PainShop Pro Graphics - Polar Coordinates and More Geography

Author

Polar Coordinates and More Geography

Spandex Rutabaga

2006-07-10, 7:43 pm

This time I going to touch for a moment on Antarctica. No, there
are not going to be any marching penguins, just the South Pole.
The attached picture shows Antarctica from space on the left with
the South Pole marked with a red dot having a blue circle around it.

The South Pole is point, which is something with a precise
location but not width or height. In other words, it's a dot that
is infinitesimally small. In an image this means that the mark
for the South Pole is a pixel in size and no bigger. Even though
it is infinitesimally small the tiniest thing we can draw in an
image is one pixel. Notice what happens to this little dot marking
the South Pole when we convert from polar to rectangular coordinates
using the Polar Coordinate filter as shown on the right.

Something that was a point, was stretched out into a row of pixels
at the top of the image spanning the entire width of the image.
This means that circular objects will have their centers stretched
a great deal when converted to rectangular coordinates and the
tops of such images will always look a little smeared out as if
they were somewhat out of focus. For practical use it is good to
plan to crop away this part of the image unless you will be
converting back to polar coordinates after some editing.

The flip side of the above observation has to be considered when
going from rectangular to polar coordinates. The entire top row
of the image gets collapsed into a single point after being
transformed. This means that fine detail at the top of the
rectangular coordinate image will not be visible after conversion
to polar coordinates. You have to plan for this, either by not
putting any important detail near the top of the image or by using
enough pixels in a big enough image to be able to represent detail
even after it has undergone severe compression.

All Things Mopar

2006-07-10, 7:43 pm

> This time I going to touch for a moment on Antarctica. No,
> there
> are not going to be any marching penguins, just the South
> Pole.
> The attached picture shows Antarctica from space on the
> left with
> the South Pole marked with a red dot having a blue circle
> around it.
>
> The South Pole is point, which is something with a precise
> location but not width or height.

only in plane geometry. likewise, a line has only length,
infinite, but no width. but to most people, used to thinking
in the real 3-D world of people, the definitions of "point"
and "line" are much broader.

In other words, it's a dot that
> is infinitesimally small. In an image this means that the
> mark
> for the South Pole is a pixel in size and no bigger. Even
> though
> it is infinitesimally small the tiniest thing we can draw
> in an
> image is one pixel. Notice what happens to this little dot
> marking
> the South Pole when we convert from polar to rectangular
> coordinates
> using the Polar Coordinate filter as shown on the right.
>
> Something that was a point, was stretched out into a row
> of pixels
> at the top of the image spanning the entire width of the
> image.
> This means that circular objects will have their centers
> stretched
> a great deal when converted to rectangular coordinates and
> the
> tops of such images will always look a little smeared out
> as if
> they were somewhat out of focus. For practical use it is
> good to
> plan to crop away this part of the image unless you will
> be
> converting back to polar coordinates after some editing.
>
> The flip side of the above observation has to be
> considered when
> going from rectangular to polar coordinates. The entire
> top row
> of the image gets collapsed into a single point after
> being
> transformed. This means that fine detail at the top of the
> rectangular coordinate image will not be visible after
> conversion
> to polar coordinates. You have to plan for this, either by
> not
> putting any important detail near the top of the image or
> by using
> enough pixels in a big enough image to be able to
> represent detail
> even after it has undergone severe compression.

Carrie Osmo

2006-07-10, 7:43 pm

Thanks for these
you have given me a hep of new ides other than making cd
labels LOL. Interestung I will try some of this
carrie
"Spandex Rutabaga" <SpRu@agabatur.xednaps> wrote in message news:44A8C1CE.A8383E7A@agabatur.xednaps...
> This time I going to touch for a moment on Antarctica. No, there
> are not going to be any marching penguins, just the South Pole.
> The attached picture shows Antarctica from space on the left with
> the South Pole marked with a red dot having a blue circle around it.
>
> The South Pole is point, which is something with a precise
> location but not width or height. In other words, it's a dot that
> is infinitesimally small. In an image this means that the mark
> for the South Pole is a pixel in size and no bigger. Even though
> it is infinitesimally small the tiniest thing we can draw in an
> image is one pixel. Notice what happens to this little dot marking
> the South Pole when we convert from polar to rectangular coordinates
> using the Polar Coordinate filter as shown on the right.
>
> Something that was a point, was stretched out into a row of pixels
> at the top of the image spanning the entire width of the image.
> This means that circular objects will have their centers stretched
> a great deal when converted to rectangular coordinates and the
> tops of such images will always look a little smeared out as if
> they were somewhat out of focus. For practical use it is good to
> plan to crop away this part of the image unless you will be
> converting back to polar coordinates after some editing.
>
> The flip side of the above observation has to be considered when
> going from rectangular to polar coordinates. The entire top row
> of the image gets collapsed into a single point after being
> transformed. This means that fine detail at the top of the
> rectangular coordinate image will not be visible after conversion
> to polar coordinates. You have to plan for this, either by not
> putting any important detail near the top of the image or by using
> enough pixels in a big enough image to be able to represent detail
> even after it has undergone severe compression.

Barbara J Bradley

2006-07-10, 7:43 pm

"Spandex Rutabaga" <SpRu@agabatur.xednaps> wrote in message
news:44A8C1CE.A8383E7A@agabatur.xednaps...
> This time I going to touch for a moment on Antarctica. No, there
> are not going to be any marching penguins, just the South Pole.
> The attached picture shows Antarctica from space on the left with
> the South Pole marked with a red dot having a blue circle around it.

<snipped>

Thank you for all of this education.
Barb

Spandex Rutabaga

2006-07-10, 7:43 pm

All Things Mopar wrote:

>
> only in plane geometry.

You didn't notice that the image constitutes a flat 2D plane. You
confused the source of the image with the image itself.

John Andrisan

2006-07-10, 7:44 pm

>From my topology classes of long ago:

A sphere is a 2-D surface embedded in 3-Space. The South pole is a 2-D
point.

Spherical Geometry and Trigonometry apply here.
john