You do not need to mix for this (and it will not work the way you want).
I think that while you determine the texture coordinate in the screen space, it should be seamless between two separate circles.
To do this, instead of using the texture coordinate passing through the vertex shader, simply use the fragment position to select the texture plus or minus some scaling:
float texcoord = gl_FragCoord / vec2(xresolution_in_pixels, yresolution_in_pixels);` gl_FragColor = glTexture2D(papertexture, texcoord);
If you do not have access to GLSL, you can do something instead of the stencil buffer. Just draw all the circles in the stencil buffer, use the merged area as a stencil mask, and then draw a full-screen square of your texture. Color will be easily put off when all circles are combined.
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