viktor.geometry
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: float¶
Vector magnitude without square root; faster than magnitude.
 Return type
float
 property magnitude: float¶
Magnitude of the Vector.
 Return type
float
 property coordinates: Tuple[float, float, float]¶
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=None, density=None, price=None, *, threejs_type='MeshStandardMaterial', roughness=1.0, metalness=0.5, opacity=1.0, color=Color(221, 221, 221))¶

Note
The following properties were renamed since v14.5.0. If you are using a lower version, please use the old naming.
threejs_roughness > roughness
threejs_metalness > metalness
threejs_opacity > opacity
 Parameters
name (
str
) – Optional name.density (
float
) – Optional density.price (
float
) – Optional price.threejs_type (
str
) – deprecatedroughness (
float
) – Between 0  1 where closer to 1 gives the material a rough texture.metalness (
float
) – Between 0  1 where closer to 1 gives the material a shiny metal look.opacity (
float
) – Between 0  1 where closer to 0 makes the material less visible.color (
Color
) – Color of the material.
TransformableObject
 class viktor.geometry.TransformableObject¶
Bases:
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. Return type
 rotate(angle, direction, point=None)¶
Rotate an object along an axis (direction) by an angle. Direction will follow right hand rule.
 Parameters
 Return type
 mirror(point, normal)¶
Mirror an object on a plane defined by a point and normal vector.
 Parameters
 Return type
Group
 class viktor.geometry.Group(objects)¶
Bases:
TransformableObject
 Parameters
objects (
Sequence
[TransformableObject
]) – Objects that are part of the group.
 add(objects)¶
 Return type
None
 property children: List[TransformableObject]¶
 Return type
List
[TransformableObject
]
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(1, 2) # create a 2D point p1.z # 0 p2 = Point(1, 2, 3) # create a 3D point p1.z # 3
 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 x: float¶
Xcoordinate.
 Return type
float
 property y: float¶
Ycoordinate.
 Return type
float
 property z: float¶
Zcoordinate.
 Return type
float
 property coordinates: numpy.ndarray¶
Coordinates of the Point as array (X, Y, Z).
 Return type
ndarray
 coincides_with(other)¶
Given another Point object, this method determines whether the two points coincide.
 Return type
bool
 vector_to(point)¶
Vector pointing from self to point.
Example usage:
p1 = Point(1, 2, 3) p2 = Point(0, 0, 0) # origin v = p1.vector_to(p2) # vector from p1 to the origin v = p1.vector_to((0, 0, 0)) # short notation
 Return type
 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, *, color=Color(0, 0, 0))¶
Bases:
TransformableObject
 Parameters
 property length: float¶
 Return type
float
 collinear(point)¶
True if point is collinear (in line) with Line, else False.
 Return type
bool
 distance_to_point(point)¶
Calculate the (minimal) distance from the given point to the (unbounded) line.
 Return type
float
 property length_vector: numpy.ndarray¶
 Return type
ndarray
 property unit_vector: numpy.ndarray¶
 Return type
ndarray
 property horizontal: bool¶
 Return type
bool
 property vertical: bool¶
 Return type
bool
 revolve(*, material=None, **kwargs)¶
Revolve line around yaxis, only possible for lines in xy plane.
 Parameters
material (
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, 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
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)¶
Check whether a given Point object is within the ends of a Line.
 Parameters
 Return type
bool
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 (2D only, Zcoordinate is ignored!).
Revolve
 class viktor.geometry.Revolve(*args, rotation_angle=None, material=None, **kwargs)¶
Bases:
TransformableObject
,ABC
Abstract base class of a revolved object.
 abstract property surface_area: float¶
 Return type
float
 abstract property inner_volume: float¶
 Return type
float
 property thickness: float¶
 Return type
float
 property mass: float¶
Calculates the mass of the object as rho * area * thickness, with rho the density of the Material.
 Return type
float
LineRevolve
 class viktor.geometry.LineRevolve(line, *args, material=None, **kwargs)¶
Bases:
Revolve
Returns a 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: UUID¶
 Return type
UUID
 property height: float¶
 Return type
float
 property surface_area: float¶
Returns the total exterior area of the revolved object.
 Return type
float
 property inner_volume: float¶
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, *, n_segments=30, color=Color(0, 0, 0))¶
Bases:
TransformableObject
Creates a constant radius arc in the xy plane. Clockwise rotation creates an outward surface.
 Parameters
centre_point (
Union
[Point
,Tuple
[float
,float
,float
]]) – Point in xy plane.start_point (
Union
[Point
,Tuple
[float
,float
,float
]]) – Point in xy plane. Should have the same distance to centre_point as end_point.end_point (
Union
[Point
,Tuple
[float
,float
,float
]]) – Point in xy plane. Should have the same distance to centre_point as start_point.short_arc (
bool
) – Angle of arc smaller than pi if True, larger than pi if False.n_segments (
int
) – Number of discrete segments of the arc (default: 30)New in v13.5.0.color (
Color
) – Visualization colorNew in v13.5.0.
 property radius: float¶
 Return type
float
 property n_segments: int¶
 Return type
int
 property theta1_theta2: Tuple[float, float]¶
Angles of the end (theta1) and start (theta2) points with respect to the xaxis in radians.
 Return type
Tuple
[float
,float
]
 property theta1: float¶
Angle of the end point with respect to the xaxis in radians.
 Return type
float
 property theta2: float¶
Angle of the start point with respect to the xaxis in radians.
 Return type
float
 property short_arc: bool¶
 Return type
bool
 property angle: float¶
Absolute angle of the arc in radians, which is the difference between theta1 and theta2.
 Return type
float
 property length: float¶
Arc length.
 Return type
float
 discretize(num=2)¶
Returns a discrete 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
]
 revolve(*, rotation_angle=None, material=None, **kwargs)¶
Returns an ArcRevolve object, revolved around the global yaxis.
 Parameters
rotation_angle (
float
) – Angle of the revolved object according to the righthandrule, with the start of the rotation in positive zdirection. Angle in radians. If not specified, 2 pi will be used.material (
Material
) – optional material
 Return type
ArcRevolve
 class viktor.geometry.ArcRevolve(arc, *args, rotation_angle=None, material=None, **kwargs)¶
Bases:
Revolve
Returns a revolved object of an arc around the global yaxis.
In the example below, rotation_angle is equal to pi / 3:
 Parameters
 property uuid: str¶
 Return type
str
 property surface_area: float¶
Total exterior area of the object.
 Return type
float
 property inner_volume: float¶
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: float¶
Height of the object.
 Return type
float
Triangle
 class viktor.geometry.Triangle(point1, point2, point3)¶

Creates a Triangle object from 3D vertices.
 Parameters
 area()¶
Returns the area of the triangle.
 Return type
float
 property centroid: Tuple[float, float, float]¶
Returns the centroid (X, Y, Z) of the triangle.
 Return type
Tuple
[float
,float
,float
]
 property moment_of_inertia: Tuple[float, float]¶
Returns the moment of inertia (Ix, Iy) (only in xy plane).
 Return type
Tuple
[float
,float
]
CartesianAxes
 class viktor.geometry.CartesianAxes(origin=Point(0.000e+00, 0.000e+00, 0.000e+00), axis_length=1, axis_diameter=0.05)¶
Bases:
Group
Helper 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_wgs_to_rd((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:
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 length: float¶
 Return type
float
ArcExtrusion
 class viktor.geometry.ArcExtrusion(profile, arc, profile_rotation=0, n_segments=50, *, material=None)¶
Bases:
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 discrete segments of the arc, which is 50 by default.material (
Material
) – optional material
CircularExtrusion
 class viktor.geometry.CircularExtrusion(diameter, line, *, shell_thickness=None, material=None)¶
Bases:
TransformableObject
This class is used to construct an extrusion which has a circular base, e.g. a circular foundation pile.
 Parameters
 property length: float¶
 Return type
float
 property diameter: float¶
 Return type
float
 property radius: float¶
 Return type
float
 property shell_thickness: Optional[float]¶
 Return type
Optional
[float
]
 property cross_sectional_area: float¶
 Return type
float
RectangularExtrusion
 class viktor.geometry.RectangularExtrusion(width, height, line, profile_rotation=0, *, material=None)¶
Bases:
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: float¶
Width of the extrusion.
 Return type
float
 property height: float¶
Height of the extrusion.
 Return type
float
 property cross_sectional_area: float¶
Returns the area of the crosssection (width x height).
 Return type
float
 property inner_volume: float¶
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:
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 (
Material
) – optional material
points_are_coplanar
 viktor.geometry.points_are_coplanar(points)¶
Determine whether all given points are coplanar (are on a twodimensional plane).
 Parameters
points (
Sequence
[Union
[Point
,Tuple
[float
,float
,float
]]]) – points to be evaluated (min. 3).
Example usage:
points = [[Point(0, 3, 1), Point(0, 5, 1), Point(2, 3, 4), Point(2, 5, 4)]] coplanar = points_are_coplanar(points) coplanar = points_are_coplanar([(0, 3, 1), (0, 5, 1), (2, 3, 4), (2, 5, 4)])
 Return type
bool
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 righthand 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
Optional
[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 (
TransformableObject
) – Object that is to be mirroredpoint (
Point
) – Point object on the desired mirror planenormal (
Union
[Vector
,Tuple
[float
,float
,float
]]) – Vector that denotes a normal vector of the desired mirror plane.
 Return type
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 (
float
) – Starting angle of arc in radians.theta2 (
float
) – Ending angle of arc in radians.r (
float
) – Radius of arc.R (
float
) – Distance from centre of arc to rotation line.
 Return type
float
 Returns
surface area of arcrevolve.
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:
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:
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:
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, skip_duplicate_vertices_check=False)¶
Bases:
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. 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 (
Material
) – optional materialskip_duplicate_vertices_check (
bool
) – if True, duplicate vertices are not filtered on serialization of the triangles. This may boost performance (default: False).
 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: float¶
 Return type
float
 property centroid: Tuple[float, float]¶
Returns the centroid (X, Y) of the polygon.
 Return type
Tuple
[float
,float
]
 property moment_of_inertia: Tuple[float, float]¶
Returns the moment of inertia (Ix, Iy) in xyplane.
 Return type
Tuple
[float
,float
]
 extrude(line, *, profile_rotation=0, material=None)¶
Extrude the Polygon in the direction of the given line. Polygon must be defined in clockwise direction.
 Parameters
 Raises
ValueError – if polygon is defined in anticlockwise direction
 Return type
Polyline
 class viktor.geometry.Polyline(points, *, color=Color(0, 0, 0))¶
Bases:
TransformableObject
Representation of a polyline made up of multiple straight line segments.
This class is immutable, meaning that all functions that perform changes on a polyline will return a mutated copy of the original polyline.
 Parameters
 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 line.
 is_equal_to(other)¶
Check if all points in this polyline coincide with all points of another polyline
 Parameters
other (
Polyline
) – Other polyline Return type
bool
 property lines: List[Line]¶
A list of lines connecting all polyline points. Lines between coincident points are skipped.
 Return type
List
[Line
]
 property x_min: Optional[float]¶
The lowest xcoordinate present within this polyline.
 Return type
Optional
[float
]
 property x_max: Optional[float]¶
The highest xcoordinate present within this polyline.
 Return type
Optional
[float
]
 property y_min: Optional[float]¶
The lowest ycoordinate present within this polyline.
 Return type
Optional
[float
]
 property y_max: Optional[float]¶
The highest ycoordinate present within this polyline.
 Return type
Optional
[float
]
 property z_min: Optional[float]¶
The lowest zcoordinate present within this polyline.
 Return type
Optional
[float
]
 property z_max: Optional[float]¶
The highest zcoordinate present within this polyline.
 Return type
Optional
[float
]
 serialize()¶
Return a json serializable dict of form:
[ {'x': point_1.x, 'y': point_1.y}, {'x': point_2.x, 'y': point_2.y} ]
 Return type
List
[dict
]
 filter_duplicate_points()¶
Returns a new Polyline object. If two consecutive points in this polyline coincide, the second point will be omitted
 Return type
 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
 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
 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 intersections 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 an intersection. If this line is completely vertical, no intersections will be found.
 Parameters
x (
float
) – Return type
List
[Point
]
 point_is_on_polyline(point)¶
Check if a given point lies on this polyline
 Parameters
point (
Point
) – Return type
bool
 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.
 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
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.
 Return type
Cone
 class viktor.geometry.Cone(diameter, height, *, origin=None, orientation=None, material=None)¶
Bases:
TransformableObject
Creates a cone object.
 Parameters
diameter (
float
) – Diameter of the circular base surface.height (
float
) – Height from base to tip.origin (
Point
) – Optional location of the centroid of the base surface (default: Point(0, 0, 0)).orientation (
Vector
) – Optional orientation from origin to the tip (default: Vector(0, 0, 1)).material (
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:
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:
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 (
Material
) – optional material
 property inner_volume: float¶
 Return type
float
TriangleAssembly
 class viktor.geometry.TriangleAssembly(triangles, *, material=None, skip_duplicate_vertices_check=False)¶
Bases:
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 params when using a
GeoPointField
. Parameters
lat (
float
) – Latitude, between 90 and 90 degrees.lon (
float
) – Longitude, between 180 and 180 degrees.
 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: Tuple[float, float]¶
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 list of
GeoPoints
.This object can be created directly, or will be returned in the params 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 list of
GeoPoints
.This object can be created directly, or will be returned in the params 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.