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

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5

$begingroup$

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 May 16 at 19:38

nanjunnanjun

50229

$endgroup$

add a comment | 

5

$begingroup$

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 May 16 at 19:38

nanjunnanjun

50229

$endgroup$

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 May 16 at 19:38

nanjunnanjun

50229

$endgroup$

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 May 16 at 19:38

nanjunnanjun

50229

share|improve this question

asked May 16 at 19:38

nanjunnanjun

50229

asked May 16 at 19:38

nanjunnanjun

50229

asked May 16 at 19:38

nanjunnanjun

50229

2 Answers
2

active

oldest

votes

6

$begingroup$

You can use Scale 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 May 17 at 3:57

answered May 16 at 19:48

kglrkglr

195k10216439

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  May 16 at 20:07
  

  
  
  
  


• 
  
  
  

  
  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
  May 16 at 20:33
  
  

  
  
  
  


• 
  
  
  

  
  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
  May 16 at 20:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you @kglr for the explanation, which was very clear.
  $endgroup$
  – nanjun
  May 16 at 20:44
  

  
  
  
  

add a comment | 

2

$begingroup$

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 May 16 at 20:02

C. E.C. E.

52.3k3102209

$endgroup$

add a comment | 

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6

$begingroup$

You can use Scale 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 May 17 at 3:57

answered May 16 at 19:48

kglrkglr

195k10216439

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  May 16 at 20:07
  

  
  
  
  


• 
  
  
  

  
  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
  May 16 at 20:33
  
  

  
  
  
  


• 
  
  
  

  
  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
  May 16 at 20:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you @kglr for the explanation, which was very clear.
  $endgroup$
  – nanjun
  May 16 at 20:44
  

  
  
  
  

add a comment | 

6

$begingroup$

You can use Scale 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 May 17 at 3:57

answered May 16 at 19:48

kglrkglr

195k10216439

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  May 16 at 20:07
  

  
  
  
  


• 
  
  
  

  
  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
  May 16 at 20:33
  
  

  
  
  
  


• 
  
  
  

  
  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
  May 16 at 20:37
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you @kglr for the explanation, which was very clear.
  $endgroup$
  – nanjun
  May 16 at 20:44
  

  
  
  
  

add a comment | 

$begingroup$

You can use Scale 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 May 17 at 3:57

answered May 16 at 19:48

kglrkglr

195k10216439

$endgroup$

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 May 17 at 3:57

answered May 16 at 19:48

kglrkglr

195k10216439

answered May 16 at 19:48

kglrkglr

195k10216439

answered May 16 at 19:48

kglrkglr

195k10216439

2

$begingroup$

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 May 16 at 20:02

C. E.C. E.

52.3k3102209

$endgroup$

add a comment | 

2

$begingroup$

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 May 16 at 20:02

C. E.C. E.

52.3k3102209

$endgroup$

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 May 16 at 20:02

C. E.C. E.

52.3k3102209

$endgroup$

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

share|improve this answer

answered May 16 at 20:02

C. E.C. E.

52.3k3102209

answered May 16 at 20:02

C. E.C. E.

52.3k3102209

answered May 16 at 20:02

C. E.C. E.

52.3k3102209