I am applying Effect-gaussian blur on an Object with 50% Opacity. Instead of producing a smooth blur effect it ends up with a box around the shape.
why does this happen? Thank you.
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My suspicion is that this has everything to do with the fact that Gaussian Blur is a rasterised effect. It basically converts your object into pixels (gasp!) and then applies a Photoshop effect to it—hence the 'Photoshop Effects' mention in the Effect menu.
As Pixels take up memory space and thus CPU power, it seems reasonable to create an upper limit to the size of the raster image that the effect creates. The default is relatively small, to keep Illustrator running smoothly.
To prevent, I lifted this from http://vectorboom.com/load/tips/basix/remove_gaussian_blur_limitation_in_illustrator/15-1-0-345:
Go to Effect > Document Raster Settings and tweak the value in the field that says 'Add: ____ around object'. Apparently, if you set this value to at least three times the radius of the Blur, the blur effect will not get clipped.
Do note that the value in the field is limited to 720px, most probably to create an upper limit to the amount of pixels in the rasterised effect.
Seemingly you have already got an explanation and how to persuade Illustrator to be less stingy when deciding how big raster image will be generated as the result of Gaussian blur effect.
The already given workaround (=use Feather) doesn't expand the shape like Gaussian blur, but makes the edges thinner - you may need to make an offset path to get the blur look expanded.
Another workaround is use Gaussian blur but at first
Consider to make big fuzzy shapes by applying gradients - radial ones in this case. They are vector objects; scaling doesn't spoil them. In the next image a big circle with radial gradient from white to 0% opaque white is placed below the full white circle:
Gradient stops need careful adjustment, blurring would be easier if it worked as wanted.
More complex shapes are possible if you use Gradient Mesh. Check it from Illustrator User's Guide.
If you can accept raster images to be mixed with your vector shapes consider also making the wanted effect in Photoshop. You can easily paste a vector shape from Illustrator into an empty image in Photoshop (assuming the empty image has transparent background and the needed resolution for your final usage), blur, draw more with brushes or process otherwise the shape.
Export the modified shape as PSD or PNG (see NOTE1) with transparent background and place the image back to Illustrator. Pasting it directly back unfortunately removes the transparency.
NOTE1: PNG is RGB only, PSD can have CMYK colors