How to transform Polar to cartesian

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Kareeman
Kareeman 2011-12-2
评论： Irena Chernova 2015-2-16
Hi, I am a MATLAB beginner. I need the steps of how to transform polar coordinates to Cartesian. As I have 2D (jpeg)images for closed curve(organic shape an I need to convert it into an opened one. Many thanks for your help. Best regards
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Walter Roberson
Walter Roberson 2011-12-2
That curve "goes back on itself", and therefore cannot be a function in the polar coordinate system.
If it were in polar coordinate system, then there would have to be an origin point, but no such point is obvious. It is not clear to me, given that diagram, that choosing the centroid of the diagram would be a correct origin.
The connection to polar coordinates still escapes me.
Rather than converting polar to cartesian coordinates, are you perhaps looking to "cut" the image and "unroll" it? If so, then I am not certain you would gain anything compared to comparing it in the original space, but that would depend on how you were thinking to compare them.
Kareeman
Kareeman 2011-12-2
Thank you very much or your reply
I see what you mean.
But the following is what i am doing:
Method B, using image processing technology
The shadow of the draped specimen is cast from below onto a white sheeting covering the top translucent lid
and centre-plates. Detailed quantitative information on the drapability of the test specimen is obtained from
digital images captured with a commercial digital camera (or a scanner) after cutting the paper around its
shadow contour. The captured images, initially having grey levels, are transformed into monochrome images
through noise filtering and thresholding. The two-dimensional monochrome images of draped shadows
described above are firstly transformed into polar (∅, r) coordinates as shown in Figure 1, where the X-axis
from 0° to 360° is the angle, in degrees, from the baseline passing through the centre of the circle, and r
(Y-axis) is the amplitude, in centimetres. The shape parameters of a two-dimensional geometric drape model
defined as the number of nodes (waves or folds), the positions of nodes, wavelength and amplitude data and
various statistical information, can then be obtained using image processing technology and frequency
analysis as well as the traditional drape coefficient. A three-dimensional drape shape can be regenerated from
its captured two-dimensional drape images, with a three-dimensional simulator.
These are the parameter I want to work out:
Calculations
10.3.1 For each test specimen diameter used, carry out separate calculations.
10.3.2 For each of the six readings on each test specimen, calculate the following, which is automatically
obtained from the evaluation software (5.3.3) (see example in Figure 5).
a) Drape coefficient, D, expressed as a percentage, using the following equation:
s d
o d
100
A A
D
A − A
−
= ×
where Ao, Ad and As are the original area of an undraped specimen, the area of a supporting plate, and
the projected shadow area of the specimen after draping, respectively.
b) Node number, one of the drape shape parameters, expressed as the number of drape waves/folds.
c) Wave amplitude, one of the drape shape parameters, indicating the size, in centimetres, of the most
dominant drape waves/folds.
d) Wavelength, one of the drape shape parameters, indicating the wavelength of the most dominant drape
waves/folds, expressed in degrees of a circle (0° to 360°).
e) Minimum amplitude, one of the statistics indicating the smallest size of drape waves/folds, expressed in
centimetres.
f) Maximum amplitude, one of the statistics indicating the largest size of drape waves/folds present,
expressed in centimetres.
g) Average amplitude, one of the statistics indicating the mean drape waves/folds present, expressed in
centimetres.
h) Variance, one of the statistics indicating the distribution of the drape waves/folds amplitude, expressed in
centimetres.
i) Fourier transform/original and dominant/original, the three fitness factors to verify the fit of the Fourier
transformation and to determine the dominant wave, expressed in percentages, using the following
equation:
f
o
Fourier transform/original 100
B
B
= ×
d
o
Dominant/original 100
B
= B ×
where Bo, Bf and Bd are the areas of the original captured draped image, its Fourier transformed shape,
and the ideal shape recomposed from a determined dominant wave, respectively, as shown in Figure 5.
j) Graph, in polar coordinates, where the X-axis (from 0° to 360°) is the wavelength, in degrees, from the
baseline passing through the centre of the centre-plate (5.1.1) and r (Y-axis) is the amplitude, in
centimetres, representing each value of the wave amplitude and the wavelength at each node.
10.3.3 Calculate the mean drape coefficient, drape shape parameters, statistics and fitness factors for face
(a) and for face (b).
10.3.4 Calculate the overall mean drape coefficient, drape shape parameters, statistics and fitness factors.

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回答（1 个）

Sean de Wolski
Sean de Wolski 2011-12-2
Perhaps pol2cart?
doc pol2cart
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Irena Chernova
Irena Chernova 2015-2-16
Hi Kareeman, I know that it´s not actual but I deal really with the same problem (draped samples of textile..) Could I ask you please, how did you solve it finally? Thanks a lot!

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