XYDelaunayGenerator

Triangulates meshes within boundaries defined by input meshes.

Examples

Using instances of the PolyLineMeshGenerator to create a boundary and a few holes, followed by a XYDelaunayGenerator object to triangulate the region between them, the Mesh block shown in the input file snippet below generates the final mesh shown in Figure 1.

For this example a specified fixed interpolation of boundary edges is used, but refinement to a desired maximum triangle size allows automatic placement of nodes in the mesh interior.

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [hole_1]
    type = PolyLineMeshGenerator
    points = '-0.5 -0.1 0.0
              -0.3 -0.1 0.0
              -0.3 0.1 0.0
              -0.5 0.1 0.0'
    loop = true
  []
  [hole_2]
    type = PolyLineMeshGenerator
    points = '0.3 -0.1 0.0
              0.5 -0.1 0.0
              0.5 0.1 0.0
              0.3 0.1 0.0'
    loop = true
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    holes = 'hole_1
             hole_2'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
  []
[]

Figure 1: Fig. 1: Resulting triangulated mesh from a polyline boundary and holes.

With the stitching options, meshes used as "holes" can be inserted into those portions of the output mesh. For this use case some care may be required: refinement of stitched hole boundaries should be disallowed so that the boundary nodes in the newly triangulated mesh still precisely match the boundary nodes in the hole mesh.

In the input file snippet below, hole stitching is done recursively, so that each internal "boundary" polyline (after refinement) remains preserved in the final mesh shown in Figure 2.

[Mesh]
  [inner_square_sbd_0]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
    xmin = -0.4
    xmax = 0.4
    ymin = -0.4
    ymax = 0.4
  []
  [inner_square]
    type = SubdomainIDGenerator
    input = inner_square_sbd_0
    subdomain_id = 1 # Exodus dislikes quad ids matching tri ids
  []
  [layer_2_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 1.0 0.0'
    loop = true
  []
  [layer_3_bdy]
    type = PolyLineMeshGenerator
    points = '-1.5 -1.5 0.0
              1.5 -1.5 0.0
              1.5 1.5 0.0
              -1.5 1.5 0.0'
    loop = true
  []
  [layer_4_bdy]
    type = PolyLineMeshGenerator
    points = '-4.0 0.0 0.0
              0.0 -4.0 0.0
              4.0 0.0 0.0
              0.0 4.0 0.0'
    loop = true
  []
  [triang_2]
    type = XYDelaunayGenerator
    boundary = 'layer_2_bdy'
    holes = 'inner_square'
    stitch_holes = 'true'
    refine_holes = 'false'
    verify_holes = false
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.05
  []
  [triang_3]
    type = XYDelaunayGenerator
    boundary = 'layer_3_bdy'
    holes = 'triang_2'
    stitch_holes = 'true'
    refine_holes = 'false'
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.1
  []
  [triang_4]
    type = XYDelaunayGenerator
    boundary = 'layer_4_bdy'
    holes = 'triang_3'
    stitch_holes = 'true'
    refine_holes = 'false'
    verify_holes = false
    add_nodes_per_boundary_segment = 2
    refine_boundary = true
    desired_area = 0.2
  []
[]

Figure 2: Fig. 2: Resulting triangulated mesh with nested polyline boundaries and an internal grid.

Input Parameters

boundaryThe input MeshGenerator that defines the output mesh outer boundary.
C++ Type:MeshGeneratorName
Controllable:No
Description:The input MeshGenerator that defines the output mesh outer boundary.

Required Parameters

add_nodes_per_boundary_segment0How many more nodes to add in each outer boundary segment.
Default:0
C++ Type:unsigned int
Controllable:No
Description:How many more nodes to add in each outer boundary segment.
algorithmBINARYControl the use of binary search for the nodes of the stitched surfaces.
Default:BINARY
C++ Type:MooseEnum
Options:BINARY, EXHAUSTIVE
Controllable:No
Description:Control the use of binary search for the nodes of the stitched surfaces.
desired_area0Desired (maximum) triangle area, or 0 to skip uniform refinement
Default:0
C++ Type:double
Controllable:No
Description:Desired (maximum) triangle area, or 0 to skip uniform refinement
desired_area_funcDesired area as a function of x,y; omit to skip non-uniform refinement
C++ Type:std::string
Controllable:No
Description:Desired area as a function of x,y; omit to skip non-uniform refinement
hole_boundariesBoundary names to set on holes. Default IDs are numbered up from 1.
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Boundary names to set on holes. Default IDs are numbered up from 1.
holesThe MeshGenerators that define mesh holes.
C++ Type:std::vector<MeshGeneratorName>
Controllable:No
Description:The MeshGenerators that define mesh holes.
input_boundary_names2D-input-mesh boundaries defining the output mesh outer boundary
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:2D-input-mesh boundaries defining the output mesh outer boundary
input_subdomain_names1D-input-mesh subdomains defining the output mesh outer boundary
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:1D-input-mesh subdomains defining the output mesh outer boundary
output_boundaryBoundary name to set on new outer boundary. Default ID 0.
C++ Type:BoundaryName
Controllable:No
Description:Boundary name to set on new outer boundary. Default ID 0.
output_subdomain_nameSubdomain name to set on new triangles.
C++ Type:SubdomainName
Controllable:No
Description:Subdomain name to set on new triangles.
refine_boundaryTrueWhether to allow automatically refining the outer boundary.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to allow automatically refining the outer boundary.
refine_holesWhether to allow automatically refining each hole boundary.
C++ Type:std::vector<bool>
Controllable:No
Description:Whether to allow automatically refining each hole boundary.
smooth_triangulationFalseWhether to do Laplacian mesh smoothing on the generated triangles.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to do Laplacian mesh smoothing on the generated triangles.
stitch_holesWhether to stitch to the mesh defining each hole.
C++ Type:std::vector<bool>
Controllable:No
Description:Whether to stitch to the mesh defining each hole.
verbose_stitchingFalseWhether mesh stitching should have verbose output.
Default:False
C++ Type:bool
Controllable:No
Description:Whether mesh stitching should have verbose output.
verify_holesTrueVerify holes do not intersect boundary or each other. Asymptotically costly.
Default:True
C++ Type:bool
Controllable:No
Description:Verify holes do not intersect boundary or each other. Asymptotically costly.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.
save_with_nameKeep the mesh from this mesh generator in memory with the name specified
C++ Type:std::string
Controllable:No
Description:Keep the mesh from this mesh generator in memory with the name specified

Advanced Parameters

nemesisFalseWhether or not to output the mesh file in the nemesisformat (only if output = true)
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to output the mesh file in the nemesisformat (only if output = true)
outputFalseWhether or not to output the mesh file after generating the mesh
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to output the mesh file after generating the mesh
show_infoFalseWhether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not to show mesh info after generating the mesh (bounding box, element types, sidesets, nodesets, subdomains, etc)

Debugging Parameters

Input Files

(tutorials/tutorial04_meshing/app/test/tests/adv_examples/oversize.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_from_2d_bcids.i)
(test/tests/meshgenerators/parsed_curve_generator/xy_curve.i)
(tutorials/tutorial04_meshing/app/test/tests/adv_examples/pcg_xyd.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_nested.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_with_hole_names.i)
(test/tests/meshgenerators/circular_correction_generator/partial_circle_span.i)
(test/tests/meshgenerators/circular_correction_generator/partial_circle_rad.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_open_polyline.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_stitching.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_area_func.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_smoothed.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_with_holes.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_multiline.i)
(test/tests/meshgenerators/circular_correction_generator/radius_corr.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_mesh_generator.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_from_1d_sbdids.i)
(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_from_2d.i)

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_with_holes.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [hole_1]
    type = PolyLineMeshGenerator
    points = '-0.5 -0.1 0.0
              -0.3 -0.1 0.0
              -0.3 0.1 0.0
              -0.5 0.1 0.0'
    loop = true
  []
  [hole_2]
    type = PolyLineMeshGenerator
    points = '0.3 -0.1 0.0
              0.5 -0.1 0.0
              0.5 0.1 0.0
              0.3 0.1 0.0'
    loop = true
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    holes = 'hole_1
             hole_2'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_nested.i)

[Mesh]
  [inner_square_sbd_0]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
    xmin = -0.4
    xmax = 0.4
    ymin = -0.4
    ymax = 0.4
  []
  [inner_square]
    type = SubdomainIDGenerator
    input = inner_square_sbd_0
    subdomain_id = 1 # Exodus dislikes quad ids matching tri ids
  []
  [layer_2_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 1.0 0.0'
    loop = true
  []
  [layer_3_bdy]
    type = PolyLineMeshGenerator
    points = '-1.5 -1.5 0.0
              1.5 -1.5 0.0
              1.5 1.5 0.0
              -1.5 1.5 0.0'
    loop = true
  []
  [layer_4_bdy]
    type = PolyLineMeshGenerator
    points = '-4.0 0.0 0.0
              0.0 -4.0 0.0
              4.0 0.0 0.0
              0.0 4.0 0.0'
    loop = true
  []
  [triang_2]
    type = XYDelaunayGenerator
    boundary = 'layer_2_bdy'
    holes = 'inner_square'
    stitch_holes = 'true'
    refine_holes = 'false'
    verify_holes = false
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.05
  []
  [triang_3]
    type = XYDelaunayGenerator
    boundary = 'layer_3_bdy'
    holes = 'triang_2'
    stitch_holes = 'true'
    refine_holes = 'false'
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.1
  []
  [triang_4]
    type = XYDelaunayGenerator
    boundary = 'layer_4_bdy'
    holes = 'triang_3'
    stitch_holes = 'true'
    refine_holes = 'false'
    verify_holes = false
    add_nodes_per_boundary_segment = 2
    refine_boundary = true
    desired_area = 0.2
  []
[]

(tutorials/tutorial04_meshing/app/test/tests/adv_examples/oversize.i)

[Mesh]
  [hex_1]
    type = PolygonConcentricCircleMeshGenerator
    num_sides = 6
    num_sectors_per_side = '4 4 4 4 4 4'
    background_intervals = 2
    ring_radii = 4.0
    ring_intervals = 2
    ring_block_ids = '10 15'
    ring_block_names = 'center_tri center'
    background_block_ids = 20
    background_block_names = background
    polygon_size = 5.0
    preserve_volumes = on
  []
  [hex_big]
    type = PolygonConcentricCircleMeshGenerator
    num_sides = 6
    num_sectors_per_side = '4 4 4 4 4 4'
    background_intervals = 2
    ring_radii = 10.0
    ring_intervals = 2
    ring_block_ids = '110 115'
    ring_block_names = 'center2_tri center2'
    background_block_ids = 120
    background_block_names = background2
    polygon_size = 13.0
    preserve_volumes = on
  []
  [bkg_rm]
    type = BlockDeletionGenerator
    input = hex_big
    block = 'background2'
    new_boundary = 'big_pin_ext'
  []
  [hex_dummy]
    type = PolygonConcentricCircleMeshGenerator
    num_sides = 6
    num_sectors_per_side = '4 4 4 4 4 4'
    background_intervals = 2
    background_block_ids = '40 45'
    background_block_names = 'background_dummy_tri background_dummy'
    polygon_size = 5.0
    preserve_volumes = on
  []
  [assm]
    type = PatternedHexMeshGenerator
    inputs = 'hex_1 hex_dummy'
    pattern = '0 0 0 0 0;
              0 0 0 0 0 0;
             0 0 0 0 0 0 0;
            0 0 0 1 1 0 0 0;
           0 0 0 1 1 1 0 0 0;
            0 0 0 1 1 0 0 0;
             0 0 0 0 0 0 0;
              0 0 0 0 0 0;
               0 0 0 0 0'
    background_block_id = 25
    background_block_name = "assem_block"
    hexagon_size = 42
  []
  [blk_del]
    type = BlockDeletionGenerator
    input = assm
    block = 'background_dummy_tri background_dummy'
    new_boundary = 'hole_bdry'
  []
  [xyd]
    type = XYDelaunayGenerator
    boundary = 'blk_del'
    input_boundary_names = 'hole_bdry'
    refine_boundary = false
    desired_area = 1
    output_boundary = 'xyd_ext'
    output_subdomain_name = '100'
    holes = 'bkg_rm'
    stitch_holes = 'true'
  []
  [stitch]
    type = StitchedMeshGenerator
    inputs = 'blk_del xyd'
    clear_stitched_boundary_ids = true
    stitch_boundaries_pairs = 'hole_bdry xyd_ext'
    parallel_type = 'replicated'
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_from_2d_bcids.i)

[Mesh]
  [left_bdy]
    type = PolyLineMeshGenerator
    points = '-3.0 0.0 0.0
              -2.0 -1.0 0.0
              -1.0 0.0 0.0
              -2.0 2.0 0.0'
    loop = true
  []
  [right_bdy]
    type = PolyLineMeshGenerator
    points = '3.0 0.0 0.0
              2.0 -1.0 0.0
              1.0 0.0 0.0
              2.0 2.0 0.0'
    loop = true
  []
  [left_2d]
    type = XYDelaunayGenerator
    boundary = 'left_bdy'
  []
  [right_2d]
    type = XYDelaunayGenerator
    boundary = 'right_bdy'
    output_boundary = 'right_outer'
  []
  [both_2d]
    type = CombinerGenerator
    inputs = 'left_2d right_2d'
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'both_2d'
    input_boundary_names = 'right_outer' # only the right half
    refine_boundary = true
    desired_area = 0.2
  []
[]

(test/tests/meshgenerators/parsed_curve_generator/xy_curve.i)

[Mesh]
  [pcg]
    type = ParsedCurveGenerator
    x_formula = 'r*cos(t)'
    y_formula = 'y1:=r*sin(t);
                 y2:=b*sin(t);
                 if(t<pi,y1,y2)'
    section_bounding_t_values = '${fparse 0.0} ${fparse pi} ${fparse 2.0*pi}'
    constant_names = 'pi r b'
    constant_expressions = '${fparse pi} 1.0 1.5'
    nums_segments = '10 10'
    is_closed_loop = true
  []
  [hole1]
    type = ParsedCurveGenerator
    constant_names = 'th a b xs ys'
    constant_expressions = '${fparse pi/4.0} 0.25 0.5 0.1 0.3'
    x_formula = 'x0:=a*cos(t);
                 y0:=b*sin(t);
                 cos(th)*x0-sin(th)*y0+xs'
    y_formula = 'x0:=a*cos(t);
                 y0:=b*sin(t);
                 sin(th)*x0+cos(th)*y0+ys'
    section_bounding_t_values = '0.0 ${fparse 2.0*pi}'
    nums_segments = 18
    is_closed_loop = true
  []
  [hole2]
    type = ParsedCurveGenerator
    constant_names = 'th a xs ys'
    constant_expressions = '${fparse pi/2.0} 0.3 -0.1 -0.8'
    x_formula = 'x0:=a*(1+cos(t))*cos(t);
                 y0:=a*(1+cos(t))*sin(t);
                 cos(th)*x0-sin(th)*y0+xs'
    y_formula = 'x0:=a*(1+cos(t))*cos(t);
                 y0:=a*(1+cos(t))*sin(t);
                 sin(th)*x0+cos(th)*y0+ys'
    section_bounding_t_values = '0 ${fparse pi} ${fparse 2.0*pi}'
    nums_segments = '9 9'
    is_closed_loop = true
  []
  [xydg]
    type = XYDelaunayGenerator
    boundary = 'pcg'
    holes = 'hole1 hole2'
    add_nodes_per_boundary_segment = 1
    refine_boundary = false
    desired_area = 0.03
  []
[]

(tutorials/tutorial04_meshing/app/test/tests/adv_examples/pcg_xyd.i)

[Mesh]
    # make a unit hexagonal pin
    [hex_1]
      type = PolygonConcentricCircleMeshGenerator
      num_sides = 6
      num_sectors_per_side = '2 2 2 2 2 2'
      background_intervals = 2
      ring_radii = 4.0
      ring_intervals = 2
      ring_block_ids = '10 15'
      ring_block_names = 'pin_tri pin_quad'
      background_block_ids = 20
      background_block_names = pin_background
      polygon_size = 5.0
      preserve_volumes = on
    []
    # stitch the unit pins into a hexagonal pattern
    [pattern]
      type = PatternedHexMeshGenerator
      inputs = 'hex_1'
      hexagon_size=25
      background_block_id = 30
      background_block_name = assembly_background
      pattern = '0 0 0;
                0 0 0 0;
               0 0 0 0 0;
                0 0 0 0;
                 0 0 0'
    []
    # Add a layer of circular peripheral region
    [tmg1]
        type = PeripheralTriangleMeshGenerator
        input = pattern
        peripheral_ring_radius = 35
        peripheral_ring_num_segments = 50
        peripheral_ring_block_name = peripheral_1
        desired_area = 8
    []
    # Add another layer of circular peripheral region
    [tmg2]
        type = PeripheralTriangleMeshGenerator
        input = tmg1
        peripheral_ring_radius = 38
        peripheral_ring_num_segments = 80
        peripheral_ring_block_name = peripheral_2
        desired_area = 6
    []
    # Define the complex boundary shape using ParsedCurveMG
    [pcg1]
        type = ParsedCurveGenerator
        x_formula = 't1:=t;
                     t2:=t-1;
                     t3:=t-2;
                     t4:=t-3;
                     x1:=r*cos(t1*(th1-th0)+th0);
                     x2_0:=r*cos(th1);
                     x2_1:=x2_0-Lx;
                     x2:=x2_0+(x2_1-x2_0)*t2;
                     rs:=abs(r*sin(th1));
                     rth0:=1.5*pi;
                     rth1:=0.5*pi;
                     x3:=x2_1+rs*cos(rth0+(rth1-rth0)*t3);
                     x4_1:=r*cos(th1);
                     x4_0:=x4_1-Lx;
                     x4:=x4_0+(x4_1-x4_0)*t4;
                     if(t<1,x1,if(t<2,x2,if(t<3,x3,x4)))'
        y_formula = 't1:=t;
                     t2:=t-1;
                     t3:=t-2;
                     t4:=t-3;
                     y1:=r*sin(t1*(th1-th0)+th0);
                     y2:=r*sin(th1);
                     rs:=abs(r*sin(th1));
                     rth0:=1.5*pi;
                     rth1:=0.5*pi;
                     y3:=rs*sin(rth0+(rth1-rth0)*t3);
                     y4:=r*sin(th0);
                     if(t<1,y1,if(t<2,y2,if(t<3,y3,y4)))'
        section_bounding_t_values  = '0 1 2 3 4'
        constant_names =       'pi           r    th0               th1                    Lx'
        constant_expressions = '${fparse pi} 100.0 ${fparse pi/9.0} ${fparse pi/9.0*17.0} 10.0'
        nums_segments = '50 3 15 3'
        is_closed_loop = true
    []
    # fill the curve defined above and include the internal patterned pin regions
    [xydg1]
        type = XYDelaunayGenerator
        boundary = 'pcg1'
        holes = 'tmg2'
        add_nodes_per_boundary_segment = 0
        refine_boundary = false
        desired_area = 30
        output_subdomain_name = xy_layer_1
        stitch_holes = 'true'
        refine_holes = 'false'
    []
    # Define the control drum pin structure
    # As we currently do not have a pure ring mesher
    # We will use PCCMG and then delete the hexagonal outermost layer to get the rings
    [cd]
      type = PolygonConcentricCircleMeshGenerator
      num_sides = 6
      num_sectors_per_side = '6 6 6 6 6 6'
      background_intervals = 2
      ring_radii = '27 30 32'
      ring_intervals = '2 2 2'
      ring_block_ids = '110 115 120 125'
      ring_block_names = 'cd_1_tri cd_1_quad cd_2 cd_3'
      background_block_ids = 130
      background_block_names = cd_background
      polygon_size = 40
      preserve_volumes = on
    []
    # Define the absorber region of the control drum
    [cd_azi_define]
        type = AzimuthalBlockSplitGenerator
        input = cd
        start_angle = 300
        angle_range = 120
        old_blocks = '120'
        new_block_ids = '121'
        new_block_names = 'absorber'
        preserve_volumes = true
    []
    # Delete the hexagonal outmost layer
    [cd_bd]
        type = BlockDeletionGenerator
        input = cd_azi_define
        block = cd_background
    []
    # Translate the control drum to desired position
    [cd_translate]
        type = TransformGenerator
        input = cd_bd
        transform = translate
        vector_value = '${fparse 100.0*cos(pi/9.0)-10.0} 0 0'
    []
    # Define the small pin near the external boundary
    # We are using the similar PCCMG+deletion approach
    [outer_pin]
      type = PolygonConcentricCircleMeshGenerator
      num_sides = 6
      num_sectors_per_side = '2 2 2 2 2 2'
      background_intervals = 2
      ring_radii = '10 12'
      ring_intervals = '2 2'
      ring_block_ids = '210 215 220'
      ring_block_names = 'op_1_tri op_1_quad op_2'
      background_block_ids = 230
      background_block_names = op_background
      polygon_size = 15
      preserve_volumes = on
    []
    # delete the outermost layer to get a circular pin mesh
    [op_bd]
        type = BlockDeletionGenerator
        input = outer_pin
        block = op_background
    []
    # translate to the desired position
    [op_translate]
        type = TransformGenerator
        input = op_bd
        transform = translate
        vector_value = '${fparse 120/sqrt(2)} ${fparse 120/sqrt(2)} 0'
    []
    # Define the circular curve boundary
    [pcg2]
        type = ParsedCurveGenerator
        x_formula = 'r*cos(t)'
        y_formula = 'r*sin(t)'
        section_bounding_t_values = '0 ${fparse 2*pi}'
        constant_names =       'pi           r'
        constant_expressions = '${fparse pi} 140.0'
        nums_segments = '100'
        is_closed_loop = true
    []
    # fill the curve defined above including the internal structure, control drum and outer pin
    [xydg2]
        type = XYDelaunayGenerator
        boundary = 'pcg2'
        holes = 'xydg1 cd_translate op_translate'
        add_nodes_per_boundary_segment = 0
        refine_boundary = false
        desired_area = 30
        output_subdomain_name = xy_layer_2
        stitch_holes = 'true true true'
        refine_holes = 'false false false'
    []
    # add another layer of circular peripheral region
    [tmg3]
        type = PeripheralTriangleMeshGenerator
        input = xydg2
        peripheral_ring_radius = 150
        peripheral_ring_num_segments = 100
        peripheral_ring_block_name = peripheral_3
        desired_area = 20
    []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_nested.i)

[Mesh]
  [inner_square_sbd_0]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
    xmin = -0.4
    xmax = 0.4
    ymin = -0.4
    ymax = 0.4
  []
  [inner_square]
    type = SubdomainIDGenerator
    input = inner_square_sbd_0
    subdomain_id = 1 # Exodus dislikes quad ids matching tri ids
  []
  [layer_2_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 1.0 0.0'
    loop = true
  []
  [layer_3_bdy]
    type = PolyLineMeshGenerator
    points = '-1.5 -1.5 0.0
              1.5 -1.5 0.0
              1.5 1.5 0.0
              -1.5 1.5 0.0'
    loop = true
  []
  [layer_4_bdy]
    type = PolyLineMeshGenerator
    points = '-4.0 0.0 0.0
              0.0 -4.0 0.0
              4.0 0.0 0.0
              0.0 4.0 0.0'
    loop = true
  []
  [triang_2]
    type = XYDelaunayGenerator
    boundary = 'layer_2_bdy'
    holes = 'inner_square'
    stitch_holes = 'true'
    refine_holes = 'false'
    verify_holes = false
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.05
  []
  [triang_3]
    type = XYDelaunayGenerator
    boundary = 'layer_3_bdy'
    holes = 'triang_2'
    stitch_holes = 'true'
    refine_holes = 'false'
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.1
  []
  [triang_4]
    type = XYDelaunayGenerator
    boundary = 'layer_4_bdy'
    holes = 'triang_3'
    stitch_holes = 'true'
    refine_holes = 'false'
    verify_holes = false
    add_nodes_per_boundary_segment = 2
    refine_boundary = true
    desired_area = 0.2
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_with_hole_names.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [hole_1]
    type = PolyLineMeshGenerator
    points = '-0.5 -0.1 0.0
              -0.3 -0.1 0.0
              -0.3 0.1 0.0
              -0.5 0.1 0.0'
    loop = true
  []
  [hole_2]
    type = PolyLineMeshGenerator
    points = '0.3 -0.1 0.0
              0.5 -0.1 0.0
              0.5 0.1 0.0
              0.3 0.1 0.0'
    loop = true
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    holes = 'hole_1
             hole_2'
    hole_boundaries = 'left_hole
                       right_hole'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
  []
[]

(test/tests/meshgenerators/circular_correction_generator/partial_circle_span.i)

[Mesh]
  [pmg]
    type = ParsedCurveGenerator
    x_formula = 't1:=t;
                   t2:=t-1;
                   t3:=t-2;
                   t4:=t-3;
                   t5:=t-4;
                   t6:=t-5;
                   x1:=t1-1;
                   x2:=0.0;
                   x3:=0.5+cos(-2/3*pi-2/3*pi*t3);
                   x4:=0.0;
                   x5:=-t5;
                   x6:=-1;
                   if(t<1,x1,(if(t<2,x2,(if(t<3,x3,(if(t<4,x4,(if(t<5,x5,x6)))))))))'
    y_formula = 't1:=t;
                   t2:=t-1;
                   t3:=t-2;
                   t4:=t-3;
                   t5:=t-4;
                   t6:=t-5;
                   y1:=-1;
                   y2:=-1+(1-sqrt(3)/2)*t2;
                   y3:=sin(-2/3*pi-2/3*pi*t3);
                   y4:=sqrt(3)/2+(1-sqrt(3)/2)*t4;
                   y5:=1;
                   y6:=1-t6*2;
                   if(t<1,y1,(if(t<2,y2,(if(t<3,y3,(if(t<4,y4,(if(t<5,y5,y6)))))))))'
    section_bounding_t_values = '0 1 2 3 4 5 6'
    constant_names = 'pi'
    constant_expressions = '${fparse pi}'
    nums_segments = '5 2 10 2 5 10'
    is_closed_loop = true
  []
  [xyd]
    type = XYDelaunayGenerator
    boundary = pmg
    desired_area = 0.05
    refine_boundary = false
  []
  [add_bdry]
    type = ParsedGenerateSideset
    input = xyd
    combinatorial_geometry = 'abs((x-0.5)^2+y^2-1.0)<tol'
    constant_names = 'tol'
    constant_expressions = '0.05'
    new_sideset_name = 'circ'
  []
  [ccg]
    type = CircularBoundaryCorrectionGenerator
    input = add_bdry
    input_mesh_circular_boundaries = 'circ'
    custom_circular_tolerance = 1e-8
    move_end_nodes_in_span_direction = true
  []
[]

(test/tests/meshgenerators/circular_correction_generator/partial_circle_rad.i)

[Mesh]
  [pmg]
    type = ParsedCurveGenerator
    x_formula = 't1:=t;
                 t2:=t-1;
                 t3:=t-2;
                 t4:=t-3;
                 t5:=t-4;
                 x1:=t1-1;
                 x2:=0.0;
                 x3:=0.5*cos(-pi/2-pi*t3/2);
                 x4:=-0.5-0.5*t4;
                 x5:=-1;
                 if(t<1,x1,(if(t<2,x2,(if(t<3,x3,(if(t<4,x4,x5)))))))'
    y_formula = 't1:=t;
                 t2:=t-1;
                 t3:=t-2;
                 t4:=t-3;
                 t5:=t-4;
                 y1:=-1;
                 y2:=-1+0.5*t2;
                 y3:=0.5*sin(-pi/2-pi*t3/2);
                 y4:=0;
                 y5:=-t5;
                 if(t<1,y1,(if(t<2,y2,(if(t<3,y3,(if(t<4,y4,y5)))))))'
    section_bounding_t_values = '0 1 2 3 4 5'
    constant_names = 'pi'
    constant_expressions = '${fparse pi}'
    nums_segments = '10 5 10 5 10'
    is_closed_loop = true
  []
  [xyd]
    type = XYDelaunayGenerator
    boundary = pmg
    desired_area = 0.05
    refine_boundary = false
  []
  [add_bdry]
    type = ParsedGenerateSideset
    input = xyd
    combinatorial_geometry = 'abs(x^2+y^2-0.25)<tol'
    constant_names = 'tol'
    constant_expressions = '0.01'
    new_sideset_name = 'circ'
  []
  [ccg]
    type = CircularBoundaryCorrectionGenerator
    input = add_bdry
    input_mesh_circular_boundaries = 'circ'
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_open_polyline.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = false
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_stitching.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [hole_1]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
    xmin = -0.5
    xmax = -0.3
    ymin = -0.1
    ymax = 0.1
  []
  [hole_2]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
    xmin = 0.3
    xmax = 0.5
    ymin = -0.1
    ymax = 0.1
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    holes = 'hole_1
             hole_2'
    stitch_holes = 'true
                    false'
    refine_holes = 'false
                    false'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
    output_subdomain_name = "triangles"
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_area_func.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [hole_1]
    type = PolyLineMeshGenerator
    points = '-0.5 -0.1 0.0
              -0.3 -0.1 0.0
              -0.3 0.1 0.0
              -0.5 0.1 0.0'
    loop = true
  []
  [hole_2]
    type = PolyLineMeshGenerator
    points = '0.3 -0.1 0.0
              0.5 -0.1 0.0
              0.5 0.1 0.0
              0.3 0.1 0.0'
    loop = true
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    holes = 'hole_1
             hole_2'
    desired_area_func = '(x+1.5)*(y+1.5)*0.01'
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_smoothed.i)

[Mesh]
  [inner_square_sbd_0]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
    xmin = -0.4
    xmax = 0.4
    ymin = -0.4
    ymax = 0.4
  []
  [inner_square]
    type = SubdomainIDGenerator
    input = inner_square_sbd_0
    subdomain_id = 1 # Exodus dislikes quad ids matching tri ids
  []
  [layer_2_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 1.0 0.0'
    loop = true
  []
  [layer_3_bdy]
    type = PolyLineMeshGenerator
    points = '-1.5 -1.5 0.0
              1.5 -1.5 0.0
              1.5 1.5 0.0
              -1.5 1.5 0.0'
    loop = true
  []
  [layer_4_bdy]
    type = PolyLineMeshGenerator
    points = '-4.0 0.0 0.0
              0.0 -4.0 0.0
              4.0 0.0 0.0
              0.0 4.0 0.0'
    loop = true
  []
  [triang_2]
    type = XYDelaunayGenerator
    boundary = 'layer_2_bdy'
    holes = 'inner_square'
    stitch_holes = 'true'
    refine_holes = 'false'
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.05
    smooth_triangulation = true
  []
  [triang_3]
    type = XYDelaunayGenerator
    boundary = 'layer_3_bdy'
    holes = 'triang_2'
    stitch_holes = 'true'
    refine_holes = 'false'
    add_nodes_per_boundary_segment = 2
    refine_boundary = false
    desired_area = 0.1
    # smooth_triangulation = false # default
  []
  [triang_4]
    type = XYDelaunayGenerator
    boundary = 'layer_4_bdy'
    holes = 'triang_3'
    stitch_holes = 'true'
    refine_holes = 'false'
    add_nodes_per_boundary_segment = 2
    refine_boundary = true
    desired_area = 0.2
    smooth_triangulation = true
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_with_holes.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [hole_1]
    type = PolyLineMeshGenerator
    points = '-0.5 -0.1 0.0
              -0.3 -0.1 0.0
              -0.3 0.1 0.0
              -0.5 0.1 0.0'
    loop = true
  []
  [hole_2]
    type = PolyLineMeshGenerator
    points = '0.3 -0.1 0.0
              0.5 -0.1 0.0
              0.5 0.1 0.0
              0.3 0.1 0.0'
    loop = true
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    holes = 'hole_1
             hole_2'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_multiline.i)

[Mesh]
  [line1]
    type = PolyLineMeshGenerator
    points = '0.0 0.0 0.0
              1.0 0.0 0.0'
  []
  [line2]
    type = PolyLineMeshGenerator
    points = '1.0 0.0 0.0
              0.0 1.0 0.0'
  []
  [outer_bdy]
    type = StitchedMeshGenerator
    inputs = "line1 line2"
    stitch_boundaries_pairs = '2 1'
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    add_nodes_per_boundary_segment = 4
    refine_boundary = false
    desired_area = 0.05
  []
[]

(test/tests/meshgenerators/circular_correction_generator/radius_corr.i)

[Mesh]
  [cir1]
    type = ParsedCurveGenerator
    x_formula = 'r*cos(t*2*pi)'
    y_formula = 'r*sin(t*2*pi)'
    section_bounding_t_values = '0 1'
    constant_names = 'pi r'
    constant_expressions = '${fparse pi} 1.0'
    nums_segments = '10'
    is_closed_loop = true
  []
  [cir2]
    type = ParsedCurveGenerator
    x_formula = 'r*cos(t*2*pi)'
    y_formula = 'r*sin(t*2*pi)+0.5'
    section_bounding_t_values = '0 1'
    constant_names = 'pi r'
    constant_expressions = '${fparse pi} 2.0'
    nums_segments = '15'
    is_closed_loop = true
  []
  [xyd1]
    type = XYDelaunayGenerator
    boundary = cir1
    desired_area = 0.5
    refine_boundary = false
    # output_boundary = '10'
    output_subdomain_name = '10'
  []
  [xyd2]
    type = XYDelaunayGenerator
    boundary = cir2
    holes = xyd1
    refine_holes = 'false'
    desired_area = 0.5
    refine_boundary = false
    output_subdomain_name = '20'
    hole_boundaries = '10'
  []
  [ccg]
    type = CircularBoundaryCorrectionGenerator
    input = xyd2
    input_mesh_circular_boundaries = '0 10'
    custom_circular_tolerance = 1e-8
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_mesh_generator.i)

[Mesh]
  [outer_bdy]
    type = PolyLineMeshGenerator
    points = '-1.0 0.0 0.0
              0.0 -1.0 0.0
              1.0 0.0 0.0
              0.0 2.0 0.0'
    loop = true
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    add_nodes_per_boundary_segment = 3
    refine_boundary = false
    desired_area = 0.05
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_from_1d_sbdids.i)

[Mesh]
  [left_bdy]
    type = PolyLineMeshGenerator
    points = '-3.0 0.0 0.0
              -2.0 -1.0 0.0
              -1.0 0.0 0.0
              -2.0 2.0 0.0'
    loop = true
  []
  [right_bdy]
    type = PolyLineMeshGenerator
    points = '3.0 0.0 0.0
              2.0 -1.0 0.0
              1.0 0.0 0.0
              2.0 2.0 0.0'
    loop = true
  []
  [right_sbd1]
    type = SubdomainIDGenerator
    input = right_bdy
    subdomain_id = 1
  []
  [both_bdy]
    type = CombinerGenerator
    inputs = 'left_bdy right_sbd1'
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'both_bdy'
    input_subdomain_names = 1 # only the right half
    refine_boundary = true
    desired_area = 0.2
  []
[]

(test/tests/meshgenerators/xy_delaunay_generator/xydelaunay_from_2d.i)

[Mesh]
  [outer_bdy]
    # Avoid squares here to make diagonal selection more well-defined
    type = ConcentricCircleMeshGenerator
    num_sectors = 4
    radii = '0.5'
    rings = '3'
    has_outer_square = false
    preserve_volumes = false
  []
  [triang]
    type = XYDelaunayGenerator
    boundary = 'outer_bdy'
    refine_boundary = true
    desired_area = 0.01
  []

  parallel_type = replicated  # for ConcentricCircleMeshGenerator
[]

Examples
Input Parameters
Input Files