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How to scale and shift the coordinates of a Graphics object?

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3

$begingroup$

I am trying to overlap two Graphics objects g1 and g2 with Show. However, I found that when the coordinates of each object is defined to quite different ranges, I need to "scale" and "shift" the coordinates of one object to get the desired look.

For example,

g1 = Graphics[GrayLevel[0.8], Rectangle[-2, -2, 2, 2]];
g2 = Graphics[GrayLevel[0.5], Rectangle[0, 0, 1, 1]];
Show[g1, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g1, g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]

The overlapped version of g1 and g2 looks like this

However, I would like to scale the coordinates of g2 to make g2 twice large and also shift its coordinates so the center can "roughly" coincide the center of g1. I say "roughly" because g1 and g2 may be some graphics not of a regular shape. The desired result will look like

So how can I manipulate the coordinates of g2 to adjust its relative position and size when Show with g1? Please avoid modifying the definition of g1 and g2 as they can be any Graphics copy-pasted over.

graphics coordinate

share|improve this question

asked 6 hours ago

nanjunnanjun

46829

$endgroup$

add a comment | 

3

$begingroup$

I am trying to overlap two Graphics objects g1 and g2 with Show. However, I found that when the coordinates of each object is defined to quite different ranges, I need to "scale" and "shift" the coordinates of one object to get the desired look.

For example,

g1 = Graphics[GrayLevel[0.8], Rectangle[-2, -2, 2, 2]];
g2 = Graphics[GrayLevel[0.5], Rectangle[0, 0, 1, 1]];
Show[g1, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g1, g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]

The overlapped version of g1 and g2 looks like this

However, I would like to scale the coordinates of g2 to make g2 twice large and also shift its coordinates so the center can "roughly" coincide the center of g1. I say "roughly" because g1 and g2 may be some graphics not of a regular shape. The desired result will look like

So how can I manipulate the coordinates of g2 to adjust its relative position and size when Show with g1? Please avoid modifying the definition of g1 and g2 as they can be any Graphics copy-pasted over.

graphics coordinate

share|improve this question

asked 6 hours ago

nanjunnanjun

46829

$endgroup$

add a comment | 

$begingroup$

I am trying to overlap two Graphics objects g1 and g2 with Show. However, I found that when the coordinates of each object is defined to quite different ranges, I need to "scale" and "shift" the coordinates of one object to get the desired look.

For example,

g1 = Graphics[GrayLevel[0.8], Rectangle[-2, -2, 2, 2]];
g2 = Graphics[GrayLevel[0.5], Rectangle[0, 0, 1, 1]];
Show[g1, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g1, g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]

The overlapped version of g1 and g2 looks like this

However, I would like to scale the coordinates of g2 to make g2 twice large and also shift its coordinates so the center can "roughly" coincide the center of g1. I say "roughly" because g1 and g2 may be some graphics not of a regular shape. The desired result will look like

So how can I manipulate the coordinates of g2 to adjust its relative position and size when Show with g1? Please avoid modifying the definition of g1 and g2 as they can be any Graphics copy-pasted over.

graphics coordinate

share|improve this question

asked 6 hours ago

nanjunnanjun

46829

$endgroup$

g1 = Graphics[GrayLevel[0.8], Rectangle[-2, -2, 2, 2]];
g2 = Graphics[GrayLevel[0.5], Rectangle[0, 0, 1, 1]];
Show[g1, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]
Show[g1, g2, AspectRatio -> 1, Axes -> True, ImageSize -> 230]

share|improve this question

asked 6 hours ago

nanjunnanjun

46829

share|improve this question

asked 6 hours ago

nanjunnanjun

46829

asked 6 hours ago

nanjunnanjun

46829

asked 6 hours ago

nanjunnanjun

46829

2 Answers
2

active

oldest

votes

4

$begingroup$

You can use Scale and Translate on First @ g2 (which contains the graphics directives and primitives):

Show[g1, Graphics @ Scale[First @ g2, 2, 1, 1], AspectRatio -> 1, 
 Axes -> True, ImageSize -> 230]

Alterantively, you can use combination of Scale and Translate:

Show[g1, Graphics @ Translate[Scale[First @ g2, 2], -1, 1/2], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

or

Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

same picture

share|improve this answer

edited 4 hours ago

answered 6 hours ago

kglrkglr

192k10214434

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks @kglr for the answer. Could you explain how the second argument of Translate is determined? Why it is -1, 1/2 instead of -1, 1?
  $endgroup$
  – nanjun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @nanjun, if you use Scale[First@g2, 2, 0, 0] (with the third argument specifying the point that is kept fixed) you can use -1,1 instead of -1,1/2) , that is, you can use Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
  $endgroup$
  – kglr
  5 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  ... since Scale[First@g2, 2] fixes the center (1/2,1/2) the origin of the rectangle is already shifted by -1/2,1/2 before Translate is applied. (Compare Show[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230] and Show[g1, Graphics@Scale[First@g2, 2, 0,0], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
  $endgroup$
  – kglr
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you @kglr for the explanation, which was very clear.
  $endgroup$
  – nanjun
  5 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

I'm not saying that this is what you need for your problem, but sometimes when you want to superimpose graphics like this, you're looking for Inset:

Show[
 g1,
 Graphics@Inset[
 Show[g2, PlotRangePadding -> 0],
 0, 0, Center, Center, 2, 2
 ],
 Axes -> True, ImageSize -> 230
 ]

share|improve this answer

answered 6 hours ago

C. E.C. E.

52k3101209

$endgroup$

add a comment | 

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4

$begingroup$

You can use Scale and Translate on First @ g2 (which contains the graphics directives and primitives):

Show[g1, Graphics @ Scale[First @ g2, 2, 1, 1], AspectRatio -> 1, 
 Axes -> True, ImageSize -> 230]

Alterantively, you can use combination of Scale and Translate:

Show[g1, Graphics @ Translate[Scale[First @ g2, 2], -1, 1/2], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

or

Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

same picture

share|improve this answer

edited 4 hours ago

answered 6 hours ago

kglrkglr

192k10214434

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks @kglr for the answer. Could you explain how the second argument of Translate is determined? Why it is -1, 1/2 instead of -1, 1?
  $endgroup$
  – nanjun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @nanjun, if you use Scale[First@g2, 2, 0, 0] (with the third argument specifying the point that is kept fixed) you can use -1,1 instead of -1,1/2) , that is, you can use Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
  $endgroup$
  – kglr
  5 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  ... since Scale[First@g2, 2] fixes the center (1/2,1/2) the origin of the rectangle is already shifted by -1/2,1/2 before Translate is applied. (Compare Show[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230] and Show[g1, Graphics@Scale[First@g2, 2, 0,0], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
  $endgroup$
  – kglr
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you @kglr for the explanation, which was very clear.
  $endgroup$
  – nanjun
  5 hours ago
  

  
  
  
  

add a comment | 

4

$begingroup$

You can use Scale and Translate on First @ g2 (which contains the graphics directives and primitives):

Show[g1, Graphics @ Scale[First @ g2, 2, 1, 1], AspectRatio -> 1, 
 Axes -> True, ImageSize -> 230]

Alterantively, you can use combination of Scale and Translate:

Show[g1, Graphics @ Translate[Scale[First @ g2, 2], -1, 1/2], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

or

Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

same picture

share|improve this answer

edited 4 hours ago

answered 6 hours ago

kglrkglr

192k10214434

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks @kglr for the answer. Could you explain how the second argument of Translate is determined? Why it is -1, 1/2 instead of -1, 1?
  $endgroup$
  – nanjun
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @nanjun, if you use Scale[First@g2, 2, 0, 0] (with the third argument specifying the point that is kept fixed) you can use -1,1 instead of -1,1/2) , that is, you can use Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
  $endgroup$
  – kglr
  5 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  ... since Scale[First@g2, 2] fixes the center (1/2,1/2) the origin of the rectangle is already shifted by -1/2,1/2 before Translate is applied. (Compare Show[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230] and Show[g1, Graphics@Scale[First@g2, 2, 0,0], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
  $endgroup$
  – kglr
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you @kglr for the explanation, which was very clear.
  $endgroup$
  – nanjun
  5 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

You can use Scale and Translate on First @ g2 (which contains the graphics directives and primitives):

Show[g1, Graphics @ Scale[First @ g2, 2, 1, 1], AspectRatio -> 1, 
 Axes -> True, ImageSize -> 230]

Alterantively, you can use combination of Scale and Translate:

Show[g1, Graphics @ Translate[Scale[First @ g2, 2], -1, 1/2], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

or

Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

same picture

share|improve this answer

edited 4 hours ago

answered 6 hours ago

kglrkglr

192k10214434

$endgroup$

Show[g1, Graphics @ Scale[First @ g2, 2, 1, 1], AspectRatio -> 1, 
 Axes -> True, ImageSize -> 230]

Show[g1, Graphics @ Translate[Scale[First @ g2, 2], -1, 1/2], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

Show[g1, Graphics@Translate[Scale[First@g2, 2, 0, 0], -1, 1], 
 AspectRatio -> 1, Axes -> True, ImageSize -> 230]

share|improve this answer

edited 4 hours ago

answered 6 hours ago

kglrkglr

192k10214434

answered 6 hours ago

kglrkglr

192k10214434

answered 6 hours ago

kglrkglr

192k10214434

1

$begingroup$

I'm not saying that this is what you need for your problem, but sometimes when you want to superimpose graphics like this, you're looking for Inset:

Show[
 g1,
 Graphics@Inset[
 Show[g2, PlotRangePadding -> 0],
 0, 0, Center, Center, 2, 2
 ],
 Axes -> True, ImageSize -> 230
 ]

share|improve this answer

answered 6 hours ago

C. E.C. E.

52k3101209

$endgroup$

add a comment | 

1

$begingroup$

I'm not saying that this is what you need for your problem, but sometimes when you want to superimpose graphics like this, you're looking for Inset:

Show[
 g1,
 Graphics@Inset[
 Show[g2, PlotRangePadding -> 0],
 0, 0, Center, Center, 2, 2
 ],
 Axes -> True, ImageSize -> 230
 ]

share|improve this answer

answered 6 hours ago

C. E.C. E.

52k3101209

$endgroup$

add a comment | 

$begingroup$

I'm not saying that this is what you need for your problem, but sometimes when you want to superimpose graphics like this, you're looking for Inset:

Show[
 g1,
 Graphics@Inset[
 Show[g2, PlotRangePadding -> 0],
 0, 0, Center, Center, 2, 2
 ],
 Axes -> True, ImageSize -> 230
 ]

share|improve this answer

answered 6 hours ago

C. E.C. E.

52k3101209

$endgroup$

Show[
 g1,
 Graphics@Inset[
 Show[g2, PlotRangePadding -> 0],
 0, 0, Center, Center, 2, 2
 ],
 Axes -> True, ImageSize -> 230
 ]

share|improve this answer

answered 6 hours ago

C. E.C. E.

52k3101209

answered 6 hours ago

C. E.C. E.

52k3101209

answered 6 hours ago

C. E.C. E.

52k3101209