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How to scale and shift the coordinates of a Graphics object?
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$begingroup$
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
asked 7 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
asked 7 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
asked 7 hours ago
nanjunnanjun
46829
$endgroup$
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
graphics coordinate
asked 7 hours ago
nanjunnanjun
46829
asked 7 hours ago
nanjunnanjun
46829
asked 7 hours ago
nanjunnanjun
46829
asked 7 hours ago
nanjunnanjun
46829
asked 7 hours ago
nanjunnanjun
46829
46829
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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
answered 6 hours ago
kglrkglr
192k10214434
$endgroup$
$begingroup$
Thanks @kglr for the answer. Could you explain how the second argument ofTranslateis determined? Why it is-{1, 1}/2instead of-{1, 1}?
$endgroup$
– nanjun
6 hours ago
1
$begingroup$
@nanjun, if you useScale[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 useShow[g1, Graphics@Translate[Scale[First@g2, 2, {0, 0}], -{1, 1}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
1
$begingroup$
... sinceScale[First@g2, 2]fixes the center ({1/2,1/2}) the origin of the rectangle is already shifted by-{1/2,1/2}beforeTranslateis applied. (CompareShow[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230]andShow[g1, Graphics@Scale[First@g2, 2, {0,0}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 hours ago
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
]
answered 6 hours ago
C. E.C. E.
52k3101209
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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
answered 6 hours ago
kglrkglr
192k10214434
$endgroup$
$begingroup$
Thanks @kglr for the answer. Could you explain how the second argument ofTranslateis determined? Why it is-{1, 1}/2instead of-{1, 1}?
$endgroup$
– nanjun
6 hours ago
1
$begingroup$
@nanjun, if you useScale[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 useShow[g1, Graphics@Translate[Scale[First@g2, 2, {0, 0}], -{1, 1}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
1
$begingroup$
... sinceScale[First@g2, 2]fixes the center ({1/2,1/2}) the origin of the rectangle is already shifted by-{1/2,1/2}beforeTranslateis applied. (CompareShow[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230]andShow[g1, Graphics@Scale[First@g2, 2, {0,0}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 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
answered 6 hours ago
kglrkglr
192k10214434
$endgroup$
$begingroup$
Thanks @kglr for the answer. Could you explain how the second argument ofTranslateis determined? Why it is-{1, 1}/2instead of-{1, 1}?
$endgroup$
– nanjun
6 hours ago
1
$begingroup$
@nanjun, if you useScale[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 useShow[g1, Graphics@Translate[Scale[First@g2, 2, {0, 0}], -{1, 1}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
1
$begingroup$
... sinceScale[First@g2, 2]fixes the center ({1/2,1/2}) the origin of the rectangle is already shifted by-{1/2,1/2}beforeTranslateis applied. (CompareShow[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230]andShow[g1, Graphics@Scale[First@g2, 2, {0,0}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 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
answered 6 hours ago
kglrkglr
192k10214434
$endgroup$
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
answered 6 hours ago
kglrkglr
192k10214434
edited 5 hours ago
answered 6 hours ago
kglrkglr
192k10214434
answered 6 hours ago
kglrkglr
192k10214434
answered 6 hours ago
kglrkglr
192k10214434
192k10214434
$begingroup$
Thanks @kglr for the answer. Could you explain how the second argument ofTranslateis determined? Why it is-{1, 1}/2instead of-{1, 1}?
$endgroup$
– nanjun
6 hours ago
1
$begingroup$
@nanjun, if you useScale[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 useShow[g1, Graphics@Translate[Scale[First@g2, 2, {0, 0}], -{1, 1}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
1
$begingroup$
... sinceScale[First@g2, 2]fixes the center ({1/2,1/2}) the origin of the rectangle is already shifted by-{1/2,1/2}beforeTranslateis applied. (CompareShow[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230]andShow[g1, Graphics@Scale[First@g2, 2, {0,0}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 hours ago
add a comment |
$begingroup$
Thanks @kglr for the answer. Could you explain how the second argument ofTranslateis determined? Why it is-{1, 1}/2instead of-{1, 1}?
$endgroup$
– nanjun
6 hours ago
1
$begingroup$
@nanjun, if you useScale[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 useShow[g1, Graphics@Translate[Scale[First@g2, 2, {0, 0}], -{1, 1}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
1
$begingroup$
... sinceScale[First@g2, 2]fixes the center ({1/2,1/2}) the origin of the rectangle is already shifted by-{1/2,1/2}beforeTranslateis applied. (CompareShow[g1, Graphics@Scale[First@g2, 2], AspectRatio -> 1, Axes -> True, ImageSize -> 230]andShow[g1, Graphics@Scale[First@g2, 2, {0,0}], AspectRatio -> 1, Axes -> True, ImageSize -> 230]
$endgroup$
– kglr
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 hours ago
$begingroup$
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
6 hours ago
$begingroup$
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
6 hours ago
1
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
6 hours ago
$begingroup$
@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
6 hours ago
1
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
6 hours ago
$begingroup$
... 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
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 hours ago
$begingroup$
Thank you @kglr for the explanation, which was very clear.
$endgroup$
– nanjun
6 hours ago
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
]
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
]
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
]
answered 6 hours ago
C. E.C. E.
52k3101209
$endgroup$
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
]
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
answered 6 hours ago
C. E.C. E.
52k3101209
52k3101209
add a comment |
add a comment |
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