Saturday, July 15, 2006

Night panoramic photography in Melbourne; complex number magic

This is going to be a mass of photographs, and tiny bit of mathematics.

On Thursday, Diana mentioned that Docklands is a promising venue for night photography. Said the bridge in that vicinity is beautiful. So I took a walk.

This is the aforementioned bridge.

Click here for large size image.

I then walked out on the old pier towards the central supports of the bridge. It was a long walk.

This was on one of the bridge's support columns, above deck level, shot with full telephoto on a tripod.

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The view back to where I snapped the first photo.

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I have no idea what this structure is, but it appears to be part of the old port’s infrastructure.
Note the new port across the harbour.

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Parts of the pier were removed, leaving the supports exposed. Suitably sized condomettes were capped over the columns, presumably to prevent idiots from dancing on them. Also to prevent rainwater from stagnating at the top of the columns and rotting through the structures.

Huge cranes used to roll majestically over these tracks, presumably.

Docklands Panorama

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A 7-frame panoramic image spanning 90 degrees (horizontally). Measuring 3330 x 600 pixels and weighing 196 KB, it is large. Be patient, and remember to scroll sideways.

Water Feature

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Bali memorial, Melbourne.

And now, the mathematics:

Assumed knowledge: elementary knowledge of complex number manipulation

I always had trouble remembering the trigonometric identities for sin(a + b) and cos(a + b). Fret no more, Roger Penrose has pointed out a very nifty derivation using complex numbers.

Using the modulus and argument (some engineers may say magnitude and phase) notation, a complex number can be written as such:

To obtain the trigonometric identities, expand the following complex number using the above expression.

Do it, and be awed.

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Anonymous NaiveIdealist said...

grrr u shud call me go ..havnt try night photography yet...

11:50 am, July 15, 2006  
Blogger Dr. Tan said...

The pillar is wicker. Try removing the shadows on top? Its a distraction.

12:17 pm, July 15, 2006  
Blogger Wuching said...

u take good shots!

3:34 pm, July 16, 2006  
Blogger Lao Chen said...

Sorry, that route is a bit too dishonest for my liking. I know I photoshop sometimes, and that boundary of mine is fuzzy, but this is way over it.

Thank you!

11:51 pm, July 16, 2006  
Blogger sonia said...

Hey, nice night pics!! Ahhh, so nice u get to go here n there, see various interesting stuffs... *envy*... Oh, I think it looks just fine, that pic with shadows =)

The blogger meeting sounded fun. Long time nvr go for (smaller group of) bloggers meeting! And weird la, yvy said the pic of ted & her not so nice.. I thought it looked ok - like they were concentrating on whoever's talking then.. Not the bored look, rite? =P

1:23 am, July 17, 2006  
Blogger xaverri said...

Hey.. it wasn't the Bolte Bridge I meant. The one I talked about is a pedestrian bridge at Yarra's Edge. But nice pics! You can teach me a thing or two bout night photography eh :P

9:13 am, July 17, 2006  
Blogger Lao Chen said...

You can get nice KL skyline pictures also la... those hilltops in Bangsar area are good i think. And the Star LRT heading towards Sentul used to give quite stunning views of the sunrise over KL.

No wonder i was a bit unimpressed by that structure! We should go and take photos one morning/day/evening/night. Im sure there are tricks to be learned both ways.

8:01 pm, July 17, 2006  
Anonymous bart said...

What a great pictures on your blog. Nice work!

6:11 pm, July 19, 2006  
Blogger SooHK said...

Nice photos.....

12:39 pm, November 13, 2006  
Blogger Required field left blank said...

Now the math:
are there any other ways to prove the identities?

I always thought they were derived originally from complex numbers.

10:41 pm, November 05, 2007  

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