Spherical Parametrization and Remeshing

Spherical Parametrization and Remeshing

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  • mémoire - matière potentielle : gather operations
Spherical Parametrization and Remeshing Emil Praun Hugues Hoppe University of Utah Microsoft Research original spherical parametrization octahedral parametrization geometry image (lit) remeshed geometry Figure 1: Demonstration of spherical parametrization and subsequent resampling into a geometry image. Abstract Recently, Gu et al. [2002] introduced geometry images, in which geometry is resampled into a completely regular 2D grid. The process involves cutting the surface into a disk using a network of cut paths, and then mapping the boundary of this disk to a square.
  • spherical parametrization
  • geometry image
  • spherical triangle
  • stretch
  • sphere
  • domain
  • mesh
  • surface
  • map



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What is the
Translated by Y. Noda
Supervised by Y. Kamide

A Message from Galileo Galilei (1564-1642
Hi, I am an Italian scientist raised in Pisa during the late
Renaissance period. Galileo was my first name. At that time
in Italy, "famous" people were called by their first names
instead of their family names. People say I laid the
foundations of modern science.
Following advice from my father, who was a music and
mathematics teacher, I enrolled in a medical course at the
University of Pisa. I became, however, totally absorbed in
mathematics, instead of medical science. Do you know that
the "Isochronism of the Pendulum" principle, which you learn
at high school, is one of my findings? Finally I quit the
While working as a private teacher to rear my younger brothers and sisters, I kept
doing research. At the age of 25, my first paper was published and was well accepted,
and I was invited to be a Lecturer at the University of Pisa. My father died 2 years
Twenty years before I was born, Copernicus published the Copernican theory that
our Earth, not the stars in the sky, is moving. But, people hardly believed this theory
because what we see in daily life is that the sun rises from the eastern horizon and
goes down in the west.
Among other findings of mine are Jupiter's four satellites, craters on the moon's
surface, and waxing and waning of the moon, all from observations with a Galilean
telescope. These discoveries cast questions on the astronomy
of that time, as proof of the heliocentric theory. My discovery
of the sunspots was criticized by the advocates who said "what
a shame to insist that there are spots on the perfect sun!" I
had to face the Inquisition several times. When Newton, who
was born in the year of my death, established the dynamics by
combining my findings, I felt my efforts were rewarded.
Because of long-time observations of the sun with the naked
eye, my retinas were damaged, and I became blind. My later
papers were written by dictation.
To the mysterious glow in the sky I gave the name "aurora"
after the Roman goddess of dawn. In 1621, a fabulous aurora
showed up in Venice. Even though I had seen auroras several
times, that was the one I could never forget. I did not have the
slightest idea that the origin of auroras is with the sunspots
that I found myself! It was not until 200 years later that
Leaning Tower of Pisapeople became to know the true scenario for the generation of
Auroral breakup seen from directly underneath. <Photos by Shiori Uchino>q
Where is today's scientific
adventure for Mol and her YellowknifeYellowknife
robotic dog Mirubo?
They are flying over
Yellowknife, Canada, at
62 north latitude.
if only we can
We are almost
there, Mirubo! Huffing, encounter an
Mol Mirubo
Oh, we have been
having a hard time
But, finallyall the way.
it will be
I am sure weWe have
can expect aBrrr, it'sfinally spectacular auroracold!
in such cold Right!arrived!
Not right! To study theWhat brings
aurora, of course.The temperature has you here,
Now, are younothing to do with the sensei? interested in ...generation of auroras.
how auroras are Yes!!
created? Could you
explain ...
Why?! Ah, it's you,
Aurora sensei!
You learned that the The Earth's geomagnetic
Earth is a huge magnet field is distorted by the
and has the geomagnetic solar wind into a
field, didn't you? shape like this.
And, charged particles
are accumulated here.We did.

The aurora appears in
That's why we callthe night sky, namely,
this area thethis part of geomagnetic
field lines. auroral belt.
Its shape is
You arelike a belt.
You see from this map
that the auroral belt is
surrounding the geomagnetic
The auroral belt willThe reason why the auroral belt
move toward lowerlies in the arctic is not because it
latitudes from the polaris cold there, but just because
regions, and will ...the geomagnetic north pole happens
to be presently
located at the
reach Japan innorthwest corner
1000 years.of Greenland.
Yes, althoughWow, will auroras
it will be in thebe seen in Japan?!
far distant future.
We can't wait The aurora does
that long. Let's But, it's too not show up before
wait for an Really?cold. nightfall.
aurora here. Huuurry up,
I didn't
know that.
At night...An intense auroraThe aurora
occurs only on the
does not occur night side for some
at any time? reason.
I think it's
about time.
I am
freeeezing!! Gasp!!It's almost
30 C!!
We have been
waiting for an
This is my limit.aurora for more
I can't be herethan 2 hours.
any longer.
?????YYes! Yes!es! Yes!
Au Au ...
Aurora, splendid,
my aurora!! super!
She sometimes
does too
much ...
5This is called theThat was a
"auroral breakup." wonderful You guys
An active one like
are very aurora. this is rare.
Hi, Aurora
It's muchThe aurora is
brighter than
inscrutable. I expected.
I wonder how the a collection of hot, charged
auroral lights are particles, called a plasma,
generated. coming out of the sun.
When these charged particles
collide with the Earth's
In the first
atmosphere, the aurora is
place, the
aurora is
by ...
VVa a
The aurora has Those colors depend on which
colors of chemicals the charged particles
collide with. Green light results
from the collision with the oxygenwhitish green that
atoms, and blue from theis most common, ... Blue
nitrogen molecules.
blue, and ...
Above 250 km where the
atmosphere is thin, the
oxygen atoms produce red
sometimes red in
its upper part of
auroral curtains. Red
It's so I want to get Join us,
a closer lookbeautiful!
sensei!!at the aurora.
No, thank you.
I will wait for
you here.
Let's go up,
We can
reach it soon.
A great
o o
o o
m mPant, pant...
10 min.later
Now it's veryWe will
close to us ...
reach it soon. I hope ...
We are not
the aurora
I have already
at all!! reached my
The aurora seems to be Welcome back!
just above the clouds.
In fact, it is very high.
Mirubo, no matter
Look at this picture.
how hard you try,
you will never catch
the aurora.
Space Shuttle
Ozone Layer
Airplane Mt. Everest
You need to ride the
Space Shuttle to fly as
What?! high as the aurora.
Heh, heh