viewZ2depth: View-Space Z to Depth Conversion

Depth buffer coordinate transformation

The view-space Z to depth conversion transforms view-space Z coordinates to normalized depth buffer values. This is essential for depth testing and z-buffer operations in 3D rendering pipelines.

Perspective Projection

For perspective projection, the depth conversion follows:

$$\text{depth} = \frac{(\text{viewZ} + \text{near}) \cdot \text{far}}{(\text{far} - \text{near}) \cdot \text{viewZ}}$$

This accounts for the non-linear depth distribution in perspective projection where near objects have higher precision.

Orthographic Projection

For orthographic projection, the depth conversion is linear:

$$\text{depth} = \frac{\text{viewZ} + \text{near}}{\text{near} - \text{far}}$$

This provides uniform depth precision across the entire view frustum.

Coordinate System Mapping

Input Range	Output Range	Projection Type
$[\text{-far}, \text{-near}]$	$[0, 1]$	Perspective
$[\text{near}, \text{far}]$	$[0, 1]$	Orthographic

ライブエディター

const fragment = () => {
      const viewZ = mix(-10, -0.1, uv.x)
      const perspDepth = viewZ2depth(viewZ, 0.1, 10)
      const orthoDepth = viewZ2depthOrthographic(viewZ, 0.1, 10)
      const isTop = uv.y.greaterThan(0.5)
      const color = select(
              vec3(perspDepth, 0, 0),
              vec3(0, orthoDepth, 0),
              isTop
      )
      return vec4(color, 1)
}