ratio: Adaptive Aspect Ratio Transformation

Dimension-aware coordinate scaling for consistent proportions

The ratio function applies adaptive transformations based on dimensional relationships between coordinate spaces and target sizes. It automatically selects appropriate scaling strategies depending on whether the target space is wider or taller.

Adaptive Scaling Logic

Given coordinates $v = (x,y)$ and size vector $s = (w,h)$:

When width ≥ height (landscape orientation): $\text{result} = \left(x \cdot \frac{w}{h} - \frac{w-h}{2h}, y\right)$

When height > width (portrait orientation): $\text{result} = \left(x, y \cdot \frac{h}{w} - \frac{h-w}{2w}\right)$

The selection between these modes uses: $\text{step}(w,h)$

Mathematical Foundation

Aspect Case	Primary Scaling	Secondary Offset	Unchanged Axis
Wide format	X-axis stretch	X-axis centering	Y-axis preserved
Tall format	Y-axis stretch	Y-axis centering	X-axis preserved

Live Editor

const fragment = () => {
      const adapted = ratio(uv, iResolution.xy)
      const waveform = adapted.x.mul(adapted.y).mul(20).sin().abs()
      const pattern = waveform.pow(adapted.length())
      return vec4(vec3(pattern), 1)
}