viktor.geometry
VisualisationError
 exception
viktor.geometry.
VisualisationError
¶ Bases:
Exception
Vector
 class
viktor.geometry.
Vector
(x, y, z=0)¶ 
A 3dimensional vector in space.
The following operations are supported:
Negation
v1 = Vector(1, 2, 3) v2 = v1 # results in Vector(1, 2, 3)
Addition
v1 = Vector(1, 2, 3) v2 = Vector(1, 2, 3) v3 = v1 + v2 # results in Vector(2, 4, 6)
Subtraction
v1 = Vector(1, 2, 3) v2 = Vector(1, 2, 3) v3 = v1  v2 # results in Vector(0, 0, 0)
(reverse) Multiplication
v1 = Vector(1, 2, 3) v2 = v1 * 3 # results in Vector(3, 6, 9) v3 = 3 * v1 # results in Vector(3, 6, 9)
Dot product
v1 = Vector(1, 2, 3) v2 = Vector(1, 2, 3) res = v1.dot(v2) # results in 14
Cross product
v1 = Vector(1, 0, 0) v2 = Vector(0, 1, 0) v3 = v1.cross(v2) # results in Vector(0, 0, 1)
 Parameters
x (
float
) – Xcoordinate.y (
float
) – Ycoordinate.z (
float
) – Zcoordinate (default: 0).
 property
squared_magnitude
¶ Vector magnitude without square root; faster than magnitude.
 Return type
float
 property
magnitude
¶ Magnitude of the Vector.
 Return type
float
 property
coordinates
¶ Coordinates of the Vector as tuple (X, Y, Z).
 Return type
Tuple
[float
,float
,float
]

normalize
()¶ Return the normalized vector (with unitlength).
 Raises
ValueError – if vector is a nullvector.
 Return type
Material
 class
viktor.geometry.
Material
(name, density=None, price=None, *, threejs_type='MeshStandardMaterial', threejs_roughness=0.7, threejs_metalness=0.8, threejs_opacity=1.0, color=Color(221, 221, 221))¶ 
 Parameters
name (
str
) –density (
Optional
[float
]) –price (
Optional
[float
]) –color (
Color
) –threejs_type (
str
) –threejs_roughness (
float
) – Between 0  1 where closer to 1 gives the material a rough texture.threejs_metalness (
float
) – Between 0  1 where closer to 1 gives the material a shiny metal look.threejs_opacity (
float
) – Between 0  1 where closer to 0 makes the material less visible.
 property
name
¶  Return type
str
 property
density
¶  Return type
Optional
[float
]
 property
price
¶  Return type
Optional
[float
]
TransformableObject
 class
viktor.geometry.
TransformableObject
¶ Bases:
abc.ABC

translate
(translation_vector)¶ Translate an object along a translation vector.
 Parameters
translation_vector (
Union
[Vector
,Tuple
[float
,float
,float
]]) – Vector along which translation is to be performed.

rotate
(angle, direction, point=None)¶ Rotate an object along an axis (direction) by an angle. Direction will follow right hand rule.

mirror
(point, normal)¶ Mirror an object on a plane defined by a point and normal vector.

Group
 class
viktor.geometry.
Group
(objects)¶ Bases:
viktor.geometry.TransformableObject
 Parameters
objects (
List
[TransformableObject
]) – Objects that are part of the group.

add
(objects)¶
 property
children
¶  Return type
List
[TransformableObject
]

duplicate
()¶
Point
 class
viktor.geometry.
Point
(x, y, z=0)¶ 
This class represents a point object, which is instantiated by means of 3dimensional coordinates X, Y, and Z. It forms a basis of many structural 2D and 3D objects.
Example usage:
p1 = Point(0, 0) # creates a point in the origin p2 = Point(1, 2, 3) p3 = p2.copy()
 Parameters
x (
float
) – Xcoordinate.y (
float
) – Ycoordinate.z (
float
) – (optional) Zcoordinate, defaults to 0.
 Raises
TypeError – if the point is instantiated with a None value.
 property
coordinates
¶ Coordinates of the Point as array (X, Y, Z).
 property
x
¶ Returns the Xcoordinate.
 Return type
float
 property
y
¶ Returns the Ycoordinate.
 Return type
float
 property
z
¶ Returns the Zcoordinate.
 Return type
float

coincides_with
(other)¶ Given another Point object, this method determines whether the two points coincide.
 Return type
bool

get_local_coordinates
(local_origin, spherical=False)¶ Method to determine the local coordinates of the current Point with respect to a ‘local origin’.
 Return type
ndarray
Line
 class
viktor.geometry.
Line
(start_point, end_point)¶ 
 property
length
¶  Return type
float

collinear
(point)¶ True if point is collinear (in line) with Line, else False.
 Return type
bool
 property
length_vector
¶
 property
unit_vector
¶
 property
geometries
¶
 property
horizontal
¶  Return type
bool
 property
vertical
¶  Return type
bool

discretize
(num=2)¶

revolve
(*, material=None, **kwargs)¶ Revolve line around yaxis, only possible for lines in xy plane.
 Parameters
material (
Optional
[Material
]) – optional material Raises
NotImplementedError – when line is not in xy plane
 Return type

get_line_function_parameters
()¶ Get parameters for y=ax+b definition of a line
 Return type
Tuple
[float
,float
] Returns
(a,b) (or nan if line is vertical)

find_overlap
(other, inclusive=False)¶ Find the overlapping part of this line with another line.
The returned value depends on the situation:
None, if no overlap is found or the two lines are not parallel
Point, if an overlap is found with length equal to 0
Line, if an overlap is found with length larger than 0
 property
calculate_intersection_bounded_line_with_y

viktor.geometry.
calculate_intersection_bounded_line_with_y
(line, y_intersection)¶ Calculate x intersection between two points and y value. Return None if no intersection is found.
Returns x: Returns None: o / y/ y /: o / : / o x o
 Parameters
line (
Line
) – Line object.y_intersection (
float
) – yvalue of the intersection line.
 Return type
Optional
[float
]
calculate_intersection_extended_line_with_y

viktor.geometry.
calculate_intersection_extended_line_with_y
(line, y_intersection)¶ Calculates the intersection x value of a line at a given y value.
Returns x: Returns x: o / y/ y /: o: / : / : o x o x
 Parameters
line (
Line
) – Line object.y_intersection (
float
) – yvalue of the intersection line.
 Return type
float
line_is_horizontal

viktor.geometry.
line_is_horizontal
(line)¶ Returns True if line is horizontal.
 Return type
bool
line_is_vertical

viktor.geometry.
line_is_vertical
(line)¶ Returns True if line is vertical.
 Return type
bool
x_between_bounds

viktor.geometry.
x_between_bounds
(x, x1, x2, inclusive=True)¶ Method checks whether the x value is between the bounds x1 and x2.
 Parameters
x (
float
) – xvalue to be evaluated.x1 (
float
) – Lower bound.x2 (
float
) – Upper bound.inclusive (
bool
) – If set to True, this method will also return True when the x value is equal to either x1 or x2.
 Return type
bool
y_between_bounds

viktor.geometry.
y_between_bounds
(y, y1, y2, inclusive=True)¶ Method checks whether the y value is between the bounds y1 and y2.
 Parameters
y (
float
) – yvalue to be evaluated.y1 (
float
) – Lower bound.y2 (
float
) – Upper bound.inclusive (
bool
) – If set to True, this method will also return True when the y value is equal to either y1 or y2.
 Return type
bool
point_is_on_bounded_line

viktor.geometry.
point_is_on_bounded_line
(point, line, inclusive=True)¶ Method checks whether a given Point object is within the ends of a Line.
calculate_intersection_extended_line_with_x

viktor.geometry.
calculate_intersection_extended_line_with_x
(line, x)¶ Returns the point at which a given line intersects a vertical axis at position x.
Returns P(x, y): Returns P(x, y): o / yP yP /: o: / : / : o x o x
get_line_function_parameters

viktor.geometry.
get_line_function_parameters
(line)¶ Returns the line function parameters (a, b) of a line (y = ax + b).
 Return type
Tuple
[float
,float
]
calculate_intersection_extended_lines

viktor.geometry.
calculate_intersection_extended_lines
(extended_line1, extended_line2)¶ Calculate intersection between two lines defined by start/end points. The lines are assumed to extend infinitely: bounds are not taken account. Returns None if lines are parallel (i.e. no intersection exists).
Returns P(x, y): Returns P(x, y): Returns None: o / oPo oo P oo / o / / oo o o
calculate_intersection_bounded_line_extended_line

viktor.geometry.
calculate_intersection_bounded_line_extended_line
(bounded_line, extended_line, inclusive=True)¶ Calculate intersection between line with fixed endpoints and line which is indefinitely extended.
calculate_intersection_bounded_lines

viktor.geometry.
calculate_intersection_bounded_lines
(bounded_line1, bounded_line2, inclusive=True)¶ Calculate intersection between two lines with fixed endpoints.
Revolve
 class
viktor.geometry.
Revolve
(*args, material=None, **kwargs)¶ Bases:
viktor.geometry.TransformableObject
,abc.ABC
Abstract base class of a revolved object.
 abstract property
surface_area
¶  Return type
float
 abstract property
inner_volume
¶  Return type
float
 property
thickness
¶  Return type
float
 property
mass
¶ Calculates the mass of the object as rho * area * thickness, with rho the density of the Material.
 Return type
float
 abstract property
LineRevolve
 class
viktor.geometry.
LineRevolve
(line, *args, material=None, **kwargs)¶ Bases:
viktor.geometry.Revolve
Returns an revolved object of a Line around the global yaxis.
An example revolve of a line between the point (1, 1, 0) and (3, 2, 0) is shown below, with the line object shown in black.
line = Line(Point(1, 1, 0), Point(3, 2, 0)) line_rev = LineRevolve(line)
 Parameters
 property
uuid
¶
 property
height
¶  Return type
float
 property
surface_area
¶ Returns the total exterior area of the revolved object.
 Return type
float
 property
inner_volume
¶ Returns the inner volume of the revolved object.
This method will only return a value if the defined Line meets the following conditions:
it should NOT be horizontal, i.e. y_start != y_end
it should be defined in positive ydirection, i.e. y_start < y_end
 Return type
float
Arc
 class
viktor.geometry.
Arc
(centre_point, start_point, end_point, short_arc=True)¶ 
Creates a constant radius arc with three Points in the xy plane. Clockwise rotation creates an outward surface.
 Parameters
centre_point (
Point
) – Point in xy plane.start_point (
Point
) – Point in xy plane. Should have same distance to centre_point as end_point.end_point (
Point
) – Point in xy plane. Should have same distance to centre_point as start_point.short_arc (
bool
) – Angle of arc smaller than pi if True, larger than pi if False.
 property
radius
¶  Return type
float
 property
theta1
¶ Angle of the end point with respect to the xaxis in radians.
 Return type
float
 property
theta2
¶ Angle of the start point with respect to the xaxis in radians.
 Return type
float
 property
short_arc
¶  Return type
bool
 property
angle
¶ Absolute angle of the arc in radians, which is the difference between theta1 and theta2.
 Return type
float
 property
length
¶ Arc length.
 Return type
float
 property
theta1_theta2
¶ Calculates the angles of the end (theta1) and start (theta2) points with respect to the xaxis in radians.
 Return type
Tuple
[float
,float
]

discretize
(num=2)¶ Returns a discretized representation of the arc, as a list of Point objects. The amount of points can be specified using ‘num’, which should be larger than 1.
 Return type
List
[Point
]
ArcRevolve
 class
viktor.geometry.
ArcRevolve
(arc, *args, material=None, **kwargs)¶ Bases:
viktor.geometry.Revolve
Returns an revolved object of an arc around the global yaxis.
In the example below, rotation_angle is equal to pi / 3:
kwargs can consist of:
rotation_angle: Angle of the revolve according to the righthandrule, with the start of the rotation in positive zdirection. Angle in radians. If not specified, 2 pi will be used.
 property
uuid
¶  Return type
str
 property
surface_area
¶ Total exterior area of the object.
 Return type
float
 property
inner_volume
¶ Returns the inner volume of the revolved object.
This method will only return a value if the defined Arc meets the following conditions:
it should be short, i.e. short_arc=True
the start and endpoint are located on the same side w.r.t. the yaxis of the centerpoint of the Arc
it is defined in clockwise direction
 Return type
float
 property
height
¶ Height of the object.
 Return type
float
Triangle
CartesianAxes
 class
viktor.geometry.
CartesianAxes
(origin=Point(0.0, 0.0, 0.0), axis_length=1, axis_diameter=0.05)¶ Bases:
viktor.geometry.Group
Helper ThreeJS visualisation object to show positive x (red), y (green) and z (blue) axes.
 Parameters
origin (
Point
) – Coordinates of the origin.axis_length (
float
) – Length of the axes.axis_diameter (
float
) – Diameter of the axes.
RDWGSConverter
 class
viktor.geometry.
RDWGSConverter
¶ 
Class that provides functions to translate latitude and longitude coordinates between the WGS system and RD system.
The RD coordinate system is a cartesian coordinate system that is frequently used for in civil engineering to describe locations in the Netherlands. The origin is located in france, so that for all of the Netherlands, both x (m) and y (m) values are positive and y is always larger then x. The domain in which the RD coordinate system is valid is:
x: [7000, 300000]
y: [289000, 629000]
About the RD coordinate system: https://nl.wikipedia.org/wiki/Rijksdriehoeksco%C3%B6rdinaten

X0
= 155000¶

Y0
= 463000¶

phi0
= 52.1551744¶

lam0
= 5.38720621¶
 static
from_rd_to_wgs
(coords)¶ Convert RD coordinates (x, y) to WGS coordinates [latitude, longitude].
lat, lon = RDWGSConverter.from_rd_to_wgs((100000, 400000))
 Parameters
coords (
Tuple
[float
,float
]) – RD coordinates (x, y) Return type
List
[float
]
 static
from_wgs_to_rd
(coords)¶ Convert WGS coordinates (latitude, longitude) to RD coordinates [x, y].
x, y = RDWGSConverter.from_rd_to_wgs((51.58622, 4.59360))
 Parameters
coords (
Tuple
[float
,float
]) – WGS coordinates (latitude, longitude) Return type
List
[float
]
spherical_to_cartesian

viktor.geometry.
spherical_to_cartesian
(spherical_coordinates)¶ Using ISO/physical convention: https://upload.wikimedia.org/wikipedia/commons/4/4f/3D_Spherical.svg
 Parameters
spherical_coordinates (
Tuple
[float
,float
,float
]) – Spherical coordinates (r, theta, phi). Return type
ndarray
 Returns
Cartesian coordinates (x, y, z).
cartesian_to_spherical

viktor.geometry.
cartesian_to_spherical
(cartesian_coordinates)¶ Using ISO/physical convention: https://upload.wikimedia.org/wikipedia/commons/4/4f/3D_Spherical.svg
 Parameters
cartesian_coordinates (
Tuple
[float
,float
,float
]) – Cartesian coordinates (x, y, z). Return type
ndarray
 Returns
Spherical coordinates (r, theta, phi).
cylindrical_to_cartesian

viktor.geometry.
cylindrical_to_cartesian
(cylindrical_coordinates)¶ Using ISO convention: https://commons.wikimedia.org/wiki/File:Coord_system_CY_1.svg
Reference plane is former Cartesian xyplane and cylindrical axis is the Cartesian zaxis.
 Parameters
cylindrical_coordinates (
Tuple
[float
,float
,float
]) – Cylindrical coordinates (rho, phi, z). Return type
ndarray
 Returns
Cartesian coordinates (x, y, z).
cartesian_to_cylindrical

viktor.geometry.
cartesian_to_cylindrical
(cartesian_coordinates)¶ Using ISO convention: https://commons.wikimedia.org/wiki/File:Coord_system_CY_1.svg
Reference plane is former Cartesian xyplane and cylindrical axis is the Cartesian zaxis.
 Parameters
cartesian_coordinates (
Tuple
[float
,float
,float
]) – Cartesian coordinates (x, y, z). Return type
ndarray
 Returns
Cylindrical coordinates (rho, phi, z) with phi between pi and +pi.
Extrusion
 class
viktor.geometry.
Extrusion
(profile, line, profile_rotation=0, *, material=None)¶ Bases:
viktor.geometry.Group
Extruded object from a given set of points, which is called the profile. This profile should meet the following requirements:
start point should be added at the end for closed profile
points should be defined in z=0 plane
circumference should be defined clockwise
Note that the profile is defined with respect to the start point of the Line object, i.e. the profile is defined in the local coordinate system. An example is given below of two extrusions with the same dimensions. Their corresponding Line objects are also visualized. The extrusion have the following profile:
# black box profile_b = [ Point(1, 1), Point(1, 2), Point(2, 2), Point(2, 1), Point(1, 1), ] box_b = Extrusion(profile_b, Line(Point(4, 1, 0), Point(4, 1, 1))) # yellow box profile_y = [ Point(0.5, 0.5), Point(0.5, 0.5), Point(0.5, 0.5), Point(0.5, 0.5), Point(0.5, 0.5), ] box_y = Extrusion(profile_y, Line(Point(2, 2, 0), Point(2, 2, 1)))
 Parameters
 property
uuid
¶  Return type
str
 property
length
¶  Return type
float
 property
transformation
¶
ArcExtrusion
 class
viktor.geometry.
ArcExtrusion
(profile, arc, profile_rotation=0, n_segments=50, *, material=None)¶ Bases:
viktor.geometry.Group
Given an Arc and a crosssection of the extrusion, a discretized Extrusion object is returned.
The coordinates of the profile are defined with respect to the Arc and have a LOCAL coordinate system:
zaxis is in direction of the arc from start to end.
xaxis is in positive global zaxis.
yaxis follows from the righthandrule.
Rotation of the profile is about the axis according to the righthandrule with LOCAL zaxis (see definition above).
Example:
profile = [ Point(1, 1), Point(1, 2), Point(3, 2), Point(3, 1), Point(1, 1), ] arc = Arc(Point(1, 1, 0), Point(3, 1, 0), Point(1, 3, 0)) arc_ext = ArcExtrusion(profile, arc, profile_rotation=10, n_segments=10)
This will result in the following visualization, where the Arc itself is also shown in the xy plane:
 Parameters
profile (
List
[Point
]) – Coordinates of crosssection.arc (
Arc
) – An Arc object is used to define the direction of the extrusion.profile_rotation (
float
) – Rotation of the profile around its local Zaxis in degrees.n_segments (
int
) – Number of discretized segments of the arc, which is 50 by default.material (
Optional
[Material
]) – optional material
CircularExtrusion
 class
viktor.geometry.
CircularExtrusion
(diameter, line, *, open_ends=False, material=None)¶ Bases:
viktor.geometry.TransformableObject
This class is used to construct an extrusion which has a circular base, e.g. a circular foundation pile.
 Parameters
 property
length
¶  Return type
float
 property
diameter
¶  Return type
float
 property
radius
¶  Return type
float
 property
cross_sectional_area
¶  Return type
float
RectangularExtrusion
 class
viktor.geometry.
RectangularExtrusion
(width, height, line, profile_rotation=0, *, material=None)¶ Bases:
viktor.geometry.Extrusion
Extruded object from a given set of points, which is called the profile. This profile should meet the following requirements:
start point should be added at the end for closed profile
points should be defined in z=0 plane
circumference should be defined clockwise
Note that the profile is defined with respect to the start point of the Line object, i.e. the profile is defined in the local coordinate system. An example is given below of two extrusions with the same dimensions. Their corresponding Line objects are also visualized. The extrusion have the following profile:
# black box profile_b = [ Point(1, 1), Point(1, 2), Point(2, 2), Point(2, 1), Point(1, 1), ] box_b = Extrusion(profile_b, Line(Point(4, 1, 0), Point(4, 1, 1))) # yellow box profile_y = [ Point(0.5, 0.5), Point(0.5, 0.5), Point(0.5, 0.5), Point(0.5, 0.5), Point(0.5, 0.5), ] box_y = Extrusion(profile_y, Line(Point(2, 2, 0), Point(2, 2, 1)))
 Parameters
 property
width
¶ Width of the extrusion.
 Return type
float
 property
height
¶ Height of the extrusion.
 Return type
float
 property
cross_sectional_area
¶ Returns the area of the crosssection (width x height).
 Return type
float
 property
inner_volume
¶ Returns the inner volume of the extruded object.
 Return type
float
SquareBeam
 class
viktor.geometry.
SquareBeam
(length_x, length_y, length_z, *, material=None)¶ Bases:
viktor.geometry.RectangularExtrusion
High level object to create a rectangular beam object around the origin. The centroid of the beam is located at the origin (0, 0, 0).
 Parameters
length_x (
float
) – Width of the extrusion in xdirection.length_y (
float
) – Length of the extrusion in ydirection.length_z (
float
) – Height of the extrusion in zdirection.material (
Optional
[Material
]) – optional material
points_are_coplanar
lines_in_same_plane
calculate_distance_vector
convert_points_for_lathe
translation_matrix
scaling_matrix
rotation_matrix

viktor.geometry.
rotation_matrix
(angle, direction, point=None)¶ Returns the rotation matrix that corresponds to a rotation about an axis defined by a point and direction. Angle in radians, direction in accordance to right hand rule.
Example:
>>> R = rotation_matrix(pi/2, [0, 0, 1], [1, 0, 0]) >>> np.allclose(np.dot(R, [0, 0, 0, 1]), [1, 1, 0, 1]) True
 Return type
ndarray
reflection_matrix

viktor.geometry.
reflection_matrix
(point, normal)¶ Returns the reflection matrix to mirror at a plane defined by a point and a normal vector.
unit_vector

viktor.geometry.
unit_vector
(data, axis=None, out=None)¶ Returns the unit vector of a given vector.
 Return type
ndarray
mirror_object

viktor.geometry.
mirror_object
(obj, point, normal)¶ Function that mirrors an object through a plane. The plane is defined by a point and a normal vector. The return is a copy of the original object, mirrored over the specified plane.
 Parameters
obj – Object that is to be mirrored
point (
Point
) – Point object on the desired mirror planenormal – Vector that denotes a normal vector of the desired mirror plane.
volume_cone

viktor.geometry.
volume_cone
(r, h)¶ Calculates the volume of a cone.
 Parameters
r (
float
) – Radius of the base.h (
float
) – Height of the cone.
 Return type
float
surface_cone_without_base

viktor.geometry.
surface_cone_without_base
(r, h)¶ Calculates the exterior surface of the cone, excluding the area of the circular base.
 Parameters
r (
float
) – Radius of the base.h (
float
) – Height of the cone.
 Return type
float
surface_area_dome

viktor.geometry.
surface_area_dome
(theta1, theta2, r, R)¶ Computes the surface area of a dome (arcrevolve).
 Parameters
theta1 – Starting angle of arc in radians.
theta2 – Ending angle of arc in radians.
r – Radius of arc.
R – Distance from centre of arc to rotation line.
 Return type
float
 Returns
surface area of arcrevolve.
hex_to_rgb

viktor.geometry.
hex_to_rgb
(value)¶ Return (red, green, blue) for the color given as #rrggbb.
 Return type
Tuple
[int
, …]
rgb_to_hex

viktor.geometry.
rgb_to_hex
(red, green, blue, include_hashtag=True)¶ Return color as #rrggbb for the given color values.
 Return type
str
circumference_is_clockwise
add_point

viktor.geometry.
add_point
(unique_points, point)¶ Adds a Point object to a unique list of Point objects. The point is only added when not already present in the list.
get_vertices_faces
find_overlap

viktor.geometry.
find_overlap
(region_a, region_b, inclusive=False)¶ Given to regions with upper and lower boundary, check if there is overlap and if so return a tuple with the overlap found
The direction of the given regions does not matter: (1, 2) will be handled exactly the same as (2, 1) The returned Tuple will always be in ascending order
Example usage:
find_overlap((2, 4), (3, 5)) > (3, 4) find_overlap((4, 2), (5, 3)) > (3, 4) find_overlap((2, 3), (3, 4)) > None find_overlap((2, 3), (3, 4), inclusive=True) > (3, 3)
 Parameters
region_a (
Tuple
[float
,float
]) – Tuple of values of the first region.region_b (
Tuple
[float
,float
]) – Tuple of values of the second region.inclusive (
bool
) – A flag to decide whether a point overlap is counted as overlap or not.
 Return type
Optional
[Tuple
[float
,float
]] Returns
A tuple with upper and lower bounds of the overlapping region, or None.
Pattern
 class
viktor.geometry.
Pattern
(base_object, duplicate_translation_list)¶ Bases:
viktor.geometry.Group
Instantiates a pattern based on a base object and several duplicates, each translated by an input vector.
 Parameters
base_object (
TransformableObject
) – the object to be duplicatedduplicate_translation_list (
List
[List
[float
]]) – a list of translation vectors, each of which generates a duplicate
LinearPattern
 class
viktor.geometry.
LinearPattern
(base_object, direction, number_of_elements, spacing)¶ Bases:
viktor.geometry.Pattern
Instantiates a linear, evenly spaced, pattern along a single direction.
 Parameters
base_object (
TransformableObject
) – the object to be duplicateddirection (
List
[float
]) – a unit vector specifying in which direction the pattern propagatesnumber_of_elements (
int
) – total amount of elements in the pattern, including the base objectspacing (
float
) – the applied spacing
BidirectionalPattern
 class
viktor.geometry.
BidirectionalPattern
(base_object, direction_1, direction_2, number_of_elements_1, number_of_elements_2, spacing_1, spacing_2)¶ Bases:
viktor.geometry.Pattern
Instantiates a twodimensional pattern, evenly spaced in two separate directions
 Parameters
base_object (
TransformableObject
) – the object to be duplicateddirection_1 (
List
[float
]) – a unit vector specifying the first directiondirection_2 (
List
[float
]) – a unit vector specifying the second directionnumber_of_elements_1 (
int
) – total amount of elements along direction 1number_of_elements_2 (
int
) – total amount of elements along direction 2spacing_1 (
float
) – the applied spacing in direction 1spacing_2 (
float
) – the applied spacing in direction 2
Polygon
 class
viktor.geometry.
Polygon
(points, *, surface_orientation=False, material=None)¶ Bases:
viktor.geometry.TransformableObject
2D closed polygon without holes in xy plane.
 Parameters
points (
List
[Point
]) – profile is automatically closed, do not add start point at the end. only the x and y coordinates are considered (z is set to 0). left hand rule around circumference determines surface directionsurface_orientation (
bool
) –if True, the left hand rule around circumference determines surface direction
if False, surface always in +z direction
material (
Optional
[Material
]) – optional material
 Raises
ValueError –
if less than 3 points are provided.
if points contains duplicates.
if points form a polygon with selfintersecting lines.
if points are all collinear.

has_clockwise_circumference
()¶  Method determines the direction of the input points, and returns:
True if the circumference is clockwise
False if the circumference is counterclockwise
 Return type
bool
 property
cross_sectional_area
¶  Return type
float
 property
centroid
¶ Returns the coordinate of the centroid (geometric center) of the polygon.
 Return type
Tuple
[float
,float
]
 property
moment_of_inertia
¶ Returns the moment of inertia in xyplane.
 Return type
Tuple
[float
,float
]
Polyline
 class
viktor.geometry.
Polyline
(points)¶ 
This is a class representing a line made up of multiple straight line segments. It can be created by providing a list of Points. The list of points can be empty or contain duplicate points The line has a directions, following the order of the provided list of points The Polyline class is immutable. All functions that perform changes on a polyline will return a mutated copy of the original polyline
 classmethod
from_lines
(lines)¶ create a polyline object from a list of lines the end of one line must always coincide with the start of the next
 Parameters
lines –
 Return type
 Returns

is_equal_to
(other)¶ check if all points in this polyline coincide with all points of another polyline
 Parameters
other (
Polyline
) – Return type
bool
 Returns
 property
lines
¶ A list of lines connecting all polyline points. Lines between coincident points are skipped.
 Return type
List
[Line
]
 property
x_min
¶ The lowest xcoordinate present within this polyline
 Return type
Optional
[float
] Returns
 property
x_max
¶ The highest xcoordinate present within this polyline
 Return type
Optional
[float
] Returns
 property
y_min
¶ The lowest ycoordinate present within this polyline
 Return type
Optional
[float
] Returns
 property
y_max
¶ The highest ycoordinate present within this polyline
 Return type
Optional
[float
] Returns
 property
z_min
¶ The lowest zcoordinate present within this polyline
 Return type
Optional
[float
] Returns
 property
z_max
¶ The highest zcoordinate present within this polyline
 Return type
Optional
[float
] Returns

get_reversed_polyline
()¶ returns a polyline that is the reverse of this one
 Return type
 Returns

serialize
()¶ return a json serializable dict of form:
>>> [{'x': point_1.x, 'y': point_1.y}, >>> {'x': point_2.x, 'y': point_2.y}]
 Returns
 classmethod
from_dict
(polyline_dict)¶ Turn a dict generated in the serialize method back into a polyline object
 Return type

filter_duplicate_points
()¶ Returns a new Polyline object. If a two consecutive points in this polyline coincide, the second point will be omitted
 Return type
 Returns

is_monotonic_ascending_x
(strict=True)¶ Check if the x coordinates of the points of this polyline are ascending.
 Parameters
strict (
bool
) – when set to false, equal x coordinates are accepted between points Return type
bool
 Returns

is_monotonic_ascending_y
(strict=True)¶ Check if the y coordinates of the points of this polyline are ascending
 Parameters
strict (
bool
) – when set to false, equal y coordinates are accepted between points Return type
bool
 Returns

intersections_with_polyline
(other_polyline)¶ Find all intersections with another polyline and return them ordered according to the direction of this polyline
If the polylines are partly parallel, the start and end points of the parallel section will be returned as intersections. If one of the polylines is a subset of the other, or the two lines are completely parallel, no intersection will be found

intersections_with_x_location
(x)¶ Find all intersections of this polyline with a given x location. Ordered from start to end of this polyline.
If this line is partly vertical, the start and end points of the vertical section will be returned as a intersection If this line is completely vertical, no intersection will be found.
 Parameters
x (
float
) – Return type
List
[Point
] Returns

point_is_on_polyline
(point)¶ Check if a given point lies on this polyline
 Parameters
point –
 Return type
bool
 Returns

get_polyline_between
(start_point, end_point, inclusive=False)¶ Given two points that both lie on a polyline, return the polyline that lies between those two points start_point has to lie before end_point on this polyline.
If the given start point lies after the given end point on this polyline, an empty polyline will be returned If the two given points are identical, it depends on the inclusive flag whether a polyline containing that point once, or an empty polyline will be returned

find_overlaps
(other)¶ Find all overlapping regions of this polyline with another polyline. The returned overlapping regions will all point in the direction of this line. The overlap polylines will contain all points of both polylines, even if they only occur in one of the lines.
if no overlaps are found, an empty list will be returned.

combine_with
(other)¶ Given two polylines that have at least one point in common and together form one line without any side branches, combine those two polylines The combined line will contain all points of both polylines.

split
(point)¶ return the two separate parts of this polyline before and after the given point
will raise a value error when the provided point does not lie on this polyline
 classmethod
get_lowest_or_highest_profile_x
(profile_1, profile_2, lowest)¶ given two polylines with n intersections, return a third polyline that will always follow the lowest (or highest) of the two lines the x locations of the points of the two polylines should be not descending (lines from left to right or vertical) the returned polyline will only cover the overlapping range in x coordinates
If one of the profiles is an empty polyline, an empty polyline will be returned.
examples:
/ / / profile_1: \ / /  \ / / _____________________________ profile_2: \/ / \_________/ get_lowest_or_highest_profile_x(cls, profile_1, profile_2, lowest=True) will return: / /  / ____________________ result: \ / \_________/
Note that only the overlapping region of the two profiles is returned!
 Parameters
 Return type
 Returns
Currently, this implementation is exclusive. Meaning that vertical line parts that lie on the start or end of the overlap region in x are not taken into account
 classmethod
Cone
 class
viktor.geometry.
Cone
(diameter, height, *, origin=None, orientation=None, material=None)¶ Bases:
viktor.geometry.TransformableObject
Creates a cone object.
 Parameters
diameter (
float
) – Diameter of the circular base surface.height (
float
) – Height from base to tip.origin (
Optional
[Point
]) – Optional location of the centroid of the base surface (default: Point(0, 0, 0)).orientation (
Optional
[Vector
]) – Optional orientation from origin to the tip (default: Vector(0, 0, 1)).material (
Optional
[Material
]) – Optional material.
 classmethod
from_line
(diameter, line, *, material=None)¶ Create a Cone object by a given base diameter and line.
 Parameters
 Return type
Sphere
 class
viktor.geometry.
Sphere
(centre_point, radius, width_segments=30, height_segments=30, material=None)¶ Bases:
viktor.geometry.TransformableObject
This class can be used to construct a spherical object around the specified coordinate.
The smoothness of the edges can be altered by setting width_segments and height_segments. In the example below both the default smoothness of 30 (left) and a rough sphere with 5 segments (right) is shown:
 Parameters

diameter
()¶  Return type
float

circumference
()¶  Return type
float

surface_area
()¶  Return type
float

volume
()¶  Return type
float
Torus
 class
viktor.geometry.
Torus
(radius_cross_section, radius_rotation_axis, rotation_angle=6.283185307179586, *, material=None)¶ Bases:
viktor.geometry.Group
Create a torus object
 Parameters
radius_cross_section (
float
) –radius_rotation_axis (
float
) – measured from central axis to centre of crosssection.rotation_angle (
float
) – optional argument to control how large of a torus section you want. 2pi for complete torusmaterial (
Optional
[Material
]) – optional material
 property
inner_volume
¶
TriangleAssembly
 class
viktor.geometry.
TriangleAssembly
(triangles, *, material=None)¶ Bases:
viktor.geometry.TransformableObject
Fundamental visualisation geometry, built up from triangles. Right hand rule on triangle circumference determines the surface direction.
GeoPoint
 class
viktor.geometry.
GeoPoint
(lat, lon)¶ 
Geographical point on the Earth’s surface described by a latitude / longitude coordinate pair.
This object can be created directly, or will be returned in the parameter set when using a
GeoPointField
. Parameters
lat (
float
) – Latitude.lon (
float
) – Longitude.
 classmethod
from_rd
(coords)¶ Instantiates a GeoPoint from the provided RD coordinates.
 Parameters
coords (
Tuple
[float
,float
]) – RD coordinates (x, y). Return type
 property
rd
¶ RD representation (x, y) of the GeoPoint.
 Return type
Tuple
[float
,float
]
GeoPolyline
 class
viktor.geometry.
GeoPolyline
(*points)¶ 
Geographical polyline on the Earth’s surface described by a a list of
GeoPoints
.This object can be created directly, or will be returned in the parameter set when using a
GeoPolylineField
. Parameters
points (
GeoPoint
) – Geo points (minimum 2).
GeoPolygon
 class
viktor.geometry.
GeoPolygon
(*points)¶ 
Geographical polygon on the Earth’s surface described by a a list of
GeoPoints
.This object can be created directly, or will be returned in the parameter set when using a
GeoPolygonField
. Parameters
points (
GeoPoint
) – Geo points (minimum 3). The profile is automatically closed, so it is not necessary to add the start point at the end.