# Geometry Base¶

abstract module provides base classes for parametric curves, surfaces and volumes contained in this library and therefore, it provides an easy way to extend the library in the most proper way.

## Abstract Curve¶

class geomdl.abstract.Curve(**kwargs)

Abstract base class for defining spline curves.

Curve ABC is inherited from abc.ABCMeta class which is included in Python standard library by default. Due to differences between Python 2 and 3 on defining a metaclass, the compatibility module six is employed. Using six to set metaclass allows users to use the abstract classes in a correct way.

The abstract base classes in this module are implemented using a feature called Python Properties. This feature allows users to use some of the functions as if they are class fields. You can also consider properties as a pythonic way to set getters and setters. You will see “getter” and “setter” descriptions on the documentation of these properties.

The Curve ABC allows users to set the FindSpan function to be used in evaluations with find_span_func keyword as an input to the class constructor. NURBS-Python includes a binary and a linear search variation of the FindSpan function in the helpers module. You may also implement and use your own FindSpan function. Please see the helpers module for details.

Code segment below illustrates a possible implementation of Curve abstract base class:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 from geomdl import abstract class MyCurveClass(abstract.Curve): def __init__(self, **kwargs): super(MyCurveClass, self).__init__(**kwargs) # Add your constructor code here def evaluate(self, **kwargs): # Implement this function pass def evaluate_single(self, uv): # Implement this function pass def evaluate_list(self, uv_list): # Implement this function pass def derivatives(self, u, v, order, **kwargs): # Implement this function pass 

The properties and functions defined in the abstract base class will be automatically available in the subclasses.

Keyword Arguments:

• id: object ID (as integer)
• precision: number of decimal places to round to. Default: 18
• normalize_kv: if True, knot vector(s) will be normalized to [0,1] domain. Default: True
• find_span_func: default knot span finding algorithm. Default: helpers.find_span_linear()
bbox

Bounding box.

Evaluates the bounding box and returns the minimum and maximum coordinates.

Please refer to the wiki for details on using this class member.

Getter: Gets the bounding box tuple
cpsize

Number of control points in all parametric directions.

Note

This is an expert property for getting and setting control point size(s) of the geometry.

Please refer to the wiki for details on using this class member.

Getter: Gets the number of control points Sets the number of control points list
ctrlpts

Control points.

Please refer to the wiki for details on using this class member.

Getter: Gets the control points Sets the control points list
ctrlpts_size

Total number of control points.

Getter: Gets the total number of control points int
data

Returns a dict which contains the geometry data.

Please refer to the wiki for details on using this class member.

degree

Degree.

Please refer to the wiki for details on using this class member.

Getter: Gets the degree Sets the degree int
delta

Evaluation delta.

Evaluation delta corresponds to the step size while evaluate function iterates on the knot vector to generate curve points. Decreasing step size results in generation of more curve points. Therefore; smaller the delta value, smoother the curve.

The following figure illustrates the working principles of the delta property:

Please refer to the wiki for details on using this class member.

Getter: Gets the delta value Sets the delta value float
derivatives(u, order, **kwargs)

Evaluates the derivatives of the curve at parameter u.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: u (float) – parameter (u) order (int) – derivative order
dimension

Spatial dimension.

Spatial dimension will be automatically estimated from the first element of the control points array.

Please refer to the wiki for details on using this class member.

Getter: Gets the spatial dimension, e.g. 2D, 3D, etc. int
domain

Domain.

Domain is determined using the knot vector(s).

Getter: Gets the domain
evalpts

Evaluated points.

Please refer to the wiki for details on using this class member.

Getter: Gets the coordinates of the evaluated points list
evaluate(**kwargs)

Evaluates the curve.

Note

This is an abstract method and it must be implemented in the subclass.

evaluate_list(param_list)

Evaluates the curve for an input range of parameters.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: param_list – array of parameters
evaluate_single(param)

Evaluates the curve at the given parameter.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: param – parameter (u)
evaluator

Evaluator instance.

Evaluators allow users to use different algorithms for B-Spline and NURBS evaluations. Please see the documentation on Evaluator classes.

Please refer to the wiki for details on using this class member.

Getter: Gets the current Evaluator instance Sets the Evaluator instance evaluators.AbstractEvaluator
id

Object ID (as an integer).

Please refer to the wiki for details on using this class member.

Getter: Gets the object ID Sets the object ID int
knotvector

Knot vector.

The knot vector will be normalized to [0, 1] domain if the class is initialized with normalize_kv=True argument.

Please refer to the wiki for details on using this class member.

Getter: Gets the knot vector Sets the knot vector list
name

Object name (as a string)

Please refer to the wiki for details on using this class member.

Getter: Gets the object name Sets the object name str
opt

Dictionary for storing custom data in the current geometry object.

opt is a wrapper to a dict in key => value format, where key is string, value is any Python object. You can use opt property to store custom data inside the geometry object. For instance:

geom.opt = ["face_id", 4]  # creates "face_id" key and sets its value to an integer
geom.opt = ["contents", "data values"]  # creates "face_id" key and sets its value to a string
print(geom.opt)  # will print: {'face_id': 4, 'contents': 'data values'}

del geom.opt  # deletes the contents of the hash map
print(geom.opt)  # will print: {}

geom.opt = ["body_id", 1]  # creates "body_id" key  and sets its value to 1
geom.opt = ["body_id", 12]  # changes the value of "body_id" to 12
print(geom.opt)  # will print: {'body_id': 12}

geom.opt = ["body_id", None]  # deletes "body_id"
print(geom.opt)  # will print: {}


Please refer to the wiki for details on using this class member.

Getter: Gets the dict Adds key and value pair to the dict Deletes the contents of the dict
opt_get(value)

Safely query for the value from the opt property.

Parameters: value (str) – a key in the opt property the corresponding value, if the key exists. None, otherwise.
order

Order.

Defined as order = degree + 1

Please refer to the wiki for details on using this class member.

Getter: Gets the order Sets the order int
pdimension

Parametric dimension.

Please refer to the wiki for details on using this class member.

Getter: Gets the parametric dimension int
range

Domain range.

Getter: Gets the range
rational

Defines the rational and non-rational B-spline shapes.

Rational shapes use homogeneous coordinates which includes a weight alongside with the Cartesian coordinates. Rational B-splines are also named as NURBS (Non-uniform rational basis spline) and non-rational B-splines are sometimes named as NUBS (Non-uniform basis spline) or directly as B-splines.

Please refer to the wiki for details on using this class member.

Getter: Returns True is the B-spline object is rational (NURBS) bool
render(**kwargs)

Renders the curve using the visualization component

The visualization component must be set using vis property before calling this method.

Keyword Arguments:
• cpcolor: sets the color of the control points polygon
• evalcolor: sets the color of the curve
• bboxcolor: sets the color of the bounding box
• filename: saves the plot with the input name
• plot: controls plot window visibility. Default: True
• animate: activates animation (if supported). Default: False
• extras: adds line plots to the figure. Default: None

plot argument is useful when you would like to work on the command line without any window context. If plot flag is False, this method saves the plot as an image file (.png file where possible) and disables plot window popping out. If you don’t provide a file name, the name of the image file will be pulled from the configuration class.

extras argument can be used to add extra line plots to the figure. This argument expects a list of dicts in the format described below:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 [ dict( # line plot 1 points=[[1, 2, 3], [4, 5, 6]], # list of points name="My line Plot 1", # name displayed on the legend color="red", # color of the line plot size=6.5 # size of the line plot ), dict( # line plot 2 points=[[7, 8, 9], [10, 11, 12]], # list of points name="My line Plot 2", # name displayed on the legend color="navy", # color of the line plot size=12.5 # size of the line plot ) ] 
Returns: the figure object
reset(**kwargs)

Resets control points and/or evaluated points.

Keyword Arguments:
• evalpts: if True, then resets evaluated points
• ctrlpts if True, then resets control points
reverse()

Reverses the curve

sample_size

Sample size.

Sample size defines the number of evaluated points to generate. It also sets the delta property.

The following figure illustrates the working principles of sample size property:

Please refer to the wiki for details on using this class member.

Getter: Gets sample size Sets sample size int
set_ctrlpts(ctrlpts, *args, **kwargs)

Sets control points and checks if the data is consistent.

This method is designed to provide a consistent way to set control points whether they are weighted or not. It directly sets the control points member of the class, and therefore it doesn’t return any values. The input will be an array of coordinates. If you are working in the 3-dimensional space, then your coordinates will be an array of 3 elements representing (x, y, z) coordinates.

Parameters: ctrlpts (list) – input control points as a list of coordinates
type

Geometry type

Please refer to the wiki for details on using this class member.

Getter: Gets the geometry type str
vis

Visualization component.

Please refer to the wiki for details on using this class member.

Getter: Gets the visualization component Sets the visualization component vis.VisAbstract
weights

Weights.

Note

Only available for rational spline geometries. Getter return None otherwise.

Please refer to the wiki for details on using this class member.

Getter: Gets the weights Sets the weights

## Abstract Surface¶

class geomdl.abstract.Surface(**kwargs)

Abstract base class for defining spline surfaces.

Surface ABC is inherited from abc.ABCMeta class which is included in Python standard library by default. Due to differences between Python 2 and 3 on defining a metaclass, the compatibility module six is employed. Using six to set metaclass allows users to use the abstract classes in a correct way.

The abstract base classes in this module are implemented using a feature called Python Properties. This feature allows users to use some of the functions as if they are class fields. You can also consider properties as a pythonic way to set getters and setters. You will see “getter” and “setter” descriptions on the documentation of these properties.

The Surface ABC allows users to set the FindSpan function to be used in evaluations with find_span_func keyword as an input to the class constructor. NURBS-Python includes a binary and a linear search variation of the FindSpan function in the helpers module. You may also implement and use your own FindSpan function. Please see the helpers module for details.

Code segment below illustrates a possible implementation of Surface abstract base class:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 from geomdl import abstract class MySurfaceClass(abstract.Surface): def __init__(self, **kwargs): super(MySurfaceClass, self).__init__(**kwargs) # Add your constructor code here def evaluate(self, **kwargs): # Implement this function pass def evaluate_single(self, uv): # Implement this function pass def evaluate_list(self, uv_list): # Implement this function pass def derivatives(self, u, v, order, **kwargs): # Implement this function pass 

The properties and functions defined in the abstract base class will be automatically available in the subclasses.

Keyword Arguments:

• id: object ID (as integer)
• precision: number of decimal places to round to. Default: 18
• normalize_kv: if True, knot vector(s) will be normalized to [0,1] domain. Default: True
• find_span_func: default knot span finding algorithm. Default: helpers.find_span_linear()
add_trim(trim)

Adds a trim to the surface.

A trim is a 2-dimensional curve defined on the parametric domain of the surface. Therefore, x-coordinate of the trimming curve corresponds to u parametric direction of the surfaceand y-coordinate of the trimming curve corresponds to v parametric direction of the surface.

trims uses this method to add trims to the surface.

Parameters: trim (abstract.Geometry) – surface trimming curve
bbox

Bounding box.

Evaluates the bounding box and returns the minimum and maximum coordinates.

Please refer to the wiki for details on using this class member.

Getter: Gets the bounding box tuple
cpsize

Number of control points in all parametric directions.

Note

This is an expert property for getting and setting control point size(s) of the geometry.

Please refer to the wiki for details on using this class member.

Getter: Gets the number of control points Sets the number of control points list
ctrlpts

1-dimensional array of control points.

Note

The v index varies first. That is, a row of v control points for the first u value is found first. Then, the row of v control points for the next u value.

Please refer to the wiki for details on using this class member.

Getter: Gets the control points Sets the control points list
ctrlpts_size

Total number of control points.

Getter: Gets the total number of control points int
ctrlpts_size_u

Number of control points for the u-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets number of control points for the u-direction Sets number of control points for the u-direction
ctrlpts_size_v

Number of control points for the v-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets number of control points on the v-direction Sets number of control points on the v-direction
data

Returns a dict which contains the geometry data.

Please refer to the wiki for details on using this class member.

degree

Degree for u- and v-directions

Getter: Gets the degree Sets the degree list
degree_u

Degree for the u-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets degree for the u-direction Sets degree for the u-direction int
degree_v

Degree for the v-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets degree for the v-direction Sets degree for the v-direction int
delta

Evaluation delta for both u- and v-directions.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta and sample_size properties correspond to the same variable with different descriptions. Therefore, setting delta will also set sample_size.

The following figure illustrates the working principles of the delta property:

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta as a tuple of values corresponding to u- and v-directions Sets evaluation delta for both u- and v-directions float
delta_u

Evaluation delta for the u-direction.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta_u and sample_size_u properties correspond to the same variable with different descriptions. Therefore, setting delta_u will also set sample_size_u.

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta for the u-direction Sets evaluation delta for the u-direction float
delta_v

Evaluation delta for the v-direction.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta_v and sample_size_v properties correspond to the same variable with different descriptions. Therefore, setting delta_v will also set sample_size_v.

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta for the v-direction Sets evaluation delta for the v-direction float
derivatives(u, v, order, **kwargs)

Evaluates the derivatives of the parametric surface at parameter (u, v).

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: u (float) – parameter on the u-direction v (float) – parameter on the v-direction order (int) – derivative order
dimension

Spatial dimension.

Spatial dimension will be automatically estimated from the first element of the control points array.

Please refer to the wiki for details on using this class member.

Getter: Gets the spatial dimension, e.g. 2D, 3D, etc. int
domain

Domain.

Domain is determined using the knot vector(s).

Getter: Gets the domain
evalpts

Evaluated points.

Please refer to the wiki for details on using this class member.

Getter: Gets the coordinates of the evaluated points list
evaluate(**kwargs)

Evaluates the parametric surface.

Note

This is an abstract method and it must be implemented in the subclass.

evaluate_list(param_list)

Evaluates the parametric surface for an input range of (u, v) parameters.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: param_list – array of parameters (u, v)
evaluate_single(param)

Evaluates the parametric surface at the given (u, v) parameter.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: param – parameter (u, v)
evaluator

Evaluator instance.

Evaluators allow users to use different algorithms for B-Spline and NURBS evaluations. Please see the documentation on Evaluator classes.

Please refer to the wiki for details on using this class member.

Getter: Gets the current Evaluator instance Sets the Evaluator instance evaluators.AbstractEvaluator
faces

Faces (triangles, quads, etc.) generated by the tessellation operation.

If the tessellation component is set to None, the result will be an empty list.

Getter: Gets the faces
id

Object ID (as an integer).

Please refer to the wiki for details on using this class member.

Getter: Gets the object ID Sets the object ID int
knotvector

Knot vector for u- and v-directions

Getter: Gets the knot vector Sets the knot vector list
knotvector_u

Knot vector for the u-direction.

The knot vector will be normalized to [0, 1] domain if the class is initialized with normalize_kv=True argument.

Please refer to the wiki for details on using this class member.

Getter: Gets knot vector for the u-direction Sets knot vector for the u-direction list
knotvector_v

Knot vector for the v-direction.

The knot vector will be normalized to [0, 1] domain if the class is initialized with normalize_kv=True argument.

Please refer to the wiki for details on using this class member.

Getter: Gets knot vector for the v-direction Sets knot vector for the v-direction list
name

Object name (as a string)

Please refer to the wiki for details on using this class member.

Getter: Gets the object name Sets the object name str
opt

Dictionary for storing custom data in the current geometry object.

opt is a wrapper to a dict in key => value format, where key is string, value is any Python object. You can use opt property to store custom data inside the geometry object. For instance:

geom.opt = ["face_id", 4]  # creates "face_id" key and sets its value to an integer
geom.opt = ["contents", "data values"]  # creates "face_id" key and sets its value to a string
print(geom.opt)  # will print: {'face_id': 4, 'contents': 'data values'}

del geom.opt  # deletes the contents of the hash map
print(geom.opt)  # will print: {}

geom.opt = ["body_id", 1]  # creates "body_id" key  and sets its value to 1
geom.opt = ["body_id", 12]  # changes the value of "body_id" to 12
print(geom.opt)  # will print: {'body_id': 12}

geom.opt = ["body_id", None]  # deletes "body_id"
print(geom.opt)  # will print: {}


Please refer to the wiki for details on using this class member.

Getter: Gets the dict Adds key and value pair to the dict Deletes the contents of the dict
opt_get(value)

Safely query for the value from the opt property.

Parameters: value (str) – a key in the opt property the corresponding value, if the key exists. None, otherwise.
order_u

Order for the u-direction.

Defined as order = degree + 1

Please refer to the wiki for details on using this class member.

Getter: Gets order for the u-direction Sets order for the u-direction int
order_v

Order for the v-direction.

Defined as order = degree + 1

Please refer to the wiki for details on using this class member.

Getter: Gets surface order for the v-direction Sets surface order for the v-direction int
pdimension

Parametric dimension.

Please refer to the wiki for details on using this class member.

Getter: Gets the parametric dimension int
range

Domain range.

Getter: Gets the range
rational

Defines the rational and non-rational B-spline shapes.

Rational shapes use homogeneous coordinates which includes a weight alongside with the Cartesian coordinates. Rational B-splines are also named as NURBS (Non-uniform rational basis spline) and non-rational B-splines are sometimes named as NUBS (Non-uniform basis spline) or directly as B-splines.

Please refer to the wiki for details on using this class member.

Getter: Returns True is the B-spline object is rational (NURBS) bool
render(**kwargs)

Renders the surface using the visualization component.

The visualization component must be set using vis property before calling this method.

Keyword Arguments:
• cpcolor: sets the color of the control points grid
• evalcolor: sets the color of the surface
• trimcolor: sets the color of the trim curves
• filename: saves the plot with the input name
• plot: controls plot window visibility. Default: True
• animate: activates animation (if supported). Default: False
• extras: adds line plots to the figure. Default: None
• colormap: sets the colormap of the surface

The plot argument is useful when you would like to work on the command line without any window context. If plot flag is False, this method saves the plot as an image file (.png file where possible) and disables plot window popping out. If you don’t provide a file name, the name of the image file will be pulled from the configuration class.

extras argument can be used to add extra line plots to the figure. This argument expects a list of dicts in the format described below:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 [ dict( # line plot 1 points=[[1, 2, 3], [4, 5, 6]], # list of points name="My line Plot 1", # name displayed on the legend color="red", # color of the line plot size=6.5 # size of the line plot ), dict( # line plot 2 points=[[7, 8, 9], [10, 11, 12]], # list of points name="My line Plot 2", # name displayed on the legend color="navy", # color of the line plot size=12.5 # size of the line plot ) ] 

Please note that colormap argument can only work with visualization classes that support colormaps. As an example, please see VisMPL.VisSurfTriangle() class documentation. This method expects a single colormap input.

Returns: the figure object
reset(**kwargs)

Resets control points and/or evaluated points.

Keyword Arguments:
• evalpts: if True, then resets evaluated points
• ctrlpts if True, then resets control points
sample_size

Sample size for both u- and v-directions.

Sample size defines the number of surface points to generate. It also sets the delta property.

The following figure illustrates the working principles of sample size property:

Please refer to the wiki for details on using this class member.

Getter: Gets sample size as a tuple of values corresponding to u- and v-directions Sets sample size for both u- and v-directions int
sample_size_u

Sample size for the u-direction.

Sample size defines the number of surface points to generate. It also sets the delta_u property.

Please refer to the wiki for details on using this class member.

Getter: Gets sample size for the u-direction Sets sample size for the u-direction int
sample_size_v

Sample size for the v-direction.

Sample size defines the number of surface points to generate. It also sets the delta_v property.

Please refer to the wiki for details on using this class member.

Getter: Gets sample size for the v-direction Sets sample size for the v-direction int
set_ctrlpts(ctrlpts, *args, **kwargs)

Sets the control points and checks if the data is consistent.

This method is designed to provide a consistent way to set control points whether they are weighted or not. It directly sets the control points member of the class, and therefore it doesn’t return any values. The input will be an array of coordinates. If you are working in the 3-dimensional space, then your coordinates will be an array of 3 elements representing (x, y, z) coordinates.

Note

The v index varies first. That is, a row of v control points for the first u value is found first. Then, the row of v control points for the next u value.

Parameters: ctrlpts (list) – input control points as a list of coordinates args (tuple[int, int]) – number of control points corresponding to each parametric dimension
tessellate(**kwargs)

Tessellates the surface.

Keyword arguments are directly passed to the tessellation component.

tessellator

Tessellation component.

Please refer to the wiki for details on using this class member.

Getter: Gets the tessellation component Sets the tessellation component
trims

Curves for trimming the surface.

Surface trims are 2-dimensional curves which are introduced on the parametric space of the surfaces. Trim curves can be a spline curve, an analytic curve or a 2-dimensional freeform shape. To visualize the trimmed surfaces, you need to use a tessellator that supports trimming. The following code snippet illustrates changing the default surface tessellator to the trimmed surface tessellator, tessellate.TrimTessellate.

 1 2 3 4 from geomdl import tessellate # Assuming that "surf" variable stores the surface instance surf.tessellator = tessellate.TrimTessellate() 

In addition, using trims initialization argument of the visualization classes, trim curves can be visualized together with their underlying surfaces. Please refer to the visualization configuration class initialization arguments for more details.

Please refer to the wiki for details on using this class member.

Getter: Gets the array of trim curves Sets the array of trim curves
type

Geometry type

Please refer to the wiki for details on using this class member.

Getter: Gets the geometry type str
vertices

Vertices generated by the tessellation operation.

If the tessellation component is set to None, the result will be an empty list.

Getter: Gets the vertices
vis

Visualization component.

Please refer to the wiki for details on using this class member.

Getter: Gets the visualization component Sets the visualization component vis.VisAbstract
weights

Weights.

Note

Only available for rational spline geometries. Getter return None otherwise.

Please refer to the wiki for details on using this class member.

Getter: Gets the weights Sets the weights

## Abstract Volume¶

class geomdl.abstract.Volume(**kwargs)

Abstract base class for defining spline volumes.

Volume ABC is inherited from abc.ABCMeta class which is included in Python standard library by default. Due to differences between Python 2 and 3 on defining a metaclass, the compatibility module six is employed. Using six to set metaclass allows users to use the abstract classes in a correct way.

The abstract base classes in this module are implemented using a feature called Python Properties. This feature allows users to use some of the functions as if they are class fields. You can also consider properties as a pythonic way to set getters and setters. You will see “getter” and “setter” descriptions on the documentation of these properties.

The Volume ABC allows users to set the FindSpan function to be used in evaluations with find_span_func keyword as an input to the class constructor. NURBS-Python includes a binary and a linear search variation of the FindSpan function in the helpers module. You may also implement and use your own FindSpan function. Please see the helpers module for details.

Code segment below illustrates a possible implementation of Volume abstract base class:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 from geomdl import abstract class MyVolumeClass(abstract.Volume): def __init__(self, **kwargs): super(MyVolumeClass, self).__init__(**kwargs) # Add your constructor code here def evaluate(self, **kwargs): # Implement this function pass def evaluate_single(self, uvw): # Implement this function pass def evaluate_list(self, uvw_list): # Implement this function pass 

The properties and functions defined in the abstract base class will be automatically available in the subclasses.

Keyword Arguments:

• id: object ID (as integer)
• precision: number of decimal places to round to. Default: 18
• normalize_kv: if True, knot vector(s) will be normalized to [0,1] domain. Default: True
• find_span_func: default knot span finding algorithm. Default: helpers.find_span_linear()
add_trim(trim)

Adds a trim to the volume.

trims uses this method to add trims to the volume.

Parameters: trim (abstract.Surface) – trimming surface
bbox

Bounding box.

Evaluates the bounding box and returns the minimum and maximum coordinates.

Please refer to the wiki for details on using this class member.

Getter: Gets the bounding box tuple
cpsize

Number of control points in all parametric directions.

Note

This is an expert property for getting and setting control point size(s) of the geometry.

Please refer to the wiki for details on using this class member.

Getter: Gets the number of control points Sets the number of control points list
ctrlpts

1-dimensional array of control points.

Please refer to the wiki for details on using this class member.

Getter: Gets the control points Sets the control points list
ctrlpts_size

Total number of control points.

Getter: Gets the total number of control points int
ctrlpts_size_u

Number of control points for the u-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets number of control points for the u-direction Sets number of control points for the u-direction
ctrlpts_size_v

Number of control points for the v-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets number of control points for the v-direction Sets number of control points for the v-direction
ctrlpts_size_w

Number of control points for the w-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets number of control points for the w-direction Sets number of control points for the w-direction
data

Returns a dict which contains the geometry data.

Please refer to the wiki for details on using this class member.

degree

Degree for u-, v- and w-directions

Getter: Gets the degree Sets the degree list
degree_u

Degree for the u-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets degree for the u-direction Sets degree for the u-direction int
degree_v

Degree for the v-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets degree for the v-direction Sets degree for the v-direction int
degree_w

Degree for the w-direction.

Please refer to the wiki for details on using this class member.

Getter: Gets degree for the w-direction Sets degree for the w-direction int
delta

Evaluation delta for u-, v- and w-directions.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta and sample_size properties correspond to the same variable with different descriptions. Therefore, setting delta will also set sample_size.

The following figure illustrates the working principles of the delta property:

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta as a tuple of values corresponding to u-, v- and w-directions Sets evaluation delta for u-, v- and w-directions float
delta_u

Evaluation delta for the u-direction.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta_u and sample_size_u properties correspond to the same variable with different descriptions. Therefore, setting delta_u will also set sample_size_u.

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta for the u-direction Sets evaluation delta for the u-direction float
delta_v

Evaluation delta for the v-direction.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta_v and sample_size_v properties correspond to the same variable with different descriptions. Therefore, setting delta_v will also set sample_size_v.

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta for the v-direction Sets evaluation delta for the v-direction float
delta_w

Evaluation delta for the w-direction.

Evaluation delta corresponds to the step size while evaluate() function iterates on the knot vector to generate surface points. Decreasing step size results in generation of more surface points. Therefore; smaller the delta value, smoother the surface.

Please note that delta_w and sample_size_w properties correspond to the same variable with different descriptions. Therefore, setting delta_w will also set sample_size_w.

Please refer to the wiki for details on using this class member.

Getter: Gets evaluation delta for the w-direction Sets evaluation delta for the w-direction float
dimension

Spatial dimension.

Spatial dimension will be automatically estimated from the first element of the control points array.

Please refer to the wiki for details on using this class member.

Getter: Gets the spatial dimension, e.g. 2D, 3D, etc. int
domain

Domain.

Domain is determined using the knot vector(s).

Getter: Gets the domain
evalpts

Evaluated points.

Please refer to the wiki for details on using this class member.

Getter: Gets the coordinates of the evaluated points list
evaluate(**kwargs)

Evaluates the parametric volume.

Note

This is an abstract method and it must be implemented in the subclass.

evaluate_list(param_list)

Evaluates the parametric volume for an input range of (u, v, w) parameter pairs.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: param_list – array of parameter pairs (u, v, w)
evaluate_single(param)

Evaluates the parametric surface at the given (u, v, w) parameter.

Note

This is an abstract method and it must be implemented in the subclass.

Parameters: param – parameter pair (u, v, w)
evaluator

Evaluator instance.

Evaluators allow users to use different algorithms for B-Spline and NURBS evaluations. Please see the documentation on Evaluator classes.

Please refer to the wiki for details on using this class member.

Getter: Gets the current Evaluator instance Sets the Evaluator instance evaluators.AbstractEvaluator
id

Object ID (as an integer).

Please refer to the wiki for details on using this class member.

Getter: Gets the object ID Sets the object ID int
knotvector

Knot vector for u-, v- and w-directions

Getter: Gets the knot vector Sets the knot vector list
knotvector_u

Knot vector for the u-direction.

The knot vector will be normalized to [0, 1] domain if the class is initialized with normalize_kv=True argument.

Please refer to the wiki for details on using this class member.

Getter: Gets knot vector for the u-direction Sets knot vector for the u-direction list
knotvector_v

Knot vector for the v-direction.

The knot vector will be normalized to [0, 1] domain if the class is initialized with normalize_kv=True argument.

Please refer to the wiki for details on using this class member.

Getter: Gets knot vector for the v-direction Sets knot vector for the v-direction list
knotvector_w

Knot vector for the w-direction.

The knot vector will be normalized to [0, 1] domain if the class is initialized with normalize_kv=True argument.

Please refer to the wiki for details on using this class member.

Getter: Gets knot vector for the w-direction Sets knot vector for the w-direction list
name

Object name (as a string)

Please refer to the wiki for details on using this class member.

Getter: Gets the object name Sets the object name str
opt

Dictionary for storing custom data in the current geometry object.

opt is a wrapper to a dict in key => value format, where key is string, value is any Python object. You can use opt property to store custom data inside the geometry object. For instance:

geom.opt = ["face_id", 4]  # creates "face_id" key and sets its value to an integer
geom.opt = ["contents", "data values"]  # creates "face_id" key and sets its value to a string
print(geom.opt)  # will print: {'face_id': 4, 'contents': 'data values'}

del geom.opt  # deletes the contents of the hash map
print(geom.opt)  # will print: {}

geom.opt = ["body_id", 1]  # creates "body_id" key  and sets its value to 1
geom.opt = ["body_id", 12]  # changes the value of "body_id" to 12
print(geom.opt)  # will print: {'body_id': 12}

geom.opt = ["body_id", None]  # deletes "body_id"
print(geom.opt)  # will print: {}


Please refer to the wiki for details on using this class member.

Getter: Gets the dict Adds key and value pair to the dict Deletes the contents of the dict
opt_get(value)

Safely query for the value from the opt property.

Parameters: value (str) – a key in the opt property the corresponding value, if the key exists. None, otherwise.
order_u

Order for the u-direction.

Defined as order = degree + 1

Please refer to the wiki for details on using this class member.

Getter: Gets the surface order for u-direction Sets the surface order for u-direction int
order_v

Order for the v-direction.

Defined as order = degree + 1

Please refer to the wiki for details on using this class member.

Getter: Gets the surface order for v-direction Sets the surface order for v-direction int
order_w

Order for the w-direction.

Defined as order = degree + 1

Please refer to the wiki for details on using this class member.

Getter: Gets the surface order for v-direction Sets the surface order for v-direction int
pdimension

Parametric dimension.

Please refer to the wiki for details on using this class member.

Getter: Gets the parametric dimension int
range

Domain range.

Getter: Gets the range
rational

Defines the rational and non-rational B-spline shapes.

Rational shapes use homogeneous coordinates which includes a weight alongside with the Cartesian coordinates. Rational B-splines are also named as NURBS (Non-uniform rational basis spline) and non-rational B-splines are sometimes named as NUBS (Non-uniform basis spline) or directly as B-splines.

Please refer to the wiki for details on using this class member.

Getter: Returns True is the B-spline object is rational (NURBS) bool
render(**kwargs)

Renders the volume using the visualization component.

The visualization component must be set using vis property before calling this method.

Keyword Arguments:
• cpcolor: sets the color of the control points
• evalcolor: sets the color of the volume
• filename: saves the plot with the input name
• plot: controls plot window visibility. Default: True
• animate: activates animation (if supported). Default: False
• grid_size: grid size for voxelization. Default: (8, 8, 8)
• use_cubes: use cube voxels instead of cuboid ones. Default: False
• num_procs: number of concurrent processes for voxelization. Default: 1

The plot argument is useful when you would like to work on the command line without any window context. If plot flag is False, this method saves the plot as an image file (.png file where possible) and disables plot window popping out. If you don’t provide a file name, the name of the image file will be pulled from the configuration class.

extras argument can be used to add extra line plots to the figure. This argument expects a list of dicts in the format described below:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 [ dict( # line plot 1 points=[[1, 2, 3], [4, 5, 6]], # list of points name="My line Plot 1", # name displayed on the legend color="red", # color of the line plot size=6.5 # size of the line plot ), dict( # line plot 2 points=[[7, 8, 9], [10, 11, 12]], # list of points name="My line Plot 2", # name displayed on the legend color="navy", # color of the line plot size=12.5 # size of the line plot ) ] 
Returns: the figure object
reset(**kwargs)

Resets control points and/or evaluated points.

Keyword Arguments:
• evalpts: if True, then resets evaluated points
• ctrlpts if True, then resets control points
sample_size

Sample size for both u- and v-directions.

Sample size defines the number of surface points to generate. It also sets the delta property.

The following figure illustrates the working principles of sample size property:

Please refer to the wiki for details on using this class member.

Getter: Gets sample size as a tuple of values corresponding to u-, v- and w-directions Sets sample size value for both u-, v- and w-directions int
sample_size_u

Sample size for the u-direction.

Sample size defines the number of evaluated points to generate. It also sets the delta_u property.

Please refer to the wiki for details on using this class member.

Getter: Gets sample size for the u-direction Sets sample size for the u-direction int
sample_size_v

Sample size for the v-direction.

Sample size defines the number of evaluated points to generate. It also sets the delta_v property.

Please refer to the wiki for details on using this class member.

Getter: Gets sample size for the v-direction Sets sample size for the v-direction int
sample_size_w

Sample size for the w-direction.

Sample size defines the number of evaluated points to generate. It also sets the delta_w property.

Please refer to the wiki for details on using this class member.

Getter: Gets sample size for the w-direction Sets sample size for the w-direction int
set_ctrlpts(ctrlpts, *args, **kwargs)

Sets the control points and checks if the data is consistent.

This method is designed to provide a consistent way to set control points whether they are weighted or not. It directly sets the control points member of the class, and therefore it doesn’t return any values. The input will be an array of coordinates. If you are working in the 3-dimensional space, then your coordinates will be an array of 3 elements representing (x, y, z) coordinates.

Parameters: ctrlpts (list) – input control points as a list of coordinates args (tuple[int, int, int]) – number of control points corresponding to each parametric dimension
trims

Trimming surfaces.

Please refer to the wiki for details on using this class member.

Getter: Gets the array of trim surfaces Sets the array of trim surfaces
type

Geometry type

Please refer to the wiki for details on using this class member.

Getter: Gets the geometry type str
vis

Visualization component.

Please refer to the wiki for details on using this class member.

Getter: Gets the visualization component Sets the visualization component vis.VisAbstract
weights

Weights.

Note

Only available for rational spline geometries. Getter return None otherwise.

Please refer to the wiki for details on using this class member.

Getter: Gets the weights Sets the weights

## Low Level API¶

The following classes provide the low level API for the geometry abstract base.

Geometry abstract base class can be used for implementation of any geometry object, whereas SplineGeometry abstract base class is designed specifically for spline geometries, including basis splines.

class geomdl.abstract.GeomdlBase(**kwargs)

Bases: object

Abstract base class for defining geomdl objects.

This class provides the following properties:

Keyword Arguments:

• id: object ID (as integer)
• precision: number of decimal places to round to. Default: 18
dimension

Spatial dimension.

Please refer to the wiki for details on using this class member.

Getter: Gets the spatial dimension, e.g. 2D, 3D, etc. int
id

Object ID (as an integer).

Please refer to the wiki for details on using this class member.

Getter: Gets the object ID Sets the object ID int
name

Object name (as a string)

Please refer to the wiki for details on using this class member.

Getter: Gets the object name Sets the object name str
opt

Dictionary for storing custom data in the current geometry object.

opt is a wrapper to a dict in key => value format, where key is string, value is any Python object. You can use opt property to store custom data inside the geometry object. For instance:

geom.opt = ["face_id", 4]  # creates "face_id" key and sets its value to an integer
geom.opt = ["contents", "data values"]  # creates "face_id" key and sets its value to a string
print(geom.opt)  # will print: {'face_id': 4, 'contents': 'data values'}

del geom.opt  # deletes the contents of the hash map
print(geom.opt)  # will print: {}

geom.opt = ["body_id", 1]  # creates "body_id" key  and sets its value to 1
geom.opt = ["body_id", 12]  # changes the value of "body_id" to 12
print(geom.opt)  # will print: {'body_id': 12}

geom.opt = ["body_id", None]  # deletes "body_id"
print(geom.opt)  # will print: {}


Please refer to the wiki for details on using this class member.

Getter: Gets the dict Adds key and value pair to the dict Deletes the contents of the dict
opt_get(value)

Safely query for the value from the opt property.

Parameters: value (str) – a key in the opt property the corresponding value, if the key exists. None, otherwise.
type

Geometry type

Please refer to the wiki for details on using this class member.

Getter: Gets the geometry type str
class geomdl.abstract.Geometry(**kwargs)

Abstract base class for defining geometry objects.

This class provides the following properties:

Keyword Arguments:

• id: object ID (as integer)
• precision: number of decimal places to round to. Default: 18
dimension

Spatial dimension.

Please refer to the wiki for details on using this class member.

Getter: Gets the spatial dimension, e.g. 2D, 3D, etc. int
evalpts

Evaluated points.

Please refer to the wiki for details on using this class member.

Getter: Gets the coordinates of the evaluated points list
evaluate(**kwargs)

Abstract method for the implementation of evaluation algorithm.

Note

This is an abstract method and it must be implemented in the subclass.

id

Object ID (as an integer).

Please refer to the wiki for details on using this class member.

Getter: Gets the object ID Sets the object ID int
name

Object name (as a string)

Please refer to the wiki for details on using this class member.

Getter: Gets the object name Sets the object name str
opt

Dictionary for storing custom data in the current geometry object.

opt is a wrapper to a dict in key => value format, where key is string, value is any Python object. You can use opt property to store custom data inside the geometry object. For instance:

geom.opt = ["face_id", 4]  # creates "face_id" key and sets its value to an integer
geom.opt = ["contents", "data values"]  # creates "face_id" key and sets its value to a string
print(geom.opt)  # will print: {'face_id': 4, 'contents': 'data values'}

del geom.opt  # deletes the contents of the hash map
print(geom.opt)  # will print: {}

geom.opt = ["body_id", 1]  # creates "body_id" key  and sets its value to 1
geom.opt = ["body_id", 12]  # changes the value of "body_id" to 12
print(geom.opt)  # will print: {'body_id': 12}

geom.opt = ["body_id", None]  # deletes "body_id"
print(geom.opt)  # will print: {}


Please refer to the wiki for details on using this class member.

Getter: Gets the dict Adds key and value pair to the dict Deletes the contents of the dict
opt_get(value)

Safely query for the value from the opt property.

Parameters: value (str) – a key in the opt property the corresponding value, if the key exists. None, otherwise.
type

Geometry type

Please refer to the wiki for details on using this class member.

Getter: Gets the geometry type str
class geomdl.abstract.SplineGeometry(**kwargs)

Abstract base class for defining spline geometry objects.

This class provides the following properties:

Keyword Arguments:

• id: object ID (as integer)
• precision: number of decimal places to round to. Default: 18
• normalize_kv: if True, knot vector(s) will be normalized to [0,1] domain. Default: True
• find_span_func: default knot span finding algorithm. Default: helpers.find_span_linear()
bbox

Bounding box.

Evaluates the bounding box and returns the minimum and maximum coordinates.

Please refer to the wiki for details on using this class member.

Getter: Gets the bounding box tuple
cpsize

Number of control points in all parametric directions.

Note

This is an expert property for getting and setting control point size(s) of the geometry.

Please refer to the wiki for details on using this class member.

Getter: Gets the number of control points Sets the number of control points list
ctrlpts

Control points.

Please refer to the wiki for details on using this class member.

Getter: Gets the control points Sets the control points list
ctrlpts_size

Total number of control points.

Getter: Gets the total number of control points int
degree

Degree

Note

This is an expert property for getting and setting the degree(s) of the geometry.

Please refer to the wiki for details on using this class member.

Getter: Gets the degree Sets the degree list
dimension

Spatial dimension.

Spatial dimension will be automatically estimated from the first element of the control points array.

Please refer to the wiki for details on using this class member.

Getter: Gets the spatial dimension, e.g. 2D, 3D, etc. int
domain

Domain.

Domain is determined using the knot vector(s).

Getter: Gets the domain
evalpts

Evaluated points.

Please refer to the wiki for details on using this class member.

Getter: Gets the coordinates of the evaluated points list
evaluate(**kwargs)

Abstract method for the implementation of evaluation algorithm.

Note

This is an abstract method and it must be implemented in the subclass.

evaluator

Evaluator instance.

Evaluators allow users to use different algorithms for B-Spline and NURBS evaluations. Please see the documentation on Evaluator classes.

Please refer to the wiki for details on using this class member.

Getter: Gets the current Evaluator instance Sets the Evaluator instance evaluators.AbstractEvaluator
id

Object ID (as an integer).

Please refer to the wiki for details on using this class member.

Getter: Gets the object ID Sets the object ID int
knotvector

Knot vector

Note

This is an expert property for getting and setting the knot vector(s) of the geometry.

Please refer to the wiki for details on using this class member.

Getter: Gets the knot vector Sets the knot vector list
name

Object name (as a string)

Please refer to the wiki for details on using this class member.

Getter: Gets the object name Sets the object name str
opt

Dictionary for storing custom data in the current geometry object.

opt is a wrapper to a dict in key => value format, where key is string, value is any Python object. You can use opt property to store custom data inside the geometry object. For instance:

geom.opt = ["face_id", 4]  # creates "face_id" key and sets its value to an integer
geom.opt = ["contents", "data values"]  # creates "face_id" key and sets its value to a string
print(geom.opt)  # will print: {'face_id': 4, 'contents': 'data values'}

del geom.opt  # deletes the contents of the hash map
print(geom.opt)  # will print: {}

geom.opt = ["body_id", 1]  # creates "body_id" key  and sets its value to 1
geom.opt = ["body_id", 12]  # changes the value of "body_id" to 12
print(geom.opt)  # will print: {'body_id': 12}

geom.opt = ["body_id", None]  # deletes "body_id"
print(geom.opt)  # will print: {}


Please refer to the wiki for details on using this class member.

Getter: Gets the dict Adds key and value pair to the dict Deletes the contents of the dict
opt_get(value)

Safely query for the value from the opt property.

Parameters: value (str) – a key in the opt property the corresponding value, if the key exists. None, otherwise.
pdimension

Parametric dimension.

Please refer to the wiki for details on using this class member.

Getter: Gets the parametric dimension int
range

Domain range.

Getter: Gets the range
rational

Defines the rational and non-rational B-spline shapes.

Rational shapes use homogeneous coordinates which includes a weight alongside with the Cartesian coordinates. Rational B-splines are also named as NURBS (Non-uniform rational basis spline) and non-rational B-splines are sometimes named as NUBS (Non-uniform basis spline) or directly as B-splines.

Please refer to the wiki for details on using this class member.

Getter: Returns True is the B-spline object is rational (NURBS) bool
render(**kwargs)

Abstract method for spline rendering and visualization.

Note

This is an abstract method and it must be implemented in the subclass.

set_ctrlpts(ctrlpts, *args, **kwargs)

Sets control points and checks if the data is consistent.

This method is designed to provide a consistent way to set control points whether they are weighted or not. It directly sets the control points member of the class, and therefore it doesn’t return any values. The input will be an array of coordinates. If you are working in the 3-dimensional space, then your coordinates will be an array of 3 elements representing (x, y, z) coordinates.

Keyword Arguments:
• array_init: initializes the control points array in the instance
• array_check_for: defines the types for input validation
• callback: defines the callback function for processing input points
• dimension: defines the spatial dimension of the input points
Parameters: ctrlpts (list) – input control points as a list of coordinates args (tuple) – number of control points corresponding to each parametric dimension
type

Geometry type

Please refer to the wiki for details on using this class member.

Getter: Gets the geometry type str
vis

Visualization component.

Please refer to the wiki for details on using this class member.

Getter: Gets the visualization component Sets the visualization component vis.VisAbstract
weights

Weights.

Note

Only available for rational spline geometries. Getter return None otherwise.

Please refer to the wiki for details on using this class member.

Getter: Gets the weights Sets the weights