glTF Light Attenuation: Point and Spot Falloff

glTF manages point and spot light falloff primarily through the KHR_lights_punctual extension, using physically based inverse-square distance attenuation coupled with an optional range clamp and angular cone factors. While point lights attenuate purely based on distance, spot lights incorporate additional angular attenuation to simulate a focused beam. This article outlines the mathematical parameters, formulas, and cutoff behaviors that dictate how light intensity decreases over space within the glTF standard.

Distance Attenuation (Point and Spot Lights)

In standard glTF, both point and spot lights behave as punctual lights that emit light from a single dimensionless point in space. Their light falloff across distance is governed by two main elements: the physical inverse-square law and the optional range property.

1. The Inverse-Square Law

By default, glTF follows the physically realistic inverse-square law, where the intensity of light diminishes inversely with the square of the distance from the source:

\[\text{Attenuation}_{\text{distance}} = \frac{1}{\max(d^2, \epsilon)}\]

Where:

  • \(d\) is the Euclidean distance from the light position to the shaded surface.
  • \(\epsilon\) is a small threshold (typically around \(0.0001\)) applied to prevent a division-by-zero anomaly when an object is at the exact center of the light.

2. Range Clamping and Smooth Windowing

Because physical light theoretically travels infinitely, real-time rendering engines introduce a cutoff distance to discard negligible light calculations. In glTF, this is configured via the range property.

When range is defined and greater than zero, glTF applies a smooth windowing function that scales the light smoothly to zero at the specified boundary, preventing harsh visual seams:

\[\text{RangeFactor} = \max\left(0.0, \min\left(1.0, 1.0 - \left(\frac{d}{\text{range}}\right)^4\right)\right)\]

Combining this with distance falloff yields the full distance attenuation formula defined in the glTF specification:

\[\text{Attenuation}_{\text{distance}} = \frac{\text{RangeFactor}^2}{\max(d^2, \epsilon)}\]

If no range is defined, the light continues to fall off infinitely according to the pure inverse-square law.

Angular Attenuation (Spot Lights Only)

Spot lights project light within a cone and introduce directional falloff alongside distance falloff. The shape and softness of the light cone are determined by two angles defined in radians:

  • innerConeAngle: The angle measured from the spotlight direction vector within which the light is at full, unmodified intensity. Defaults to \(0.0\).
  • outerConeAngle: The angle beyond which the light completely attenuates to zero. Defaults to \(\pi / 4\) radians (\(45^\circ\)).

The region between innerConeAngle and outerConeAngle defines the light's penumbra—a smooth transition from peak brightness to complete darkness.

Angular Factor Calculation

To compute angular falloff, the cosine of the angle between the light’s central forward axis (\(L_{\text{dir}}\)) and the vector from the light to the surface (\(L\)) is compared against the cosines of the cone boundaries:

  1. Calculate the scale and offset: \[\text{lightAngleScale} = \frac{1.0}{\max(0.001, \cos(\text{innerConeAngle}) - \cos(\text{outerConeAngle}))}\] \[\text{lightAngleOffset} = -\cos(\text{outerConeAngle}) \times \text{lightAngleScale}\]

  2. Compute the angular attenuation factor: \[C_d = \max(0.0, L_{\text{dir}} \cdot L)\] \[\text{Attenuation}_{\text{angle}} = \text{clamp}(C_d \times \text{lightAngleScale} + \text{lightAngleOffset}, 0.0, 1.0)^2\]

Squaring the clamped linear transition produces a smooth, quadratic curve that avoids abrupt banding along the edge of the spotlight beam.

Summary of Falloff Execution

  • Point Lights: Total attenuation is strictly a function of distance:
    \(\text{Total Attenuation} = \text{Attenuation}_{\text{distance}}\)
  • Spot Lights: Total attenuation is the product of both distance and angular limits:
    \(\text{Total Attenuation} = \text{Attenuation}_{\text{distance}} \times \text{Attenuation}_{\text{angle}}\)