Dialysis Photoshop Polar coordinates filter

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For some abstract effect graphs, the polar coordinates filter in Photoshop is worth studying ...

"Summary" for some abstract effect graphs, the polar coordinates filter in Photoshop is worth studying ...

On the foreign website to see someone to the Photoshop filter into two categories, one is not destructive to the original image of the filter, the other is a destructive filter on the original artwork. Destructive filters are mostly twisted filters, where the destructive of polar coordinates can be a fairly large one.

Because of the destructive polar coordinates, many people think that the filter for the image, photo processing is not much of a practical application, but if for some abstract images, I think this filter is still some places worth studying, I hope you have read this article will also be inspired.

deformation of a polar coordinate　　 Perceptual Knowledge

Let's look at what the polar coordinates do to the image. As shown in figure

This picture is the square, the circle and the color block through the polar coordinate transformation before and after the image.

　　Rectangular to polar coordinates of the change: can be considered as the top edge of the concave, bottom and sides of the flanging process.
　　The change of polar coordinates to a rectangular coordinate: it can be considered as the process of the bottom concave, the top edge and the side flanging.

Here the "process" is only used to deepen the memory, in fact, the process of turning the flip is not there, but directly through the mapping of the coordinates.

　　1. Coordinate-> Polar coordinates

The vertical line in the original image is transformed by polar coordinates and becomes radioactive .
The horizontal lines in the original image are transformed into concentric circles by polar coordinates.
Of course, the interlaced painting is a spider web.

Observe the position of each color swatch after the transformation, the top of the original image shrinks to the center of the Circle, and the red at the bottom becomes the canvas incircle . The left and right two blue color blocks are flipped upwards and eventually merged into one fan type, and the original two sides overlap above .

Remember that the position of each color block before and after the change is not only in the understanding of the polar coordinates filter but also in the practical application, at least now you have learned to draw radiation, concentric circles, fan type.

　　2. Polar coordinate-> rectangular coordinates

The vertical and horizontal lines (except the axes) of the original image are transformed into a parabola/hyperbola in the diagram (specifically that line I have not yet figured out, but I prefer a hyperbola).
After transformation, the axes change to a longitudinal 5 divider, where 1,3,5 is the original longitudinal axis and the 2,4 is the original axis.
For color swatch changes, please pay attention to the position and amplitude is, this I do not study much.

BTW: In the preface I have said that polar coordinates to the image is destructive, in fact, polar coordinates filter also has a certain degree of reduction, after all, this is the mapping between the coordinate system. Some information about the original image can be recovered by performing the reverse transformation for the graph that performs the positive transformation. However, because polar coordinates are not one by one corresponding relationships, the information on the edges of the graph cannot be restored. More alternative applications can also use the polar coordinates of the restoration of the image encryption.
　　Two, polar coordinates filter application

I use polar coordinates filters primarily to draw circles, or to draw a circle based image. We often see the use of vector software to draw some repetitive and regular graphics, in fact, some graphs using polar coordinates filter can be done, sometimes better than using vector software, change more.

　　2.1 Production of the radioactivity, see part I.

2.2 The production of concentric circles, see the first part.

2.3 Fan type, ring type, Rainbow, see the first part.

　　2.4 Helix

Spirals are fairly straightforward to draw in vector software, and some software itself has a spiral tool. But for PS, there is no particularly suitable tool or formula to draw the helix. There is a spin twist (twirl) filter in the Twist filter that can do the same thing with a spiral, but it feels less manageable.

I draw a concentric circle from the inspiration, found that you can use polar coordinates filter to draw a spiral, whether the isometric or open can be drawn, the steps are relatively simple, only a few steps.

First create a rectangular blank file (400*20), draw a slash (if it is a thick slash, then pay attention to slash in the canvas of the other two corners also want to draw a slash processing to ensure that the next fill when the normal connection), define the pattern. As shown in figure

Create a new file (400*400) to fill with the pattern you just defined. As shown in figure

Apply polar coordinates filter, rectangular coordinates--polar coordinate

Apply the lighting filter.

Then apply the spherical filter and other modifications to complete.

The above figure is used to draw an isometric spiral, and if you draw an unequal helix, you need to change the spacing and slope of each slash.

　　Description: The image of the bottom right there will be a black trace, this black line is the bottom of the original map of the black dots mapped over. The bottom edge of the original image is mapped to a circle that is cut inside the outer border of the new diagram (a square canvas, if the rectangle is an ellipse), and all the blanks outside the circle. If you want to avoid this black line, just pay attention to the bottom edge of the original image is the background color. In fact, this line also has its special use, see the following examples.

The painted spiral can also be made into GIF animation with ImageReady.
　　Http://cimg.163.com/catchpic/E/EC/ECDD08BD788F9E98FD9A0A2041EFA065.gif
　2.5 vertical slash and grid change in polar coordinates

The truth is the same, see one, the other will be. Note, however, that if you are filling a vertical bar, the new canvas size is best to be an integral multiple of the original defined pattern size. Otherwise, the left and right sides of the original image will not be well coordinated after the polar coordinates filter.

The following two charts use the black line just introduced to make the radiation outside the incircle.

The evolution of complex graphs

　　Polar coordinates change of 2.6 grids

Using a simple mesh with some other filters can make a variety of unexpected effects. 6~ Group 9, as shown in Fig group. Let's take group 8 as an example to briefly introduce the method of making.

First draw the grid, I do not know what method to draw the grid? Fill or some other way, you can communicate later. I draw the grid with a collage (Tiles).

Flip vertically using the polar coordinates filter (polar-> rectangular coordinates).

Again s uses polar coordinates filter (polar coordinate-> rectangular coordinates), flip vertically.

Then use the polar coordinates filter (rectangular-> polar coordinates)

Using light filters, curves

The finished effect is as follows.

Group 7 and group 9 are made in a similar way to group 8, except that there are some other steps in between.

Other applications

2.7 Making CD

There are a lot of ways to make a disc, of course, it was painted in polar coordinates, but it didn't feel good.

　　2.8 Radioactive writings

Group 11, there are many tutorials on this web, no longer repeat.

　　2.9 Change of polar coordinates of shape

I like this most, was accidentally tried to come out. Group 12.

The specific application is here, and finally talk about a little bit of theory, say the polar coordinate conversion filter work process.
working process of the polar coordinates filter (rectangular to polar coordinates)

In general, any point (pixel) in a bitmap image can be represented by rectangular coordinates (X,Y). The same pixel can also be represented by polar coordinates (R,A). The working process of the polar coordinates filter is the process of representing the pixel (X,y) based on the rectangular coordinate system after the polar coordinate mapping (r,a) and then the rectangular coordinates (x ', Y ').

The formulas for the interaction of rectangular and polar coordinates are as follows:

R = sqrt (x * x + y * y)
A = ARCTG (y/x)
x = R * COS (a)
y = R * Sin (a)

The following is a pseudo code that simulates the work of the polar coordinates filter. This code is not written by me, I just read it, more detailed explanation can refer to the following links:

　　Http://www.jasonwaltman.com/thesis/filter-polar.html

(This is a foreign website, the station Master uses C + + to simulate some PS filter effect, but also provides the source code and the source program.) ）

For every pixel in the original image do
{
X and y are the coordinates of the current pixel in the rectangular coordinates.
The coordinate of the image center point is x = 0, y = 0.
R and a are polar coordinates of pixels. Where angle A is a radian unit.
R = sqrt (x * x + y * y);
A = atan2 (y/x);
R takes half of the minimum value of the length and width of the image.
R= min[image_width, Image_height]/2
The new X and Y are the new coordinates of the pixel in the rectangular coordinate system after the polar coordinate filter transformation. The purpose of this conversion, especially the choice of R and 6.2832 (2PI), I think is to limit the converted image to the size of the original canvas. At the same time this step eventually leads to the distortion of the image.
x = R * IMAGE_HEIGHT/R;
y = a * image_width/6.2832;
filterpixel.x = x;
Filterpixel.y = y;
}

This is just a piece of pseudo code, the real implementation process to be more complex, if you continue to go deep on the topic seriously, so the in-depth discussion or see the link, go to see for yourself.

Last quote from that website as a closing remark.

"If used creatively, the effect is worth more than just its novelty."

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