 2  0 2  
curve 4 line 0 2  0 -1
curve 5 circle center 2 $((2 + -1)/2.0) radius 0.75
curve 11 line 0 -1 -1 -1
curve 12 line -1 -1 -1 2
curve 23 line 0 2 -1 2
subregion 1  property 1 boundary 1 2 3 4 hole -5
subregion 2  property 2 boundary 5
subregion 3  property 3 boundary -12 -11 23 -4
m-ctl-point constant 0.25
""", show = true);
```
<img src=  "rectangle-uniform-3.png" height=300>
The colors obviously refer to the numerical identifiers of the subregions (call for the color legend in the figure). Also we may note here that the numbering of the curves is arbitrary as long as the identifiers of the curves are unique.

## Mesh of two regions with nodes on a given curve

We can enforce the location of nodes on some curves. For instance here we enforce the presence of an additional circle inside the circular subregion 2. And we also enforce the presence of an inclined straight line in subregion 1. This is accomplished by embedding a curve inside the domain with both the positive and negative orientation. In this way the curve is incorporated in the domain triangulation: there is no crack, the triangulation is continuous along the curve from both sides. 
```
demo("rectangle-uniform-2-c", """
curve 1 line 0 -1 4 -1
curve 2 line 4 -1  4 2 
curve 3 line 4 2  0 2  
curve 4 line 0 2  0 -1
curve 5 circle center 2 $((2 + -1)/2.0) radius 0.75
curve 7 circle center 2 $((2 + -1)/2.0) radius 0.7
curve 40 line 0.5 -0.5  1.5 1.5
subregion 1  property 1 boundary 1 2 3 4 40 -40 hole -5
subregion 2  property 2 boundary 5 7 -7
m-ctl-point constant 0.21
""", show = true);
```
<img src=  "rectangle-uniform-2-c.png" height=300>


## Graded mesh of a rectangle with a filled circular subregion

Now we will fill the hole with a second subregion.
```
demo("rectangle-graded-2", """
curve 1 line 0 -1 4 -1
curve 2 line 4 -1  4 2 
curve 3 line 4 2  0 2  
curve 4 line 0 2  0 -1
curve 5 circle center 2 $((2 + -1)/2.0) radius 0.75
subregion 1  property 1 boundary 1 2 3 4 hole -5
subregion 2  property 2 boundary 5
m-ctl-point 1 xy 2 $((2 + -1)/2.0) near 0.05 influence 0.15
m-ctl-point constant 3
""", show = true);
```
<img src=  "rectangle-graded-2.png" height=300>



## Mesh of region with a slit


```
demo("rectangle-uniform-slit", """
curve 1 line 0 -1 4 -1
curve 2 line 4 -1  4 2 
curve 3 line 4 2  0 2  
curve 4 line 0 2  0 -1
curve 40 line  1 0 2 0.501
curve 41 line  2 0.501 3. 1. 
curve 42 line  3. 1.  2 0.499
curve 43 line  2 0.499 1 0
subregion 1  property 1 boundary 1 2 3 4 hole 40 41 42 43
m-ctl-point constant 0.31
""", show = true);
```
<img src=  "rectangle-uniform-slit.png" height=300>


## Mesh of region with a Rounded slit


```
a, b, w = 1.0, 0.6, 0.025
cb, sw = b * 0.999, sqrt(2.0)/2 * w
demo("rectangle-uniform-rounded-slit", """
curve 1 line $(-a) $(-a) $(+a) $(-a)
curve 2 line $(+a) $(-a) $(+a) $(+a)
curve 3 line $(+a) $(+a) $(-a) $(+a)
curve 4 line $(-a) $(+a) $(-a) $(-a)
curve 40 arc $(-b+sw) $(-b-sw) $(-b-sw) $(-b+sw) center $(-cb) $(-cb) 
curve 41 arc $(+b-sw) $(+b+sw) $(+b+sw) $(+b-sw) center $(+cb) $(+cb) 
curve 42 line $(+b+sw) $(+b-sw) $(-b+sw) $(-b-sw)
curve 43 line $(-b-sw) $(-b+sw) $(+b-sw) $(+b+sw)
subregion 1  property 1 boundary 1 2 3 4 hole 40 41 42 43
m-ctl-point constant 0.05
""", show = true);
```
<img src=  "rectangle-uniform-rounded-slit.png" height=300>

## Graded mesh of region with a Rounded slit


```
a, b, w = 1.0, 0.6, 0.025
cb, sw = b * 0.999, sqrt(2.0)/2 * w
demo("rectangle-graded-rounded-slit", """
curve 1 line $(-a) $(-a) $(+a) $(-a)
curve 2 line $(+a) $(-a) $(+a) $(+a)
curve 3 line $(+a) $(+a) $(-a) $(+a)
curve 4 line $(-a) $(+a) $(-a) $(-a)
curve 40 arc $(-b+sw) $(-b-sw) $(-b-sw) $(-b+sw) center $(-cb) $(-cb) 
curve 41 arc $(+b-sw) $(+b+sw) $(+b+sw) $(+b-sw) center $(+cb) $(+cb) 
curve 42 line $(+b+sw) $(+b-sw) $(-b+sw) $(-b-sw)
curve 43 line $(-b-sw) $(-b+sw) $(+b-sw) $(+b+sw)
subregion 1  property 1 boundary 1 2 3 4 hole 40 41 42 43
m-ctl-point constant $(a/2)
m-ctl-point 1 xy $(-cb) $(-cb) near $(w/5) influence $(w)
m-ctl-point 2 xy $(+cb) $(+cb) near $(w/5) influence $(w)
""", show = true);
```
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More games you may like...Kalamazoo is among four Michigan locations that will begin hosting the nationwide Truth, Racial Healing & Transformation enterprise this year.
Council of Michigan Foundations will receive $4.2 million over five years from the W.K. Kellogg Foundation for TRHT work in Michigan. Of that, Kalamazoo Community Foundation will receive $865,000 over those five years to facilitate the enterprise here in Kalamazoo. A portion of the WKKF funds includes a challenge grant to develop an endowment fund at the Community Foundation for this work.
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More than 60 individuals, including many representatives from local nonprofits and businesses, are coming together in this work.
According to Lanna Lewis (pictured at left), who is leading the Community Foundation's TRHT work, the enterprise is modeled on truth and reconciliation processes that have happened around the world. “In Kalamazoo," she says, "we hope to create a platform that brings people together to build relationships, honor and elevate the powerful work already happening, and collectively develop new strategies to transform our community.”
October 1, 2017
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