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Abstract

Spherical harmonics are often used for compact description of
incident radiance in low-frequency but distant lighting
environments. For interaction with nearby emitters, computing
the incident radiance at the center of an object only is
not sufficient. Previous techniques then require expensive
sampling of the incident radiance field at many points
distributed over the object. Our technique alleviates this
costly requirement using a first-order Taylor expansion of the
spherical-harmonic lighting coefficients around a point. We
propose an interpolation scheme based on these gradients
requiring far fewer samples (one is often sufficient). We show
that the gradient of the incident-radiance spherical harmonics
can be computed for little additional cost compared to the
coefficients alone. We introduce a semi-analytical formula to
calculate this gradient at run-time and describe how a simple vertex shader can
interpolate the shading. The interpolated
representation of the incident radiance can be used with any
low-frequency light-transfer technique.