An Adaptive Point Sampler on a Regular Lattice


ACM Transactions on Graphics (Proceedings of SIGGRAPH 2017)

Abdalla Ahmed1           Till Nies1          Hui Huang2         Oliver Deussen1,3

1University of Konstanz             2Shenzhen University             3SIAT

Fig. 1. (a) The proposed ART (Adaptive Regular Tiles) sampler uses a self-similar regular tile set with 1 sample per tile to supply sequences of blue-noise samples. (b) Tiled multi-class sets can be used to partition a tiled blue noise set into separate blue-noise sets. The two bottom lines show the filling order of our recursive tile in (a). First, sample points are filled in that are shared by one of the respective child tiles. The parent tile then visits the remaining children (in an optimized order) and instructs them to add their samples. For each subsequent 16 (number of children) samples, control is passed recursively to the children – in the same order – to add more samples.


We present a framework to distribute point samples with controlled spectral properties using a regular lattice of tiles with a single sample per tile. We employ a word-based identification scheme to identify individual tiles in the lattice. Our scheme is recursive, permitting tiles to be subdivided into smaller tiles that use the same set of IDs. The corresponding framework offers a very simple setup for optimization towards different spectral properties. Small lookup tables are sufficient to store all the information needed to produce different point sets. For blue noise with varying densities, we employ the bit-reversal principle to recursively traverse sub-tiles. Our framework is also capable of delivering multi-class blue noise samples. It is well-suited (uniform and adaptive), and importance sampling. Other applications include stippling and distributing objects.

Interactive Demos

Grid Morphing: In this demo, you can draw samples right from this page, scaled to unit area. Drag to move around, use the mouse wheel or pinch to zoom. What You See Is What You Get!

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Show Strata

Sequences: In this demo we compare the progressive (self-coincident) variant of ART (left) to the post-optimized variant (right). The size of the tables is larger for the latter. Drag the slider to increase or decrease the number of samples.



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Fig. 2. Adaptive localized subdivision of the tiles to add more samples.


Fig. 3. Example importance Sampling. Our method is able to distributesamples over a large density variation.

Fig. 4. Individual and combined shadow samples for different samplers. A typical blue noise sampler like BNOT offers excellent individual sets, but the combined set is poor. In contrast, Low discrepancy sampling is capable of maintaining the same quality for the sub-sets and the combined set. Our framework tries to emulate this capability, as discussed in Section 5.1.

Fig. 5. Rendering results for soft shadows. The ground truth images use four samples per pixel and 1024 light samples. Detail images of different methods use four samples per pixel and a varying number of light sample per pixel sample. Low discrepancy refers to the scrambled low discrepancy sequences of PBRT. Please note the banding in low discrepancy towards the end of shadow in the sphere scene. Our samplers, in contrast, provide the typical noise-aliasing trading of blue noise [Glassner 1995]. The complete set of full-resolution images is available in the supplementary materials.

We thank the anonymous reviewers for their detailed feedback to improve the paper. Thanks to Cengiz Öztireli for sharing the grid test scene. Thanks to Carla Avolio for the voice over of the supporting video clip. This work was partially funded by Deutsche Forschungsgemeinschaft Grant (DE-620/22-1), the National Foreign 1000 Talent Plan (WQ201344000169), Leading Talents of Guangdong Program (00201509), NSFC (61522213, 61379090, 61232011), Guangdong Science and Technology Program (2015A030312015), and Shenzhen Innovation Program (JCYJ20151015151249564).

@article {Sampler17,
title = {An Adaptive Point Sampler on a Regular Lattice},
author = {Abdalla Ahmed and Till Nies and Hui Huang and Oliver Deussen},
journal = {ACM Transactions on Graphics (Proc. of SIGGRAPH 2017},
volume = {36},
number = {4},
pages = {138:1–138:13},
year = {2017},