Vis Comput (2013) 29:917–926 DOI 10.1007/s00371-013-0856-7 ORIGINAL ARTICLE Dual space directional occlusion Sebastian Herholz · Jens-Uwe Hahn · Andreas Schilling Published online: 2 July 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract Current real-time ambient or directional occlu- sion approximation methods are either screen space or ob- ject space based. Both methods suffer from drawbacks such as time incoherence and occlusion popping for screen space methods or loss of detailed occlusion effects caused by ge- ometry simplification for object space methods. We present an algorithm that combines both methods to overcome these drawbacks. To avoid over or underestimations during the combination, we use the Spherical Harmonics representa- tion of the directional occlusion information. We therefore combine “Screen Space Spherical Harmonics Occlusion” (Herholz et al. in VMV, 2012) with “Interactive Voxel Cone Tracing” (CT) (Crassin et al. in Comput. Graph. Forum, 2011). The result is a directional occlusion approximation including both occlusions from distant or not directly visible objects and detailed occlusions effects from fine geometrical structures. To increase the quality of CT for occlusion sam- pling, we also present several extensions such as view de- pendent cascaded voxelization and a method for voxel cov- erage estimation. Keywords Ambient occlusion · Real-time · Directional occlusion · Spherical harmonics · Shadows · Voxelization S. Herholz ( ) · A. Schilling University of Tübingen, Sand 14, 72076 Tübingen, Germany e-mail: Sebastian.Herholz@gmail.com J.-U. Hahn Stuttgart Media University, Nobelstrasse 10, 70569 Stuttgart, Germany 1 Introduction Evaluating the visibility of a point is one major challenge when solving the rendering equation introduced by Ka- jiya [9]. Global illumination techniques such as ambient or environmental lighting approximate distant incoming light over the whole upper hemisphere of a point. Langer and Bülthof [11] found that local occlusion shadows can signif- icantly increase the perceived realism of a rendered object when considered during the environmental lighting approx- imation, especially when the object contains fine structures. 1.1 Ambient Occlusion Ambient Occlusion (AO) is a method to approximate local occlusion effects. Its concept originates from Miller’s [14] methods for accessibility shading. The key approximation of AO is the assumption that local occlusion shadows are independent of the direction of incoming light and only de- pend on neighboring geometry. This allows calculating the visibility function and the incoming radiance integral sepa- rately. The diffuse environmental irradiance E diff of a point p is approximated by evaluating the integral for the unoc- cluded incoming radiance L in over the upper hemisphere +Ω of p. This unoccluded irradiance is then weighted by the scalar AO factor A(p), expressing the ratio of the upper hemisphere of p, which is unoccluded. E diff (p) = A(p)  +Ω L in (p,ω i ) cos ω i dω. (1) The AO factor is calculated by solving the visibility inte- gral over the upper hemisphere of a point. In off-line render- ing, this factor is evaluated using Monte-Carlo ray tracing or Point Based Global Illumination [2]. In interactive real-time applications, such as games, these methods are only appli- cable for static scenes where the AO does not change and,