Tessellation¶

The tessellate module provides tessellation algorithms for surfaces. The following example illustrates the usage scenario of the tessellation algorithms with surfaces.

from geomdl import NURBS
from geomdl import tessellate

# Create a surface instance
surf = NURBS.Surface()

# Set tessellation algorithm (you can use another algorithm)
surf.tessellator = tessellate.TriangularTessellate()

# Tessellate surface
surf.tessellate()

NURBS-Python uses TriangularTessellate class for surface tessellation by default.

Note

To get better results with the surface trimming, you need to use a relatively smaller evaluation delta or a bigger sample size value. Recommended evaluation delta is $d = 0.01$ .

Class Reference¶

Abstract Tessellator¶

class geomdl.tessellate.AbstractTessellate(**kwargs)¶

Bases: object

Abstract base class for tessellation algorithms.

arguments¶

Arguments passed to the tessellation function.

This property allows customization of the tessellation algorithm, and mainly designed to allow users to pass additional arguments to the tessellation function or change the behavior of the algorithm at runtime. This property can be thought as a way to input and store extra data for the tessellation functionality.

Getter:	Gets the tessellation arguments (as a dict)
Setter:	Sets the tessellation arguments (as a dict)

faces¶

Objects generated after tessellation.

Getter:	Gets the faces
Type:	elements.AbstractEntity

is_tessellated()¶

Checks if vertices and faces are generated.

Returns:	tessellation status
Return type:	bool

reset()¶: Clears stored vertices and faces.

tessellate(points, **kwargs)¶

Abstract method for the implementation of the tessellation algorithm.

This algorithm should update vertices and faces properties.

Note

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

Parameters:	points – points to be tessellated

vertices¶

Vertex objects generated after tessellation.

Getter:	Gets the vertices
Type:	elements.AbstractEntity

Triangular Tessellator¶

class geomdl.tessellate.TriangularTessellate(**kwargs)¶

Bases: geomdl.tessellate.AbstractTessellate

Triangular tessellation algorithm for surfaces.

arguments¶

Arguments passed to the tessellation function.

This property allows customization of the tessellation algorithm, and mainly designed to allow users to pass additional arguments to the tessellation function or change the behavior of the algorithm at runtime. This property can be thought as a way to input and store extra data for the tessellation functionality.

Getter:	Gets the tessellation arguments (as a dict)
Setter:	Sets the tessellation arguments (as a dict)

faces¶

Objects generated after tessellation.

Getter:	Gets the faces
Type:	elements.AbstractEntity

is_tessellated()¶

Checks if vertices and faces are generated.

Returns:	tessellation status
Return type:	bool

reset()¶: Clears stored vertices and faces.

tessellate(points, **kwargs)¶

Applies triangular tessellation.

This function does not check if the points have already been tessellated.

Keyword Arguments:

size_u: number of points on the u-direction
size_v: number of points on the v-direction

Parameters:	points (list, tuple) – array of points

vertices¶

Vertex objects generated after tessellation.

Getter:	Gets the vertices
Type:	elements.AbstractEntity

Trim Tessellator¶

New in version 5.0.

class geomdl.tessellate.TrimTessellate(**kwargs)¶

Bases: geomdl.tessellate.AbstractTessellate

Triangular tessellation algorithm for trimmed surfaces.

arguments¶

Arguments passed to the tessellation function.

This property allows customization of the tessellation algorithm, and mainly designed to allow users to pass additional arguments to the tessellation function or change the behavior of the algorithm at runtime. This property can be thought as a way to input and store extra data for the tessellation functionality.

Getter:	Gets the tessellation arguments (as a dict)
Setter:	Sets the tessellation arguments (as a dict)

faces¶

Objects generated after tessellation.

Getter:	Gets the faces
Type:	elements.AbstractEntity

is_tessellated()¶

Checks if vertices and faces are generated.

Returns:	tessellation status
Return type:	bool

reset()¶: Clears stored vertices and faces.

tessellate(points, **kwargs)¶

Applies triangular tessellation w/ trimming curves.

Keyword Arguments:

size_u: number of points on the u-direction
size_v: number of points on the v-direction

Parameters:	points (list, tuple) – array of points

vertices¶

Vertex objects generated after tessellation.

Getter:	Gets the vertices
Type:	elements.AbstractEntity

Quadrilateral Tessellator¶

New in version 5.2.

class geomdl.tessellate.QuadTessellate(**kwargs)¶

Bases: geomdl.tessellate.AbstractTessellate

Quadrilateral tessellation algorithm for surfaces.

arguments¶

Arguments passed to the tessellation function.

This property allows customization of the tessellation algorithm, and mainly designed to allow users to pass additional arguments to the tessellation function or change the behavior of the algorithm at runtime. This property can be thought as a way to input and store extra data for the tessellation functionality.

Getter:	Gets the tessellation arguments (as a dict)
Setter:	Sets the tessellation arguments (as a dict)

faces¶

Objects generated after tessellation.

Getter:	Gets the faces
Type:	elements.AbstractEntity

is_tessellated()¶

Checks if vertices and faces are generated.

Returns:	tessellation status
Return type:	bool

reset()¶: Clears stored vertices and faces.

tessellate(points, **kwargs)¶

Applies quadrilateral tessellation.

This function does not check if the points have already been tessellated.

Keyword Arguments:

size_u: number of points on the u-direction
size_v: number of points on the v-direction

Parameters:	points (list, tuple) – array of points

vertices¶

Vertex objects generated after tessellation.

Getter:	Gets the vertices
Type:	elements.AbstractEntity

Function Reference¶

geomdl.tessellate.make_triangle_mesh(points, size_u, size_v, **kwargs)¶

Generates a triangular mesh from an array of points.

This function generates a triangular mesh for a NURBS or B-Spline surface on its parametric space. The input is the surface points and the number of points on the parametric dimensions u and v, indicated as row and column sizes in the function signature. This function should operate correctly if row and column sizes are input correctly, no matter what the points are v-ordered or u-ordered. Please see the documentation of ctrlpts and ctrlpts2d properties of the Surface class for more details on point ordering for the surfaces.

This function accepts the following keyword arguments:

vertex_spacing: Defines the size of the triangles via setting the jump value between points
trims: List of trim curves passed to the tessellation function
tessellate_func: Function called for tessellation. Default: tessellate.surface_tessellate()
tessellate_args: Arguments passed to the tessellation function (as a dict)

The tessellation function is designed to generate triangles from 4 vertices. It takes 4 Vertex objects, index values for setting the triangle and vertex IDs and additional parameters as its function arguments. It returns a tuple of Vertex and Triangle object lists generated from the input vertices. A default triangle generator is provided as a prototype for implementation in the source code.

The return value of this function is a tuple containing two lists. First one is the list of vertices and the second one is the list of triangles.

Parameters:	points (list, tuple) – input points size_u (int) – number of elements on the u-direction size_v (int) – number of elements on the v-direction
Returns:	a tuple containing lists of vertices and triangles
Return type:	tuple

geomdl.tessellate.polygon_triangulate(tri_idx, *args)¶

Triangulates a monotone polygon defined by a list of vertices.

The input vertices must form a convex polygon and must be arranged in counter-clockwise order.

Parameters:	tri_idx (int) – triangle numbering start value args (Vertex) – list of Vertex objects
Returns:	list of Triangle objects
Return type:	list

geomdl.tessellate.make_quad_mesh(points, size_u, size_v)¶

Generates a mesh of quadrilateral elements.

Parameters:	points (list, tuple) – list of points size_u (int) – number of points on the u-direction (column) size_v (int) – number of points on the v-direction (row)
Returns:	a tuple containing lists of vertices and quads
Return type:	tuple

Helper Functions¶

geomdl.tessellate.surface_tessellate(v1, v2, v3, v4, vidx, tidx, trim_curves, tessellate_args)¶

Triangular tessellation algorithm for surfaces with no trims.

This function can be directly used as an input to make_triangle_mesh() using tessellate_func keyword argument.

Parameters:	v1 (Vertex) – vertex 1 v2 (Vertex) – vertex 2 v3 (Vertex) – vertex 3 v4 (Vertex) – vertex 4 vidx (int) – vertex numbering start value tidx (int) – triangle numbering start value trim_curves – trim curves tessellate_args (dict) – tessellation arguments
Type:	list, tuple
Returns:	lists of vertex and triangle objects in (vertex_list, triangle_list) format
Type:	tuple

geomdl.tessellate.surface_trim_tessellate(v1, v2, v3, v4, vidx, tidx, trims, tessellate_args)¶

Triangular tessellation algorithm for trimmed surfaces.

This function can be directly used as an input to make_triangle_mesh() using tessellate_func keyword argument.

Parameters:	v1 (Vertex) – vertex 1 v2 (Vertex) – vertex 2 v3 (Vertex) – vertex 3 v4 (Vertex) – vertex 4 vidx (int) – vertex numbering start value tidx (int) – triangle numbering start value trims (list, tuple) – trim curves tessellate_args (dict) – tessellation arguments
Returns:	lists of vertex and triangle objects in (vertex_list, triangle_list) format
Type:	tuple