_segment(segment: geom3d.basic.Line, n: int) → geom3d.basic.Line

Get n-th segment in regards to the one currently passed in

get_point_on_polygon(distance_from_start: float, offset: float = 0) → geom3d.polygons.twodimensional.PointOnPolygon2D

Return a point somewhere on the perimeter of this polygon

Parameters:
  • distance_from_start – distance from the first point of this polygon. Can be negative, in which case we will count backwards.
  • offset – offset to add in while calculating the distance. This value is fixed.
get_point_on_polygon_relative(**kwargs)

Return a point on polygon counted as a fraction of it’s total perimeter.

Eg. 0.5 will get you a point on polygon directly at half of it’s perimeter.

Parameters:
  • distance_from_start – fraction of polygon’s total perimeter. Must be greater or equal than zero, must be less than 1
  • offset – offset to use, also a fraction of polygon’s total length
get_points_along(step: float, include_last_point: bool = False) → Iterator[geom3d.basic.Vector]

Return a list of vectors corresponding to equally-spaced points on this line

Parameters:
  • step – the distance between two consecutive points
  • include_last_point – whether to include last point. Distance from the almost last to last might not be equal to step
get_previous_segment(segment: geom3d.basic.Line) → geom3d.basic.Line

Return the previous segment in regards to the one currently passed

get_segment_at_distance(offset: float) → geom3d.basic.Line

Return the segment backing some distance along the polygon’s perimeter

Parameters:offset – the distance to travel to get the polygon’s segment. If this appears directly on a vertex, the segment which starts at this vertex will be returned.
get_signed_area() → float

Area of this polygon as calculated by the shoelace formula

get_surface_area() → float

Return the surface area of this polygon

iter_from(offset: float = 0) → Iterator[geom3d.basic.Vector]

Return all points that this polygon consists of, but starting from offset

Parameters:offset – length from start from where to start counting. The next vertex specified

will come in first. If the offset is directly on a vertex, this vertex will be returned.

iter_segments() → Iterator[geom3d.basic.Line]

Get all segments

Returns:an iterator, yielding subsequent segments of this polygon
to_path(step: float, size: geom3d.basic.Vector) → geom3d.paths.path.Path

Return a path flying around the perimeter of this polygon

Parameters:
  • step – step to which advance the path with
  • size – size of the box that will determine the path
class geom3d.polygons.PointOnPolygon2D(polygon: 'Polygon2D', _distance_from_start: 'float', offset: 'float' = 0)
advance(v: float)

Move the pointer v ahead.

The only routine to move inside the polygon at all

Parameters:v – amount to move the pointer along the perimeter, or a negative value to move it backwards.
get_segment_and_vector() → Tuple[geom3d.basic.Line, geom3d.basic.Vector]

Return both the vector (as in to_vector()) and the segment on which it lies.

Returns:a tuple of (Line - the segment, Vector - coordinates of this point)
get_unit_vector_away_polygon() → geom3d.basic.Vector

Return exactly the opposite vector that get_unit_vector_towards_polygon() would return

get_unit_vector_towards_polygon() → geom3d.basic.Vector

Get a unit vector, that if applied to self.to_vector() would direct us inside the polygon

is_on_vertex() → bool

Does this point occur right on a vertex of the polygon?

to_vector() → geom3d.basic.Vector

Returns the coordinates of the point on the perimeter.

The point will lie precisely on the perimeter

Note that PointOnPolygon2D will behave correctly when faced with calculating the vector towards the polygon then such point occurs on the vertex. It will take the average of two segment’s unit vectors into consideration in that case.

More complex 3D structures

class geom3d.meshes.Triangle(a: Vector, b: Vector, c: Vector)

A triangle defined by it’s 3 vertices

get_edges() → Tuple[geom3d.basic.Line, geom3d.basic.Line, geom3d.basic.Line]

Return edges of this triangle

get_edges_length() → Tuple[float, float, float]

Return lengths of edges corresponding to n-th edge

get_perimeter_length() → float

Return the length of triangle’s perimeter

get_surface_area() → float

Return the surface area of this triangle