Overview

This tutorial provides detailed configuration methods for various local size fields in mesh generation to control the size of generated meshes.

Feature Description

Control mesh size by setting local size fields, such as adaptive calculation based on curvature or narrow regions, or manually specifying sizes for specific areas.
Supports multiple local size fields. The base class in JSON files is LocalSizeField, with member functions including: AutomaticField, MaxField, MinField, BallField, BoxField, CylinderField, DistanceField, ThresholdField, RestrictField.

Local Size Field Settings

Multiple local size fields can be configured, but only one background field can be set which controls the global mesh size.
DistanceField is typically used together with ThresholdField.
The program will assert and prevent any cyclic dependencies in size field configuration. Example: MinField calls RestrictField, RestrictField calls ThresholdField, ThresholdField calls MinField. MinField->RestrictField->ThresholdField->MinField

JSON Template Example

{
  "MeshSize": [
    {
      "MaxSize": 5,
      "MinSize": 0.5,
      "GrowthRate": 1.4,
      "MeshingDim": 2,
      "SelectedEntities": []
    }
  ],
 
  "LocalSizeField": {
    "BGField": 1,
 
    "AutomaticField": {
      "CurvatureFactor": 0.5,
      "NarrowRegionResolution2D": 1.0,
      "NarrowRegionResolution3D": 0.5,
      "GrowthRate": 1.4,
      "Tag": 1
    },
    "MinField": {
        "SelectedFieldTags": [
          4,
          6,
          7
        ],
        "Tag": 2
    },
    "MaxField": {
        "SelectedFieldTags": [
          4,
          6,
          7
        ],
        "Tag": 3
    },
    "BallField": [
      {
        "Center": [
          11.0,
          13.0,
          15.5
        ],
        "Radius": 20.0,
        "InterLocSize": 1,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 4
      },
      {
        "Center": [
          11.0,
          13.0,
          15.5
        ],
        "Radius": 20.0,
        "InterLocSize": 1,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 5
      }
    ],
    "BoxField": [
      {
        "MinPoint": [
          0.0,
          0.0,
          0.0
        ],
        "MaxPoint": [
          20.0,
          20.0,
          20.0
        ],
        "InterLocSize": 1.0,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 6
      }
    ],
    "CylinderField": [
      {
        "Center": [
          0.0,
          0.0,
          0.0
        ],
        "Axis": [
          0.0,
          0.0,
          1.0
        ],
        "Radius": 20.0,
        "InterLocSize": 1,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 7
      }
    ],
    "DistanceField": [
      {
        "SelectedVertexTags": [
          0,
          1,
          2
        ],
        "SelectedEdgeTags": [
          69,
          73
        ],
        "SelectedFaceTags": [
          20,
          48
        ],
        "SelectedSolidTags": [],
        "Tag": 8
      }
    ],
    "ThresholdField": [
      {
        "MinDist": 5.0,
        "MaxDist": 10.0,
        "MaxSize": 5.0,
        "MinSize": 1.0,
        "SelectedFieldTag": 8,
        "Tag": 9
      }
    ],
    "RestrictField": [
      {
        "IsBoundary": true,
       "SelectedVertexTags": [
          0,
          1,
          2
        ],
        "SelectedEdgeTags": [
          73
        ],
        "SelectedFaceTags": [
          20
        ],
        "SelectedSolidTags": [],
        "SelectedFieldTag": 8,
        "Tag": 10
      }
    ]
  }
}

Class	Key	Required	Value Range	Default	Description
LocalSizeField	BGField	Yes	Integer [1, inf]	1	The Tag value of the local size field, used as the background size field
LocalSizeField	AutomaticField	No			Automatically calculates global mesh size based on curvature and narrow regions
AutomaticField	CurvatureFactor	No	[0, inf]	0.5	Determines if curvature-based sizing is enabled. Smaller values result in smaller sizes (denser mesh) in high-curvature regions
AutomaticField	NarrowRegionResolution2D	No	[0, inf]	1	Determines if sizing is calculated based on 2D narrow regions (self-intersections). Value represents number of mesh layers in narrow regions - higher values mean denser mesh
AutomaticField	NarrowRegionResolution3D	No	[0, inf]	1	Determines if sizing is calculated based on 3D narrow regions (between surfaces). Value represents number of mesh layers in narrow regions - higher values mean denser mesh
AutomaticField	GrowthRate	Yes	[1, inf]	1.4	Allowed growth rate between adjacent size transitions
AutomaticField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag (must not duplicate other Tags)
LocalSizeField	MinField	No	Integer [1, inf]		Takes the minimum size from all input size fields
MinField	SelectedFieldTags	Yes	[1, 2, 3...]	-	Input the Tags of size fields to take minimum size from (must exist)
MinField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	MaxField	No			Takes the maximum size from all input size fields
MaxField	SelectedFieldTags	Yes	[1, 2, 3...]	-	Input the Tags of size fields to take maximum size from (must exist)
MaxField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	BallField	No			Specifies size values within a defined sphere
BallField	Center	Yes	Any 3D coordinates	-	Sphere center coordinates (three floating-point numbers)
BallField	Radius	Yes	[0, inf]	0.0	Sphere radius
BallField	InterLocSize	Yes	[0, inf]	0.0	Size value inside the sphere
BallField	OutLocSize	No	[0, inf]	0.0	Size value outside the sphere
BallField	Thickness	No	[0, inf]	0.0	Sphere boundary transition layer - size in this layer is interpolated between InterLocSize and OutLocSize. Setting Thickness requires OutLocSize
BallField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	BoxField	No			Specifies size values within a defined box (determined by min/max points)
BoxField	MinPoint	Yes	Any 3D coordinates	-	Box minimum point
BoxField	MaxPoint	Yes	Any 3D coordinates	-	Box maximum point
BoxField	InterLocSize	Yes	[0, inf]	0.0	Size value inside the box
BoxField	OutLocSize	No	[0, inf]	0.0	Size value outside the box
BoxField	Thickness	No	[0, inf]	0.0	Box boundary transition layer (similar to BallField). Setting Thickness requires OutLocSize
BoxField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	CylinderField	No			Specifies size values within a defined cylinder
CylinderField	Center	Yes	Any 3D coordinates	-	Cylinder center coordinates (three floating-point numbers)
CylinderField	Axis	Yes	Any 3D non-zero vector	-	Cylinder axis (three floating-point numbers)
CylinderField	Radius	Yes	[0, inf]	0.0	Cylinder radius
CylinderField	InterLocSize	Yes	[0, inf]	0.0	Size value inside the cylinder
CylinderField	OutLocSize	No	[0, inf]	0.0	Size value outside the cylinder
CylinderField	Thickness	No	[0, inf]	0.0	Cylinder boundary transition layer (similar to BallField). Setting Thickness requires OutLocSize
CylinderField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	DistanceField	No			Uses distance to input geometry (points, edges, faces, solids) as size, typically used with ThresholdField
DistanceField	SelectedVertexTags	No	[1, 2, 3...]	-	Input point Tags
DistanceField	SelectedEdgeTags	No	[1, 2, 3...]	-	Input edge Tags
DistanceField	SelectedFaceTags	No	[1, 2, 3...]	-	Input face Tags
DistanceField	SelectedSolidTags	No	[1, 2, 3...]	-	Input solid Tags
DistanceField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	ThresholdField	No			Interpolates new sizes between MinDist and MaxDist based on input field's calculated sizes
ThresholdField	MinDist	Yes	[0, inf]	0.0	Minimum size threshold
ThresholdField	MaxDist	Yes	[0, inf]	0.0	Maximum size threshold
ThresholdField	MaxSize	Yes	[0, inf]	0.0	Returns MaxSize if input field's calculated size exceeds MinDist
ThresholdField	MinSize	Yes	[0, inf]	0.0	Returns MinSize if input field's calculated size is less than MinDist
ThresholdField	SelectedFieldTag	Yes	Integer [1, inf]	1	Input size field Tag (typically DistanceField)
ThresholdField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag
LocalSizeField	RestrictField	No			Only calculates sizes on input geometry (points, edges, faces, solids) using the input size field
RestrictField	IsBoundary	No	[true, false]	true	Whether to calculate sizes on the boundary of input geometry
RestrictField	SelectedVertexTags	No	[1, 2, 3...]	-	Input point Tags
RestrictField	SelectedEdgeTags	No	[1, 2, 3...]	-	Input edge Tags
RestrictField	SelectedFaceTags	No	[1, 2, 3...]	-	Input face Tags
RestrictField	SelectedSolidTags	No	[1, 2, 3...]	-	Input solid Tags
RestrictField	SelectedFieldTag	Yes	Integer [1, inf]	1	Input size field Tag
RestrictField	Tag	Yes	Integer [1, inf]	1	Current size field's Tag

Function Description

The JSON file above provides the configuration methods for each size field. In practical use, you can set the corresponding size field according to your needs or change the value of BGField in the JSON file to use different size fields. Next, we will set different values for BGField in the JSON file to use different size fields.

AutomaticField: Automatically calculates global size based on curvature and narrow regions

Set "BGField": 1. In this case, BGField is the Tag parameter of AutomaticField, so AutomaticField will be used.

"AutomaticField": {
      "CurvatureFactor": 0.5,
      "NarrowRegionResolution2D": 1.0,
      "NarrowRegionResolution3D": 0.5,
      "GrowthRate": 1.4,
      "Tag": 1
    }

If coupling with other size fields is needed, set MinField or MaxField as the background field. Input the Tag of AutomaticField and other size fields to be coupled into MinField or MaxField.
The result is as follows:

MinField: Takes the minimum size from all input size fields

Set "BGField": 2. In this case, BGField is the Tag parameter of MinField, so MinField will be used.

"MinField": {
        "SelectedFieldTags": [
          4,
          6,
          7
        ],
        "Tag": 2
    }

For any point, the size is calculated from all input fields, and the minimum size is returned.The result is as follows:

MaxField: Takes the maximum size from all input size fields

Set "BGField": 3. In this case, BGField is the Tag parameter of MaxField, so MaxField will be used.

"MaxField": {
        "SelectedFieldTags": [
          4,
          6,
          7
        ],
        "Tag": 3
    }

For any point, the size is calculated from all input fields, and the maximum size is returned. The result is as follows:

BallField: Specifies the mesh size inside a sphere

Set "BGField": 4. In this case, BGField is the Tag parameter of BallField, so BallField will be used.

"BallField": [
      {
        "Center": [
          11.0,
          13.0,
          15.5
        ],
        "Radius": 20.0,
        "InterLocSize": 1,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 4
      }
    ]

Thickness and OutLocSize are optional.The result is as follows:

BoxField: Specifies the mesh size inside a box

Set "BGField": 6. In this case, BGField is the Tag parameter of BoxField, so BoxField will be used.

"BoxField": [
      {
        "MinPoint": [
          0.0,
          0.0,
          0.0
        ],
        "MaxPoint": [
          20.0,
          20.0,
          20.0
        ],
        "InterLocSize": 1.0,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 6
      }
    ]

Thickness and OutLocSize are optional.

The result is as follows:

CylinderField: Specifies the mesh size inside a cylinder

Set "BGField": 7. In this case, BGField is the Tag parameter of CylinderField, so CylinderField will be used.

"CylinderField": [
      {
        "Center": [
          0.0,
          0.0,
          0.0
        ],
        "Axis": [
          0.0,
          0.0,
          1.0
        ],
        "Radius": 20.0,
        "InterLocSize": 1,
        "OutLocSize": 5,
        "Thickness": 10,
        "Tag": 7
      }
    ]

Thickness and OutLocSize are optional.

The result is as follows:

DistanceField: Calculates the distance from any point on the model to the input geometry (points, edges, faces, or solids)

Set "BGField": 8. In this case, BGField is the Tag parameter of DistanceField, so DistanceField will be used.

"DistanceField": [
      {
        "SelectedVertexTags": [
          0,
          1,
          2
        ],
        "SelectedEdgeTags": [
          69,
          73
        ],
        "SelectedFaceTags": [
          20,
          48
        ],
        "SelectedSolidTags": [],
        "Tag": 8
      }
    ]

The distance is used as the mesh size. Therefore, when the distance is smaller than the global minsize, minsize is used. When the distance is larger than the global maxsize, maxsize is used. Some geometries can be omitted.

The result is as follows:

ThresholdField: Returns an appropriate size based on the distance or size value of the lookup point

Set "BGField": 9. In this case, BGField is the Tag parameter of ThresholdField, so ThresholdField will be used.

"ThresholdField": [
      {
        "MinDist": 5.0,
        "MaxDist": 10.0,
        "MaxSize": 5.0,
        "MinSize": 1.0,
        "SelectedFieldTag": 8,
        "Tag": 9
      }
    ]

This is typically used in combination with DistanceField (i.e., specifying DistanceField as the selected size field in ThresholdField).

If the distance or size value ls of the lookup point is < MinDist, MinSize (from the threshold field) is returned.

If the distance or size value ls of the lookup point is > MaxDist, MaxSize (from the threshold field) is returned.

If the distance or size value ls of the lookup point is between MinDist and MaxDist, a new size is interpolated based on MinSize and MaxSize.
The result is as follows:

RestrictField: Applies the input size field only on the input geometry (points, edges, faces, or solids)

Set "BGField": 10. In this case, BGField is the Tag parameter of RestrictField, so RestrictField will be used.

 "RestrictField": [
  {
    "IsBoundary": true,
   "SelectedVertexTags": [
      0,
      1,
      2
    ],
    "SelectedEdgeTags": [
      73
    ],
    "SelectedFaceTags": [
      20
    ],
    "SelectedSolidTags": [],
    "SelectedFieldTag": 8,
    "Tag": 10
  }
]

The result is as follows:

Click here example03 to get the complete source code for the mesh size control example. Everyone can download it as needed.