"$xgradualdiv" 修訂間的差異

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(已建立頁面,內容為 "This function is to determine how the segment is divided. There are two columns to fill in. The first column ''i'' should be filled in an integer 0, 1, or 2. : {| |'...")
 
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|-
 
|-
 
|''i'' = 1:
 
|''i'' = 1:
| Gradual. This means the segment is divided whether from small spacing to large spacing or in the opposite way.
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| Gradual. This means the segment is divided whether from small spacing to large spacing or in the opposite way. The spacing is distributed like a geometric progression
 
|-
 
|-
 
|''i'' = 2:
 
|''i'' = 2:
 
|Bump. This means the segment can be divided into two forms small-large-small or large-small-large.
 
|Bump. This means the segment can be divided into two forms small-large-small or large-small-large.
 
|}
 
|}
The second column ''r'' should be filled in a real number. number 1 for gradual this means the spacing between each point becomes smaller.
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The second column ''r'' should be filled in a real number.
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<br>
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[[File:Mesh2.png|600px]]
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<br>
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
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|small -> large -> small
 
|small -> large -> small
 
|}
 
|}
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<br>
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If the total layer thickness is <math>l </math> and i=1, then if the smallest separation distance is a
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<math>l = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N} </math>
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where N is the total grid number defined in [[$xdiv]]
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Then <math>l = a\frac{r^{N}-1}{r-1} </math>
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<br>
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If the total layer thickness is <math>l </math> and i=2, then if the smallest separation distance is a
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<math>l/2 = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N/2} </math>
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where N is the total grid number defined in [[$ydiv]]
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Then <math>l = 2 \cdot a\frac{r^{N/2}-1}{r-1} </math>
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<br>
 
<br>
 
: Example
 
: Example
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$xgradualdiv
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0 1
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1 1.1
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1 1.1
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2 1.1
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2 1.1
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<br><br>
 
<br><br>
 
: Related commands
 
: Related commands

於 2018年3月13日 (二) 09:52 的修訂

This function is to determine how the segment is divided. There are two columns to fill in. The first column i should be filled in an integer 0, 1, or 2.

i = 0: Uniform. This means the segment is divided equally with the same spacing.
i = 1: Gradual. This means the segment is divided whether from small spacing to large spacing or in the opposite way. The spacing is distributed like a geometric progression
i = 2: Bump. This means the segment can be divided into two forms small-large-small or large-small-large.

The second column r should be filled in a real number.
Mesh2.png

If r < 1 If r = 1 If r > 1
Uniform (0) uniform uniform uniform
Gradual (1) large -> small uniform small -> large
Bump (2) large -> small -> large uniform small -> large -> small


If the total layer thickness is l  and i=1, then if the smallest separation distance is a 
l = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N} 
where N is the total grid number defined in $xdiv
Then   l = a\frac{r^{N}-1}{r-1} 


If the total layer thickness is l  and i=2, then if the smallest separation distance is a 
l/2 = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N/2} 
where N is the total grid number defined in $ydiv
Then   l = 2 \cdot a\frac{r^{N/2}-1}{r-1} 


Example
$xgradualdiv
0 1
1 1.1
1 1.1
2 1.1
2 1.1



Related commands
$ygradualdiv