The context of the question is OpenGL ES 2.0 in the Android environment. I have a texture. No problem to display or use it.
Is there a method to know its width and
I'll suggest a hack for doing this. Use ESSL's textureSize function. To access its result from the CPU side you're going to have to pass the texture as an uniform to a shader, and output the texture size as the r & g components of your shader output. Apply this shader to an 1x1px primitive drawn to a 1x1px FBO, then readback the drawn value from the GPU with glReadPixels
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You'll have to be careful with rounding, clamping and FBO formats. You may need a 16-bit integer FBO format.