gambit 2.3 lecture 05a facemeshing

Fluent User Services Center

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Introductory GAMBIT Training

GAMBIT 2.3 June 2006

Edge and Face Meshing

5-1 © 2006 Fluent Inc.

Edge and Face Meshing


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Meshing - General

� To reduce overall mesh size, confine smaller cells to areas where they

are needed

� Locations of large flow field gradients.

� Locations of geometric details you wish to resolve.

� Controlling cell size distribution

� Edges, faces, and volumes can be meshed directly.


� Edges, faces, and volumes can be meshed directly.

� A uniform mesh is generated unless pre-meshing or size functions are

used.

� Pre-meshing

� Edge meshes can be graded (varying interval size on edge)

� A graded edge mesh can be used to control the cell size distribution of a

face mesh.

� Controlling distribution of cell size on face mesh also controls the cell size

distribution of the volume mesh.

� Size functions and boundary layers

� Allow direct control of cell size distribution on edges, faces and volumes

directly for automatic meshing.


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Edge Meshing

� Edge mesh distribution is controlled through the

spacing and grading parameters on the Mesh Edges

form.

� Picking

� Temporary graphics

� Links, Directions


� Links, Directions

� Grading/Spacing

� Special characteristics

� Apply and Defaults

� Invert and Reverse

� Options


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Edge Meshing

� Sense

� Sense is used to show direction of grading

� Every picked edge will show its sense direction using an arrow

� The sense can be reversed by a shift+middle-click on the last edge picked

(this is in addition to the “next” functionality) or by clicking the Reverse

button


� Edge mesh preview

� When you pick an edge, the edge mesh is displayed using white nodes.

� This is a temporary mesh that has not been applied to the edge.

� Displayed edge mesh is based on current grading and spacing parameters

� If you modify the grading or spacing, the temporary mesh will be updated

immediately.

� Meshing the edge

� The edge mesh is generated by clicking the Apply button.

� The nodes will then be displayed in blue.


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Grading

� Controls mesh density distribution along an edge.

� Grading can produce single-sided or double-sided mesh

� Doubled-sided mesh can be symmetric or asymmetric.

� Symmetric schemes produce symmetric mesh about edge

center.

� Asymmetric schemes can produce asymmetric mesh about

edge center.

Single-sided grading

Symmetric grading


edge center.

� Single-sided grading:

� Uses a multiplicative constant, R, to describe the ratio of

the length of two adjacent mesh elements:

� R can be a user-specified value (Successive Ratio) or

calculated by GAMBIT.

� GAMBIT also uses edge length and spacing information to

determine R.

Asymmetric grading


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Double Sided Grading

� Double-sided grading can be generated by activating the

double sided option in the Mesh Edge form.

� Asymmetric grading is possible when the double-sided

option is used with:

� Successive Ratio, First Length, Last Length, First-Last

Ratio, and Last-First Ratio

� The mesh is symmetric if R = R


� The mesh is symmetric if R1 = R2

� The mesh is asymmetric if R1 ≠ R2.

� Edge center is determined automatically.

� Some schemes implicitly generate double sided grading

that is symmetric.


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Soft Links

� Picking and soft links

� Pick with links

� By enabling this option, soft-linked edges can be selected in a single pick

� Linked edges share the same information and can be picked in a single pick

� Modifying soft links

� At any time, you can


� At any time, you can

� Form links

� Break links

� Maintain links

� By default, GAMBIT will form links between unmeshed edges that are picked

together

� By default, GAMBIT will maintain links between meshed edges that are

picked together


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Spacing

� In all meshing forms, the following spacing functions can

be specified:

� Interval Count (recommended for edge mesh only)

� Example – Entering a value of 5 will create 5 intervals along

the selected edge(s) (6 nodes, including end nodes)

� Interval Size (default setting)

� Requires input of distance between nodes.


� Requires input of distance between nodes.

� Edge is meshed with “average” interval size if grading is

used.

� Example: An edge length of 10 and a value of 2 creates 5

intervals on the edge

� Shortest Edge %

� Meshes the selected edge according to a percentage of the

length of the shortest edge in the model.

� Example – Shortest edge in model has length of 1. Entering

a value of 20 will create a mesh with interval size 0.2.


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First Edge Settings

� Use First Edge Settings option

� If enabled:

� First edge selected in pick list updates all

entries in the form.

� This mode is useful to copy settings from one

meshed edge to other edge(s).


� If disabled:

� Use this setting any time you pick two or more

meshed edges where there is a difference in

type or spacing.

� The local Apply button for that option will be

turned off

� This allows you to maintain pre-existing grading

and/or spacing settings for each edge.

� Enforce a change in grading and/or spacing by

enabling Apply button.


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Meshing Options

� Mesh

� This option is useful in cases where you want to impose a scheme without prescribing the number of intervals

� The higher level meshing scheme will decide (and match) the intervals

5-10 © 2006 Fluent Inc.

� Remove old mesh

� Deletes old mesh

� When selected, option to also delete lower geometry mesh appears.

� Ignore size function

� Toggle to either obey or ignore size functions

� Size function takes precedence when this option is disabled.


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Specify interval

size, no grading,

apply without

meshing

Meshing Options – Example

Face Mesh Generated Using Quad

1

5-11 © 2006 Fluent Inc.

Specify grading

only, apply without

meshing

Face Mesh Generated Using Quad

Pave Scheme

(Pave face meshing schemes

require an even number of

elements on edge meshes)

Face Mesh Generated

Using Submap Scheme

2

Generate

face mesh.3


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Face Meshing� Mesh Faces form

� Upon picking a face:

� GAMBIT automatically chooses quad elements

� GAMBIT chooses the type based on the solver/face

vertex types

� Available element/scheme type combinations

� Quadrilaterial: Map, Submap, Tri-Primitive, Pave

5-12 © 2006 Fluent Inc.

� Quadrilaterial: Map, Submap, Tri-Primitive, Pave

� Triangular: Pave

� Quad/Tri (hybrid): Map, Pave, Wedge

� Quad-to-tri conversion utility.


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Face Meshing - Quad Examples

� Quad: Map

� Quad: Submap

5-13 © 2006 Fluent Inc.

� Quad: Tri-Primitive

� Quad: Pave


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Face Meshing - Quad/Tri and Tri Examples

Quad/Tri Map Quad/Tri Wedge

Face must be split to generate

5-14 © 2006 Fluent Inc.

Quad/Tri PaveTri Pave

Face must be split to generate

more than one cell across

Triangular

cell

Triangular

cell

Quad cells


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Deleting Old Mesh

� Existing mesh must be removed before

remeshing.

� Mesh can be deleted using

delete mesh form.

� Lower topology mesh can also be deleted (default)

5-15 © 2006 Fluent Inc.

� Alternatively, existing mesh can be deleted by

selecting the Remove Old Mesh option

� Remove old mesh alone will leave all lower

topology mesh

� Remove old mesh + remove lower mesh will delete

all lower topology mesh that is not shared with

another entity

� Undo after any meshing operation also works.


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� All vertices that are connected to a face are assigned initial face vertex types based on the angle between the edges connected to the vertex.

� Vertices shared by multiple faces can have multiple types, depending on which face you

Face Vertex Types

E

R

E

E

S

φ

5-16 © 2006 Fluent Inc.

multiple types, depending on which face you are considering.

� The combination of vertex types describes the topology of the face.

� Face vertex types are used automatically to determine all quad face meshing schemes (except quad pave and tri pave).

E E

S


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Face Vertex Types

End (E)

� zero internal grid lines

Side (S)

� One internal grid line

E

E E

S SS

oo 1200 <φ<

oo 216120 <φ<

5-17 © 2006 Fluent Inc.

Corner (C)

� Two internal grid lines

Reverse (R)

� Three internal grid lines

S S

CC C

RR

oo 309216 <φ<

oo 360309 <φ<


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Modifying Face Vertex Types

� Face vertex types can be changed from their default settings:

� Automatically

� By enforcing certain meshing schemes in face and volume meshing.

� Can sometimes result in undesirable mesh.

� Manually

� By direct modification in the Face Vertex Type form.

5-18 © 2006 Fluent Inc.

� By direct modification in the Face Vertex Type form.

� Select Face

� symbols appear in graphics window

� Select New Vertex Type

� Select Vertices to be affected

� Vertex Types can be applied to just Boundary Layers as option.

� A vertex can have multiple types; one for each associated face.

� For a given set of face vertex types, GAMBIT will choose which meshing scheme to use based on predefined formulae.

S E


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Formula for Submap Scheme

� A face can be made submappable by

manually changing vertex types

� Consider which vertex should be

changed to type S (side)

� In the Set Face Vertex Type form,

change vertex type to S by enforcing the

submap scheme.Which R

E

E E

R

E

E

E

E

E

S

E

5-19 © 2006 Fluent Inc.

submap scheme.

� In the Face Mesh form, change the

scheme from default to submap and

click Apply.

� GAMBIT will attempt to change the

vertex types so that the scheme is

honored.

� User has less control – the resulting

mesh may be undesirable!

( )( )[ ]ReverseEnd2

SideEnd4

+×+

+×Submap

Which

vertex to

change?

E

R

E

E

E

R

E

E

E

E

E

S

E


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Formula for Map Scheme

Map

E

E

E

ES+

E E

EE

( ) ( )SidenEnd4 ×+×

5-20 © 2006 Fluent Inc.

Periodic Map

Project intervals can be specified for more control.

E E

Siden×


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How to Make a Face Mappable

� Enforce the Map scheme (most common

method)

� In the Face Mesh form, change the scheme from

default to “Map” and click Apply.

� GAMBIT will attempt to change the vertex types so

that the chosen scheme is honored

E

E EE E

E

CC

( ) ( )SidenEnd4Map

×+×

5-21 © 2006 Fluent Inc.

� Manually change the vertex types

� In Set Face Vertex Type form, change vertices

(default) to "Side“.

� Open the Face Mesh form and pick the face.

� GAMBIT should automatically select the map

scheme)

E EE E

S

E EE E

S

SS

E

S

E

E

E

E

E

E

( ) ( )SidenEnd4Map

×+×


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Submap:

(additional terms when interior loops exist)

Formula for Submap Schemes

EE

C CC

S

E

E

E

( ) ( ) ( ) ( )End2ReversepCornerEndnSidemEnd4 ++++×+×

E

C

C

C

C

E

5-22 © 2006 Fluent Inc.

Periodic Submap where m > 2.

(additional terms when interior loops exist)

E E

C

EE

C

SE

E

E

S

S

( ) ( )CornerEndmSiden ++×

E

E

C

C

C

C

C

C

E E


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Tri-Primitive

� To mesh a rectangular face with the tri-primitive scheme:

Formula for Tri-Primitive Sheme

( ) ( )SidenEnd3 ×+×

E

E

E

S

5-23 © 2006 Fluent Inc.

� Manually change one of the vertex types to "Side" in this example

� The Tri Primitive scheme can not be enforced

E E

E S

E E

E E


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� Quad/Tri: Tri-Map

� The face vertex types must be changed manually to Trielement (T)

� The Tri-Map scheme must be selected.

� Quad/Tri: Pave

Triangle2×

Meshing Faces with Hybrid Quad/Tri Schemes

T T

T

5-24 © 2006 Fluent Inc.

� All vertex types are ignored except Trielement (T) and Notrielement (N)

� Trielement (T) will force a triangular element.

� Notrielement (N) will avoid a triangular element.

� Quad/Tri: Wedge

� Used for creating cylindrical/polar type meshes

� The Vertex marked (T) is where rectangular elements are collapsed into triangles

EC

N

T

E

E


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Hard Links

� Mesh linked entities have identical mesh

� Created for periodic boundary conditions

� Applicable to edge, face, and volume entities

� Best to use soft links for edge meshing

� To link volume meshes, all faces must be hard linked first.

� Hard links for faces

5-25 © 2006 Fluent Inc.

� Hard links for faces

� Select faces and reference vertices

� The sense of each edge appears.

� Reverse orientation on by default

� Periodic option should be used for periodic boundary conditions, which creates a matched mesh even if the edges are split differently.

� Meshing one of the faces either before or after hard linking will generate an identical mesh on the linked face.

� Multiple pairs of hard links can be created.


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Mesh Smoothing

� Smoothing can increase mesh quality beyond that of the default meshing algorithms

� Most noticable in complicated geometry.

� May have little or no effect in simple geometries.

� Mesh smoothing algorithms adjust interior node locations to obtain marginal improvement in mesh quality.

� Boundary meshes are not altered.

5-26 © 2006 Fluent Inc.

� Boundary meshes are not altered.� The mesh at the boundary is not altered.

� Face and volume meshes are smoothed using a default scheme.

� Different schemes can be selected and applied after meshing.� Face mesh smoothing

� Length-weighted Laplacian: Uses the average edge length of the elements surrounding each node to adjust the nodes.

� Centroid Area: Adjust node locations to equalize areas of adjacent elements.

� Winslow (quad meshes only): Optimizes element shapes with respect to perpendicularity.

� Volume mesh smoothing� Length-weighted Laplacian: same as for face mesh smoothing

� Equipotential: Adjusts node locations to equalize the volumes of the mesh elements surrounding each node.


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Examining the Mesh

� Display Type

� Plane/Sphere

� View mesh elements that fall in plane or sphere.

� Range

� View mesh elements within quality range.

� Histogram shows quality distribution.

Show worst element zooms the view to the worst

5-27 © 2006 Fluent Inc.

� Show worst element zooms the view to the worst element

� Select 2D/3D and element type

� Select Quality Type

� Display Mode – Change cell display attributes

� Show Worst Element – Automatically zooms the display to the worst element (based on current settings).

� Update button – Will update values reported in the panel when options are changed.


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Assessing Mesh Quality

� GAMBIT has several methods for assessing mesh quality.

� Aspect Ratio

� Diagonal Ratio

� Edge Ratio

� EquiAngle Skew

EquiSize Skew

5-28 © 2006 Fluent Inc.

� EquiSize Skew

� MidAngle Skew

� Size Change

� Stretch

� Taper

� Volume

� The most important of these quality metrics are EquiAngle Skew and Size Change.


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Mesh Quality – EquiAngle Skew

� The most important mesh quality metric is EquiAngle Skew (QEAS).

θθ−θ

θ−θ−θ

=e

e

e

eEASQ minmax ,

180max

cellor facein angleLargest max

=θ

=θ

maxθ

minθ

maxθ

5-29 © 2006 Fluent Inc.

� Range of EquiAngle Skew values

� QEAS = 0 describes a perfectly orthogonal element

� QEAS = 1 describes a degenerate element

0

(best)

1

(worst)

cellor facer equiangulafor Angle

cellor facein angleSmallest min

=θ

=θ

e

min

minθ

eθ

o60=θeTri/Tet

eθ

o90=θeQuad/Hex


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� Another important mesh quality metric is Size Change (QSC).

Mesh Quality – Size Change

[ ]nSC rrrQ ,,,max 21 K=

j

iri

element neighbor of Volumeor Area

element of Volumeor Area=

iV 1=jV

2=jV

3=jV

5-30 © 2006 Fluent Inc.

� This metric applies only to 3D elements.

� By definition, QSC > 0.

� QSC = 0 describes an element whose neighbor elements have exactly

the same volume as the element of interest (i.e. uniform mesh).

jelement neighbor of Volumeor AreaiV 1=jV3=jV

4=jV

3D Example

QSC,i = Vj=1/Vi since j=1

has largest volume ratio


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Striving for Quality

� A poor quality grid can cause inaccurate solutions and/or slow convergence.

� Minimize EquiAngle Skew:

� Hex, Tri, Quad: Skewness for all/most cells should be less than 0.85.

� Tetrahedral: Skewness for all/most cells should be less than 0.9.

� All elements: Size Change for cells in regions of interest should be less than 2

� Minimize local variations in cell size, such as large jumps in size between

adjacent cells.

5-31 © 2006 Fluent Inc.

adjacent cells.

� If Examine Mesh shows such violations:

� Determine the reason(s) for the violations

� Differences in spacing and grading on adjacent edges

� Geometry with small features or other defects

� Geometric complexity and size

� Mesh that grows too rapidly

� Delete mesh completely or partially.

� Clean and/or decompose geometry, premesh edges and faces or adjust meshing

parameters

� Remesh the domain.


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Mesh Quality – Aspect Ratio

� Tri/Tet

� f is a scaling factor

� Quad/Hex

� e is the average length of edges in a

r

RfQAR =

[ ][ ]N

NAR

eee

eeeQ

,,,min

,,,max

21

21

K

K

=

� The Aspect Ratio metric (QAR) applies to tri, tet, quad, and hex elements and is

defined differently for each element type. The definitions are as follows:

5-33 © 2006 Fluent Inc.

� f is a scaling factor

� R and r are radii of circles (tri

elements) or spheres (tet elements)

that inscribe and circumscribe the

mesh element.

� f = 1/2 for tri elements and f = 1/3 for

tet elements.

� ei is the average length of edges in a

coordinate system local to the

element.

� N is the number of coordinate

directions associated with the

element

� N = 2 for quad elements

� N = 3 for hex elements

R

ra

b

c

d 21

cae

+=

22

dbe

+=

Inscribed circle

Circumscribed circle


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Mesh Quality – Diagonal Ratio

� The Diagonal Ratio metric (QDR) applies only to quad and hex elements

and is defined as follows:

� The di are the diagonals of the element.

� N is the total number of diagonals for a given element

[ ][ ]N

NDR

ddd

dddQ

,,,min

,,,max

21

21

K

K

=

5-34 © 2006 Fluent Inc.

� N is the total number of diagonals for a given element

� N = 2 for quad elements

� N = 4 for hex elements.

1d

2d1d

2d

3d

4d


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Mesh Quality – Edge Ratio

� The Edge Ratio quality metric (QER) is defined as follows:

� The si are the edge lengths of the element.

� N is the total number of edges for the element of interest.

[ ][ ]N

NER

sss

sssQ

,,,min

,,,max

21

21

K

K

=

5-35 © 2006 Fluent Inc.

Quad

N = 4

Tri

N = 3

Tet

N = 6

Pyramid

N = 8

Wedge

N = 9

Hex

N = 12


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Mesh Quality – EquiSize Skew

� The EquiSize Skew metric (QEVS) applies only to quad and hex elements

and is defined as follows:

� S is the area (2D) or volume (3D) of the element of interest.

� S is the maximum area (2D) or volume (3D) of an equilateral cell the

eq

eqEVS

S

SSQ

−=

5-36 © 2006 Fluent Inc.

� Seq is the maximum area (2D) or volume (3D) of an equilateral cell the

circumscribing radius of which is identical to that of the mesh element.

Actual element

Area = S

0 < QEVS < 1

Equilateral element

Area = Seq

QEVS = 0


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Mesh Quality – MidAngle Skew

� The MidAngle Skew (QMAS) applies only to quadrilateral and hexahedral

elements.

� Defined by the cosine of the minimum angle formed between the

bisectors of the element edges (quad) or faces (hex).

� For quad elements: θ= cosMASQ

5-37 © 2006 Fluent Inc.

� For hex elements:

Bisectors

θ

[ ]321 cos,cos,cosmax θθθ=MASQ


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Mesh Quality – Stretch

� The Stretch quality metric (QS) applies only to quadrilateral and

hexahedral elements and is defined as follows:

� di is the length of diagonal i

� s is the length of the element edge j,

[ ][ ]n

mS

ddd

sssKQ

,,,max

,,,min1

21

21

K

K

−=

5-38 © 2006 Fluent Inc.

� sj is the length of the element edge j,

� n and m are the total numbers of diagonals and edges, respectively.

� Quad elements: n = 2, m = 4, and K = 2;

� Hex elements: n = 4, m = 12, and K = 3.

� By definition, 0 < QS < 1.

� QS = 0 describes an equilateral element

� QS = 1 describes a completely degenerate element.


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Mesh Quality – Taper

� The Taper quality metric (QT) applies only to quadrilateral and hexahedral mesh elements and is defined as follows:� For any quadrilateral (or hexahedral)

mesh element, it is possible to construct a parallelogram (or parallelepiped) such that the distance between any given corner of the

Bisectors

Cornernode

T T1

T2

5-39 © 2006 Fluent Inc.

between any given corner of the parallelogram (or parallelepiped) and its nearest element corner node is a constant value.

� As a result, any vector, T, constructed from an element corner node to the nearest corner of the parallelogram (or parallelepiped) possesses a magnitude identical to that of all other such vectors.

� Each vector T can be resolved into components, Ti, that are parallel to the bisectors of the mesh element.

� Quad elements: two components

� Hex elements: three components

Element edge

� The Taper quality metric is defined as the normalized maximum of all such components for the element.

� By definition, 0 < QT < 1.� QT = 0 describes an equilateral element

� QT = 2 describes a degenerate element


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Mesh Quality – Volume and Warpage

� Volume

� The Volume quality metric (QV) applies only to 3D elements and represents quality in terms of element volume.

� Warpage

� The Warpage (QW) applies only to quad elements and is defined as follows:

5-40 © 2006 Fluent Inc.

� Z is the deviation from a best-fit plane that contains the element

� a and b are the lengths of the line segments that bisect the edges of the element.

� By definition, 0 < QW < 1

� QW = 0 describes an equilateral element

� QW = 1 describes a degenerate element.

[ ]baZ

QW,min

=

Element edge

Best-fit plane

Bisectors

gambit 2.3 lecture 05a facemeshing

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