Normalizing pixel coordinates to [-1,1] makes shaders resolution-independent and centers the mathematical origin

A Shadertoy fragment shader receives pixel coordinates fragCoord in [0,resolution] pixels. Dividing by resolution maps to [0,1]; subtracting 0.5 and multiplying by 2 gives [-1,1]. For a non-square viewport, dividing x by the aspect ratio corrects for pixel aspect, so circles remain circular. This normalized coordinate system matches how mathematicians define curves and is the standard for all distance-field shaders. Any SDF or camera ray defined in these units is automatically resolution-independent: the same code runs at 800×450 or 1920×1080 without changing shape sizes.

Examples

vec2 uv = (fragCoord - 0.5*iResolution.xy) / iResolution.y; // aspect-corrected [-1,1]

Assessment

A shader designed at 800×450 is run at 1920×1080 without coordinate normalization. Describe the visual distortion that occurs and how normalization fixes it.