RFC: candidates for a new default colormap

Development matplotlib-devel
21

This is a really nice tool!

Attached is an example of a map that circles the other direction, and that sacrifices some visual delta for less extreme ends. Although I think the "sunrise" type of map that you offered in versions A, B, and C is a good one to have in the arsenal, I am not convinced that it should be the only category to be considered as a default. Do we really want to reject the somewhat Parula-like category just because Matlab uses the real Parula?

I'm not saying the attached example is particularly good; it is intended to re-introduce the category. (It is somewhat similar to a reversal of our ColorBrewer YlGnBu, so I tried to name it following that scheme.)

It seems that the fundamental constraints in this map generator tend to yield a somewhat muddy dark end and a muted middle. That's one compromise among many that are possible.

Eric

PuBuGnYl_r.py (12.9 KB)

···

On 2015/06/02 7:58 PM, Nathaniel Smith wrote:

On Tue, Jun 2, 2015 at 10:03 PM, Paul Ivanov <pi@...453...> wrote:

That said, if you want to play around with the editor tool, it's
linked on the webpage :-).

22

That said, if you want to play around with the editor tool, it's
linked on the webpage :-).

This is a really nice tool!

Attached is an example of a map that circles the other direction, and that
sacrifices some visual delta for less extreme ends. Although I think the
"sunrise" type of map that you offered in versions A, B, and C is a good one
to have in the arsenal, I am not convinced that it should be the only
category to be considered as a default. Do we really want to reject the
somewhat Parula-like category just because Matlab uses the real Parula?

I'm not saying the attached example is particularly good; it is intended to
re-introduce the category. (It is somewhat similar to a reversal of our
ColorBrewer YlGnBu, so I tried to name it following that scheme.)

That is nice! For those following along at home, here's what Eric's
colormap looks like:
   https://bids.github.io/colormap/images/screenshots/erics_PuBuGnYl_r.png

We also tried tweaking it a bit to end on a more saturated yellow,
which I think helps increase contrast in the deuteranomalous version
in particular, and put this on the website as an "option D":
   https://bids.github.io/colormap/images/screenshots/option_d.png

We also previously designed a colormap that follows parula's ideas
pretty closely, in terms of starting/ending points, overall
brightness, and the trick of kinking over through orange at the top
end. It ends up being much much more green than parula though:
   https://bids.github.io/colormap/images/screenshots/fake_parula.png

It seems that the fundamental constraints in this map generator tend to
yield a somewhat muddy dark end and a muted middle. That's one compromise
among many that are possible.

You can somewhat avoid the muddy end by bumping up the minimum
brightness (option C does this to some extent), but of course that has
other trade-offs.

-n

···

On Wed, Jun 3, 2015 at 1:51 PM, Eric Firing <efiring@...229...> wrote:

On 2015/06/02 7:58 PM, Nathaniel Smith wrote:

On Tue, Jun 2, 2015 at 10:03 PM, Paul Ivanov <pi@...453...> wrote:

--
Nathaniel J. Smith -- http://vorpus.org

23

I prefer C, but am not too fond of any of them :frowning:

I wonder if it would be beneficial to give up a little on the quantitative properties of the cm in favor of moving towards something that is a bit more aesthetic and pleasant to look at.

···

On Wed, Jun 3, 2015 at 1:47 PM, Paul Hobson <pmhobson@…149…> wrote:

A brief poll of my office gave
3 A’s and a B.

One of the A’s came from someone who can’t remember their distinct flavor of color blindness, but definitely gets tripped up by reds and greens.

-p

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–

On Wed, Jun 3, 2015 at 1:29 PM, Arnd Baecker <arnd.baecker@…9…> wrote:

In our group I also recieved quite mixed responses:

  • C B A (2 x)

  • B A C

  • A B C

  • C

  • B

One collegue having anomalous color vision

(something between protanomaly and protanopia)

called all three versions “harsh” to his eye (like looking into a cars lights at night) and rather unpleasant.

He considered C as the least unpleasant, but not that easy to look at.

Moreover, he stated that, the parula may be flawed, but at least it doesn’t make one want to look away immediately.

Best, Arnd

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Brian E. Granger
Cal Poly State University, San Luis Obispo
@ellisonbg on Twitter and GitHub
bgranger@…882… and ellisonbg@…149…

24

We also tried tweaking it a bit to end on a more saturated yellow,
which I think helps increase contrast in the deuteranomalous version
in particular, and put this on the website as an "option D":
    https://bids.github.io/colormap/images/screenshots/option_d.png

Thank you. To me, this is more comfortable to look at than A, B, and especially C.

We also previously designed a colormap that follows parula's ideas
pretty closely, in terms of starting/ending points, overall
brightness, and the trick of kinking over through orange at the top
end. It ends up being much much more green than parula though:
    https://bids.github.io/colormap/images/screenshots/fake_parula.png

Interesting. That kink comes through as a visible over-emphasis of the orange range in the images.

Attached are two more variations on the clockwise dark-to-light theme. They achieve more dynamic range, and perhaps "colorfulness", but at the cost of more relative loss of contrast in the colorblind cases. Is the tradeoff worthwhile?

Eric

RdBuGnYl_r.py (12.9 KB)

RdBuGnYl_r_v2.py (12.9 KB)

···

On 2015/06/03 12:27 PM, Nathaniel Smith wrote:

25

Ooooh, I am liking “D” a lot. It is almost like what Parula should have been. Still not quite perfect, but I can’t put my finger on it.

Ben Root

···

On Wed, Jun 3, 2015 at 6:27 PM, Nathaniel Smith <njs@…503…> wrote:

On Wed, Jun 3, 2015 at 1:51 PM, Eric Firing <efiring@…229…> wrote:

On 2015/06/02 7:58 PM, Nathaniel Smith wrote:

On Tue, Jun 2, 2015 at 10:03 PM, Paul Ivanov <pi@…453…> wrote:

That said, if you want to play around with the editor tool, it’s

linked on the webpage :-).

This is a really nice tool!

Attached is an example of a map that circles the other direction, and that

sacrifices some visual delta for less extreme ends. Although I think the

“sunrise” type of map that you offered in versions A, B, and C is a good one

to have in the arsenal, I am not convinced that it should be the only

category to be considered as a default. Do we really want to reject the

somewhat Parula-like category just because Matlab uses the real Parula?

I’m not saying the attached example is particularly good; it is intended to

re-introduce the category. (It is somewhat similar to a reversal of our

ColorBrewer YlGnBu, so I tried to name it following that scheme.)

That is nice! For those following along at home, here’s what Eric’s

colormap looks like:

https://bids.github.io/colormap/images/screenshots/erics_PuBuGnYl_r.png

We also tried tweaking it a bit to end on a more saturated yellow,

which I think helps increase contrast in the deuteranomalous version

in particular, and put this on the website as an “option D”:

https://bids.github.io/colormap/images/screenshots/option_d.png

We also previously designed a colormap that follows parula’s ideas

pretty closely, in terms of starting/ending points, overall

brightness, and the trick of kinking over through orange at the top

end. It ends up being much much more green than parula though:

https://bids.github.io/colormap/images/screenshots/fake_parula.png

It seems that the fundamental constraints in this map generator tend to

yield a somewhat muddy dark end and a muted middle. That’s one compromise

among many that are possible.

You can somewhat avoid the muddy end by bumping up the minimum

brightness (option C does this to some extent), but of course that has

other trade-offs.

-n

–

Nathaniel J. Smith – http://vorpus.org

Matplotlib-devel mailing list

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26

I’m a big fan of option D. So much so that when I needed to make a movie of ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

···

On Wed, Jun 3, 2015 at 4:43 PM, Benjamin Root <ben.root@…553…> wrote:

Ooooh, I am liking “D” a lot. It is almost like what Parula should have been. Still not quite perfect, but I can’t put my finger on it.

Ben Root

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On Wed, Jun 3, 2015 at 6:27 PM, Nathaniel Smith <njs@…503…> wrote:

On Wed, Jun 3, 2015 at 1:51 PM, Eric Firing <efiring@…229…> wrote:

On 2015/06/02 7:58 PM, Nathaniel Smith wrote:

On Tue, Jun 2, 2015 at 10:03 PM, Paul Ivanov <pi@…453…> wrote:

That said, if you want to play around with the editor tool, it’s

linked on the webpage :-).

This is a really nice tool!

Attached is an example of a map that circles the other direction, and that

sacrifices some visual delta for less extreme ends. Although I think the

“sunrise” type of map that you offered in versions A, B, and C is a good one

to have in the arsenal, I am not convinced that it should be the only

category to be considered as a default. Do we really want to reject the

somewhat Parula-like category just because Matlab uses the real Parula?

I’m not saying the attached example is particularly good; it is intended to

re-introduce the category. (It is somewhat similar to a reversal of our

ColorBrewer YlGnBu, so I tried to name it following that scheme.)

That is nice! For those following along at home, here’s what Eric’s

colormap looks like:

https://bids.github.io/colormap/images/screenshots/erics_PuBuGnYl_r.png

We also tried tweaking it a bit to end on a more saturated yellow,

which I think helps increase contrast in the deuteranomalous version

in particular, and put this on the website as an “option D”:

https://bids.github.io/colormap/images/screenshots/option_d.png

We also previously designed a colormap that follows parula’s ideas

pretty closely, in terms of starting/ending points, overall

brightness, and the trick of kinking over through orange at the top

end. It ends up being much much more green than parula though:

https://bids.github.io/colormap/images/screenshots/fake_parula.png

It seems that the fundamental constraints in this map generator tend to

yield a somewhat muddy dark end and a muted middle. That’s one compromise

among many that are possible.

You can somewhat avoid the muddy end by bumping up the minimum

brightness (option C does this to some extent), but of course that has

other trade-offs.

-n

–

Nathaniel J. Smith – http://vorpus.org

Matplotlib-devel mailing list

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27

Beautiful! How hard would it be to also do this for the other
proposed colormaps?

Stéfan

···

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@...149...> wrote:

I'm a big fan of option D. So much so that when I needed to make a movie of
ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

28

May I suggest an update to the code showing the 3d sRGB colorspace? Can you add a “shade=False” to it? Currently, in pycam02ucs.viscm.py, around line 279, it calls the 3d scatter function without the kwarg. This means that mplot3d will apply an alpha transparancy to dots that are farther away to give the perception of depth. Since we actually want to see the correct color, we probably shouldn’t have that feature on.

Ben Root

···

On Wed, Jun 3, 2015 at 8:17 PM, Stéfan van der Walt <stefan@…1217…7…> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

I’m a big fan of option D. So much so that when I needed to make a movie of

ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other

proposed colormaps?

Stéfan

Matplotlib-devel mailing list

Matplotlib-devel@lists.sourceforge.net

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29

I’m really digging option D too – it has the bonus of being unambiguously distinct from GNUPlot,

···

On Wed, Jun 3, 2015 at 5:29 PM, Benjamin Root <ben.root@…553…> wrote:

May I suggest an update to the code showing the 3d sRGB colorspace? Can you add a “shade=False” to it? Currently, in pycam02ucs.viscm.py, around line 279, it calls the 3d scatter function without the kwarg. This means that mplot3d will apply an alpha transparancy to dots that are farther away to give the perception of depth. Since we actually want to see the correct color, we probably shouldn’t have that feature on.

Ben Root

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On Wed, Jun 3, 2015 at 8:17 PM, Stéfan van der Walt <stefan@…337…> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

I’m a big fan of option D. So much so that when I needed to make a movie of

ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other

proposed colormaps?

Stéfan

Matplotlib-devel mailing list

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30

> I'm a big fan of option D. So much so that when I needed to make a
movie of
> ony my galaxy simulations today I went ahead and used it:
>
> https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other
proposed colormaps?

Thankfully you made it pretty easy to script this.

jet: https://www.youtube.com/watch?v=dsvT5hImPmo

parula: https://www.youtube.com/watch?v=8146CMi-OaQ

option a: https://www.youtube.com/watch?v=IqvxuQSzWO4

option b: https://www.youtube.com/watch?v=wa7bpV3XPV0

option c: https://www.youtube.com/watch?v=3rHbq4jw1ew

option d: https://www.youtube.com/watch?v=2_HiUXVNm2k

···

On Wed, Jun 3, 2015 at 5:17 PM, Stéfan van der Walt <stefan@...337...> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@...149...> > wrote:

Stéfan

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31

Fun activity: watch all 6 videos in a row then watch the text on this email spin and spin. =P

Gorgeous! Thanks Nathan!

I hope this kills C dead. It clearly makes certain features of the simulation harder to spot.

A great demo of the terribleness of jet, too: it looks like a huge mess.

···

On Thu, Jun 4, 2015 at 5:42 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

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On Wed, Jun 3, 2015 at 5:17 PM, Stéfan van der Walt <stefan@…337…> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

I’m a big fan of option D. So much so that when I needed to make a movie of

ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other

proposed colormaps?

Thankfully you made it pretty easy to script this.

jet: https://www.youtube.com/watch?v=dsvT5hImPmo

parula: https://www.youtube.com/watch?v=8146CMi-OaQ

option a: https://www.youtube.com/watch?v=IqvxuQSzWO4

option b: https://www.youtube.com/watch?v=wa7bpV3XPV0

option c: https://www.youtube.com/watch?v=3rHbq4jw1ew

option d: https://www.youtube.com/watch?v=2_HiUXVNm2k

Stéfan

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32

One other (admittedly very minor) consideration is how the colormaps look with shading applied. To borrow from the hillshading example:

(The image appears to be too large to attatch. Try here: http://www.geology.beer/images/hillshaded.png)

I personally really like option D for a lot of reasons, but this is another reason to prefer it. Providing additional information through “shading” etc, still works quite well. Option C also does well in this particular test, though it appears too “washed out” for my tastes.

At least to my eyes, options B fairs particularly poorly. In B’s case, the fact that the colormap runs towards black means that hillshading is difficult to distinguish from elevation changes. A suffers from similar problems in this case, though they’re much less severe.

In my personal opinion: D >> A > C > B

Cheers,
-Joe

Fun activity: watch all 6 videos in a row then watch the text on this email spin and spin. =P

Gorgeous! Thanks Nathan!

I hope this kills C dead. It clearly makes certain features of the simulation harder to spot.

A great demo of the terribleness of jet, too: it looks like a huge mess.

···

On Thu, Jun 4, 2015 at 5:42 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

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On Wed, Jun 3, 2015 at 5:17 PM, Stéfan van der Walt <stefan@…337…> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

I’m a big fan of option D. So much so that when I needed to make a movie of

ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other

proposed colormaps?

Thankfully you made it pretty easy to script this.

jet: https://www.youtube.com/watch?v=dsvT5hImPmo

parula: https://www.youtube.com/watch?v=8146CMi-OaQ

option a: https://www.youtube.com/watch?v=IqvxuQSzWO4

option b: https://www.youtube.com/watch?v=wa7bpV3XPV0

option c: https://www.youtube.com/watch?v=3rHbq4jw1ew

option d: https://www.youtube.com/watch?v=2_HiUXVNm2k

Stéfan

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33

Well that got horribly garbled somehow (and I hit send too early). Let me try that again:

hillshaded.png
hillshaded.png640×720 1 MB

​

···

On Thu, Jun 4, 2015 at 11:27 AM, Joe Kington <joferkington@…149…> wrote:

One other (admittedly very minor) consideration is how the colormaps look with shading applied. To borrow from the hillshading example:

(The image appears to be too large to attatch. Try here: http://www.geology.beer/images/hillshaded.png)

I personally really like option D for a lot of reasons, but this is another reason to prefer it. Providing additional information through “shading” etc, still works quite well. Option C also does well in this particular test, though it appears too “washed out” for my tastes.

At least to my eyes, options B fairs particularly poorly. In B’s case, the fact that the colormap runs towards black means that hillshading is difficult to distinguish from elevation changes. A suffers from similar problems in this case, though they’re much less severe.

In my personal opinion: D >> A > C > B

Cheers,
-Joe

Fun activity: watch all 6 videos in a row then watch the text on this email spin and spin. =P

Gorgeous! Thanks Nathan!

I hope this kills C dead. It clearly makes certain features of the simulation harder to spot.

A great demo of the terribleness of jet, too: it looks like a huge mess.

Matplotlib-devel mailing list

Matplotlib-devel@lists.sourceforge.net

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On Thu, Jun 4, 2015 at 5:42 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

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On Wed, Jun 3, 2015 at 5:17 PM, Stéfan van der Walt <stefan@…337…> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

I’m a big fan of option D. So much so that when I needed to make a movie of

ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other

proposed colormaps?

Thankfully you made it pretty easy to script this.

jet: https://www.youtube.com/watch?v=dsvT5hImPmo

parula: https://www.youtube.com/watch?v=8146CMi-OaQ

option a: https://www.youtube.com/watch?v=IqvxuQSzWO4

option b: https://www.youtube.com/watch?v=wa7bpV3XPV0

option c: https://www.youtube.com/watch?v=3rHbq4jw1ew

option d: https://www.youtube.com/watch?v=2_HiUXVNm2k

Stéfan

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34

I very much like D.

hillshaded.png
hillshaded.png640×720 1 MB

···

On Thu, Jun 4, 2015 at 9:34 AM, Joe Kington <joferkington@…149…> wrote:

Well that got horribly garbled somehow (and I hit send too early). Let me try that again:

​

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–

On Thu, Jun 4, 2015 at 11:27 AM, Joe Kington <joferkington@…149…> wrote:

One other (admittedly very minor) consideration is how the colormaps look with shading applied. To borrow from the hillshading example:

(The image appears to be too large to attatch. Try here: http://www.geology.beer/images/hillshaded.png)

I personally really like option D for a lot of reasons, but this is another reason to prefer it. Providing additional information through “shading” etc, still works quite well. Option C also does well in this particular test, though it appears too “washed out” for my tastes.

At least to my eyes, options B fairs particularly poorly. In B’s case, the fact that the colormap runs towards black means that hillshading is difficult to distinguish from elevation changes. A suffers from similar problems in this case, though they’re much less severe.

In my personal opinion: D >> A > C > B

Cheers,
-Joe

Fun activity: watch all 6 videos in a row then watch the text on this email spin and spin. =P

Gorgeous! Thanks Nathan!

I hope this kills C dead. It clearly makes certain features of the simulation harder to spot.

A great demo of the terribleness of jet, too: it looks like a huge mess.

Matplotlib-devel mailing list

Matplotlib-devel@lists.sourceforge.net

https://lists.sourceforge.net/lists/listinfo/matplotlib-devel

On Thu, Jun 4, 2015 at 5:42 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

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On Wed, Jun 3, 2015 at 5:17 PM, Stéfan van der Walt <stefan@…337…> wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@…149…> wrote:

I’m a big fan of option D. So much so that when I needed to make a movie of

ony my galaxy simulations today I went ahead and used it:

https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other

proposed colormaps?

Thankfully you made it pretty easy to script this.

jet: https://www.youtube.com/watch?v=dsvT5hImPmo

parula: https://www.youtube.com/watch?v=8146CMi-OaQ

option a: https://www.youtube.com/watch?v=IqvxuQSzWO4

option b: https://www.youtube.com/watch?v=wa7bpV3XPV0

option c: https://www.youtube.com/watch?v=3rHbq4jw1ew

option d: https://www.youtube.com/watch?v=2_HiUXVNm2k

Stéfan

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Brian E. Granger
Cal Poly State University, San Luis Obispo
@ellisonbg on Twitter and GitHub
bgranger@…882… and ellisonbg@…149…

35

I’m not sure what I’m looking at in that picture exactly, or how to distinguish a good result from a poor one – could you elaborate?

FYI I should also note that we’re planning on additionally providing isoluminant (or approximately isoluminant) variants for whatever colormaps we end up contributing, exactly for cases where you want to preserve the lightness channel for shading effects. So in any case you’ll have a choice between “mapA” and “mapA-isoluminant”, etc.

-n

···

On Jun 4, 2015 9:28 AM, “Joe Kington” <joferkington@…149…> wrote:

One other (admittedly very minor) consideration is how the colormaps look with shading applied. To borrow from the hillshading example:

(The image appears to be too large to attatch. Try here: http://www.geology.beer/images/hillshaded.png)

I personally really like option D for a lot of reasons, but this is another reason to prefer it. Providing additional information through “shading” etc, still works quite well. Option C also does well in this particular test, though it appears too “washed out” for my tastes.

36

I’m
not sure what I’m looking at in that picture exactly, or how to distinguish a good result from a poor one – could you elaborate?

It an nutshell, it’s whether shading can be distinguished from value changes.

FYI I should also note that we’re planning on additionally providing isoluminant (or approximately isoluminant) variants for whatever colormaps we end up contributing, exactly for cases where you want to preserve the lightness channel for shading effects. So in any case you’ll have a choice between “mapA” and “mapA-isoluminant”, etc.

-n

It’s essentially isoluminance, but also the absolute value of the luninance. (Ideally, you’d want a more-or-less isoluminant colormap with an average
luminance near 0.5.)

A colormap with all dark colors or all light colors can be isoluminant, but is largely useless for this application, as it will be difficult to distinguish shaded slopes from low areas or highlighted slopes from high areas.

Also, from a purely subjective level for this example, it’s how effectively the shading tricks your brain into seeing a topographic surface. The colormap has a good bit of influence on this, but I have no idea how to quantify it.

At any rate, including an isoluminant version solves a large amount of the problem. Thanks!

Also, to illustrate the exact issue I was referring to a touch more clearly, here’s a zoomed-in version of the previous example:

hillshaded.png
hillshaded.png800×720 802 KB

shaded_topography.py (1.33 KB)

···

P.S. Sorry, Nathaniel, you’re going to get this twice. I didn’t look closely enough when I hit reply. I seem to be rather bad at the whole “e-mail” thing today.

37

Awesome! Added these to the webpage.

For extra fun (90 mb download, but worth it):
http://vorpus.org/~njs/goldbaum-galaxies-all-colormaps.mkv

···

On Thu, Jun 4, 2015 at 12:42 AM, Nathan Goldbaum <nathan12343@...149...> wrote:

On Wed, Jun 3, 2015 at 5:17 PM, Stéfan van der Walt <stefan@...1271....> > wrote:

On Wed, Jun 3, 2015 at 5:08 PM, Nathan Goldbaum <nathan12343@...149...> >> wrote:
> I'm a big fan of option D. So much so that when I needed to make a
> movie of
> ony my galaxy simulations today I went ahead and used it:
>
> https://youtu.be/bnm554et0T8

Beautiful! How hard would it be to also do this for the other
proposed colormaps?

Thankfully you made it pretty easy to script this.

jet: https://www.youtube.com/watch?v=dsvT5hImPmo

parula: https://www.youtube.com/watch?v=8146CMi-OaQ

option a: https://www.youtube.com/watch?v=IqvxuQSzWO4

option b: https://www.youtube.com/watch?v=wa7bpV3XPV0

option c: https://www.youtube.com/watch?v=3rHbq4jw1ew

option d: https://www.youtube.com/watch?v=2_HiUXVNm2k

--
Nathaniel J. Smith -- http://vorpus.org