Unit 3 sec 4.2
Aspect ratios
12 November 2015
23:52
The cape of a rectangle can be conveniently described using
the idea of aspect ratio.
The aspect ratio of the rectangle is the ratio of its
longest side to the shorter side. For example, the aspect ratio of the
left-hand rectangle is 25 : 15 , when simplifies to 5 : 3. The aspect ratio of
the right-hand rectangle is 10 : 6, when simplifies to 5 :3, so these 2
rectangles have the same aspect ratio. So the 2 rectangles have the same gate
though the 2nd is smaller.
A rectangular image can be in line all reduced to any
rectangle that has the same aspect ratio as the original image. Every different
aspect ratio is required, then the image has to be cropped.
Scale factors
if an image that measured
3 cm × 2 cm is enlarged to 9 cm × 6 cm, then they went and height both triple.
We say that the scale factor is 3. Similarly, the same image is instead reduced
to 1.5 cm × 1 cm, then the web and height both half, and the scale factor is
half.
Whether line is that whether or height of the image,
although I felt anything that appears in the image. The scale factors displayed
on photocopiers are usually expressed as percentages. For example, if you want
a photocopier to produce an image that is double the height of the original
image, then you need a scale factor of 2, so you will certainly copier to
enlarge by 200%.
Videos
aspect ratio is also an important issue. Many older video
programs that are made with the aspect ratio of 4 : 3, but in recent years 16 :
9, has become the most common video standard throughout the world. When a 4 : 3
image is displayed on a 16 :9 screen, the image has to be pillar boxed
(displayed with black bars on the side), stretched or cropped.
Paper sizes
we consider the aspect ratio of sheets of paper. You are probably
familiar with the paper size A4, A3, and so on. The largest paper size in this
series is A0, and the next largest is A1, and so on. This series of paper
sizes. It is known as the ISO 216 standard.
The paper sizes in the series by design so that they all
have the same aspect ratio. This means that an A4 image, can be scaled up to an
A3 one with no need for cropping. They were also designed to have the
additional property that each side of paper is exactly the same size and shape
as the 2 of the next small sizes placed side-by-side. For example, if you fold
an A3 sheet of paper in half, then it becomes the same size as it is sheet of
A4. There are various advantages of this property. For example, an envelope
sized to fit an A5 sheet of paper will fit an A4 sheet folded in half, or an A3
sheet folded in quarters, and so on.
The aspect ratio that is needed at the paper sizes are to
have the properties described above can be worked out as follows. Suppose that
the aspect ratio needed is a:1 . Where A represents some number. Consider a
sheet of paper with this aspect ratio. If it is shorter side has length w cm,
say, then its longest side has length aw cm, since aw: w = a:1. Since paper
sizes have the same aspect ratio, these ratios must be equal. So that we can
compare them, let us make the 1st ratio have 2nd number
a, the same as the 2nd ratio. To do this, we multiply both numbers
in the 1st ratio by a.
Therefore, a must be √ 2. So the aspect ratio that is needed
is √2:1 . It involves an irrational number. Each size of paper in the ISO216
standard has an aspect ratio of approximately √2: 1.
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