B-Spline Geometry¶

BSpline module provides data storage and evaluation functions for non-rational spline geometries.

Inheritance Diagram¶ B-Spline Curve¶

class geomdl.BSpline.Curve(**kwargs)

Data storage and evaluation class for n-variate B-spline (non-rational) curves.

This class provides the following properties:

The following code segment illustrates the usage of Curve class:

from geomdl import BSpline

# Create a 3-dimensional B-spline Curve
curve = BSpline.Curve()

# Set degree
curve.degree = 3

# Set control points
curve.ctrlpts = [[10, 5, 10], [10, 20, -30], [40, 10, 25], [-10, 5, 0]]

# Set knot vector
curve.knotvector = [0, 0, 0, 0, 1, 1, 1, 1]

# Set evaluation delta (controls the number of curve points)
curve.delta = 0.05

# Get curve points (the curve will be automatically evaluated)
curve_points = curve.evalpts


Keyword Arguments:

Please refer to the abstract.Curve() documentation for more details.

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
binormal(parpos, **kwargs)

Evaluates the binormal vector of the curve at the given parametric position(s).

The param argument can be

• a float value for evaluation at a single parametric position
• a list of float values for evaluation at the multiple parametric positions

The return value will be in the order of the input parametric position list.

This method accepts the following keyword arguments:

• normalize: normalizes the output vector. Default value is True.
Parameters: parpos (float, list or tuple) – parametric position(s) where the evaluation will be executed an array containing “point” and “vector” pairs 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=0, **kwargs)

Evaluates n-th order curve derivatives at the given parameter value.

Parameters: u (float) – parameter value order (int) – derivative order a list containing up to {order}-th derivative of the curve 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)

Evaluates the curve.

The evaluated points are stored in evalpts property.

Keyword arguments:
• start: start parameter
• stop: stop parameter

The start and stop parameters allow evaluation of a curve segment in the range [start, stop], i.e. the curve will also be evaluated at the stop parameter value.

The following examples illustrate the usage of the keyword arguments.

# Start evaluating from u=0.2 to u=1.0
curve.evaluate(start=0.2)

# Start evaluating from u=0.0 to u=0.7
curve.evaluate(stop=0.7)

# Start evaluating from u=0.1 to u=0.5
curve.evaluate(start=0.1, stop=0.5)

# Get the evaluated points
curve_points = curve.evalpts

evaluate_list(param_list)

Evaluates the curve for an input range of parameters.

Parameters: param_list (list, tuple) – list of parameters evaluated surface points at the input parameters list
evaluate_single(param)

Evaluates the curve at the input parameter.

Parameters: param (float) – parameter evaluated surface point at the given parameter list
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
insert_knot(param, **kwargs)

Inserts the knot and updates the control points array and the knot vector.

Keyword Arguments:
• num: Number of knot insertions. Default: 1
Parameters: param (float) – knot to be inserted
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
load(file_name)

Loads the curve from a pickled file.

Deprecated since version 5.2.4: Use exchange.import_json() instead.

Parameters: file_name (str) – name of the file to be loaded
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
normal(parpos, **kwargs)

Evaluates the normal vector of the curve at the given parametric position(s).

The param argument can be

• a float value for evaluation at a single parametric position
• a list of float values for evaluation at the multiple parametric positions

The return value will be in the order of the input parametric position list.

This method accepts the following keyword arguments:

• normalize: normalizes the output vector. Default value is True.
Parameters: parpos (float, list or tuple) – parametric position(s) where the evaluation will be executed an array containing “point” and “vector” pairs tuple
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
remove_knot(param, **kwargs)

Removes the knot and updates the control points array and the knot vector.

Keyword Arguments:
• num: Number of knot removals. Default: 1
Parameters: param (float) – knot to be removed
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
save(file_name)

Saves the curve as a pickled file.

Deprecated since version 5.2.4: Use exchange.export_json() instead.

Parameters: file_name (str) – name of the file to be saved
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
tangent(param, **kwargs)

Evaluates the tangent vector of the curve at the given parametric position(s).

The param argument can be

• a float value for evaluation at a single parametric position
• a list of float values for evaluation at the multiple parametric positions

The return value will be in the order of the input parametric position list.

This method accepts the following keyword arguments:

• normalize: normalizes the output vector. Default value is True.
Parameters: param (float, list or tuple) – parametric position(s) where the evaluation will be executed an array containing “point” and “vector” pairs tuple
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

B-Spline Surface¶

class geomdl.BSpline.Surface(**kwargs)

Data storage and evaluation class for B-spline (non-rational) surfaces.

This class provides the following properties:

The following code segment illustrates the usage of Surface class:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 from geomdl import BSpline # Create a BSpline surface instance (Bezier surface) surf = BSpline.Surface() # Set degrees surf.degree_u = 3 surf.degree_v = 2 # Set control points control_points = [[0, 0, 0], [0, 4, 0], [0, 8, -3], [2, 0, 6], [2, 4, 0], [2, 8, 0], [4, 0, 0], [4, 4, 0], [4, 8, 3], [6, 0, 0], [6, 4, -3], [6, 8, 0]] surf.set_ctrlpts(control_points, 4, 3) # Set knot vectors surf.knotvector_u = [0, 0, 0, 0, 1, 1, 1, 1] surf.knotvector_v = [0, 0, 0, 1, 1, 1] # Set evaluation delta (control the number of surface points) surf.delta = 0.05 # Get surface points (the surface will be automatically evaluated) surface_points = surf.evalpts 

Keyword Arguments:

Please refer to the abstract.Surface() documentation for more details.

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
ctrlpts2d

2-dimensional array of control points.

The getter returns a tuple of 2D control points (weighted control points + weights if NURBS) in [u][v] format. The rows of the returned tuple correspond to v-direction and the columns correspond to u-direction.

The following example can be used to traverse 2D control points:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 # Create a BSpline surface surf_bs = BSpline.Surface() # Do degree, control points and knot vector assignments here # Each u includes a row of v values for u in surf_bs.ctrlpts2d: # Each row contains the coordinates of the control points for v in u: print(str(v)) # will be something like (1.0, 2.0, 3.0) # Create a NURBS surface surf_nb = NURBS.Surface() # Do degree, weighted control points and knot vector assignments here # Each u includes a row of v values for u in surf_nb.ctrlpts2d: # Each row contains the coordinates of the weighted control points for v in u: print(str(v)) # will be something like (0.5, 1.0, 1.5, 0.5) 

When using NURBS.Surface class, the output of ctrlpts2d property could be confusing since, ctrlpts always returns the unweighted control points, i.e. ctrlpts property returns 3D control points all divided by the weights and you can use weights property to access the weights vector, but ctrlpts2d returns the weighted ones plus weights as the last element. This difference is intentionally added for compatibility and interoperability purposes.

To explain this situation in a simple way;

Note

Please note that the setter doesn’t check for inconsistencies and using the setter is not recommended. Instead of the setter property, please use set_ctrlpts() function.

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

Getter: Gets the control points as a 2-dimensional array in [u][v] format Sets the control points as a 2-dimensional array in [u][v] format 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=0, **kwargs)

Evaluates n-th order surface derivatives at the given (u, v) parameter pair.

• SKL will be the surface point itself
• SKL will be the 1st derivative w.r.t. v
• SKL will be the 2nd derivative w.r.t. u and 1st derivative w.r.t. v
Parameters: u (float) – parameter on the u-direction v (float) – parameter on the v-direction order (integer) – derivative order A list SKL, where SKL[k][l] is the derivative of the surface S(u,v) w.r.t. u k times and v l times 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)

Evaluates the surface.

The evaluated points are stored in evalpts property.

Keyword arguments:
• start_u: start parameter on the u-direction
• stop_u: stop parameter on the u-direction
• start_v: start parameter on the v-direction
• stop_v: stop parameter on the v-direction

The start_u, start_v and stop_u and stop_v parameters allow evaluation of a surface segment in the range [start_u, stop_u][start_v, stop_v] i.e. the surface will also be evaluated at the stop_u and stop_v parameter values.

The following examples illustrate the usage of the keyword arguments.

 1 2 3 4 5 6 7 8 # Start evaluating in range u=[0, 0.7] and v=[0.1, 1] surf.evaluate(stop_u=0.7, start_v=0.1) # Start evaluating in range u=[0, 1] and v=[0.1, 0.3] surf.evaluate(start_v=0.1, stop_v=0.3) # Get the evaluated points surface_points = surf.evalpts 
evaluate_list(param_list)

Evaluates the surface for a given list of (u, v) parameters.

Parameters: param_list (list, tuple) – list of parameter pairs (u, v) evaluated surface point at the input parameter pairs tuple
evaluate_single(param)

Evaluates the surface at the input (u, v) parameter pair.

Parameters: param (list, tuple) – parameter pair (u, v) evaluated surface point at the given parameter pair list
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
insert_knot(u=None, v=None, **kwargs)

Inserts knot(s) on the u- or v-directions

Keyword Arguments:
• num_u: Number of knot insertions on the u-direction. Default: 1
• num_v: Number of knot insertions on the v-direction. Default: 1
Parameters: u (float) – knot to be inserted on the u-direction v (float) – knot to be inserted on the v-direction
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
load(file_name)

Loads the surface from a pickled file.

Deprecated since version 5.2.4: Use exchange.import_json() instead.

Parameters: file_name (str) – name of the file to be loaded
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
normal(parpos, **kwargs)

Evaluates the normal vector of the surface at the given parametric position(s).

The param argument can be

• a float value for evaluation at a single parametric position
• a list of float values for evaluation at the multiple parametric positions

The parametric positions should be a pair of (u,v) values. The return value will be in the order of the input parametric position list.

This method accepts the following keyword arguments:

• normalize: normalizes the output vector. Default value is True.
Parameters: parpos (list or tuple) – parametric position(s) where the evaluation will be executed an array containing “point” and “vector” pairs tuple
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
remove_knot(u=None, v=None, **kwargs)

Inserts knot(s) on the u- or v-directions

Keyword Arguments:
• num_u: Number of knot removals on the u-direction. Default: 1
• num_v: Number of knot removals on the v-direction. Default: 1
Parameters: u (float) – knot to be removed on the u-direction v (float) – knot to be removed on the v-direction
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
save(file_name)

Saves the surface as a pickled file.

Deprecated since version 5.2.4: Use exchange.export_json() instead.

Parameters: file_name (str) – name of the file to be saved
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.

This method also generates 2D control points in [u][v] format which can be accessed via ctrlpts2d.

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
tangent(parpos, **kwargs)

Evaluates the tangent vectors of the surface at the given parametric position(s).

The param argument can be

• a float value for evaluation at a single parametric position
• a list of float values for evaluation at the multiple parametric positions

The parametric positions should be a pair of (u,v) values. The return value will be in the order of the input parametric position list.

This method accepts the following keyword arguments:

• normalize: normalizes the output vector. Default value is True.
Parameters: parpos (list or tuple) – parametric position(s) where the evaluation will be executed an array containing “point” and “vector”s on u- and v-directions, respectively tuple
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
transpose()

Transposes the surface by swapping u and v parametric directions.

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

B-Spline Volume¶

New in version 5.0.

class geomdl.BSpline.Volume(**kwargs)

Data storage and evaluation class for B-spline (non-rational) volumes.

This class provides the following properties:

Keyword Arguments:

Please refer to the abstract.Volume() documentation for more details.

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 volume.

The evaluated points are stored in evalpts property.

Keyword arguments:
• start_u: start parameter on the u-direction
• stop_u: stop parameter on the u-direction
• start_v: start parameter on the v-direction
• stop_v: stop parameter on the v-direction
• start_w: start parameter on the w-direction
• stop_w: stop parameter on the w-direction
evaluate_list(param_list)

Evaluates the volume for a given list of (u, v, w) parameters.

Parameters: param_list (list, tuple) – list of parameters in format (u, v, w) evaluated surface point at the input parameter pairs tuple
evaluate_single(param)

Evaluates the volume at the input (u, v, w) parameter.

Parameters: param (list, tuple) – parameter (u, v, w) evaluated surface point at the given parameter pair list
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
insert_knot(u=None, v=None, w=None, **kwargs)

Inserts knot(s) on the u-, v- and w-directions

Keyword Arguments:
• num_u: Number of knot insertions on the u-direction. Default: 1
• num_v: Number of knot insertions on the v-direction. Default: 1
• num_w: Number of knot insertions on the w-direction. Default: 1
Parameters: u (float) – knot to be inserted on the u-direction v (float) – knot to be inserted on the v-direction w (float) – knot to be inserted on the w-direction
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
load(file_name)

Loads the volume from a pickled file.

Deprecated since version 5.2.4: Use exchange.import_json() instead.

Parameters: file_name (str) – name of the file to be loaded
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
remove_knot(u=None, v=None, w=None, **kwargs)

Inserts knot(s) on the u-, v- and w-directions

Keyword Arguments:
• num_u: Number of knot removals on the u-direction. Default: 1
• num_v: Number of knot removals on the v-direction. Default: 1
• num_w: Number of knot removals on the w-direction. Default: 1
Parameters: u (float) – knot to be removed on the u-direction v (float) – knot to be removed on the v-direction w (float) – knot to be removed on the w-direction
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
save(file_name)

Saves the volume as a pickled file.

Deprecated since version 5.2.4: Use exchange.export_json() instead.

Parameters: file_name (str) – name of the file to be saved
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