Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Generating antialiased images at low sampling densities
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Free form surface analysis using a hybrid of symbolic and numeric computation
Free form surface analysis using a hybrid of symbolic and numeric computation
Programs to generate Niederreiter's low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
A fast method for estimating discrete field values in early engineering design
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Equidistribution on the Sphere
SIAM Journal on Scientific Computing
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Computational investigations of low-discrepancy sequences
ACM Transactions on Mathematical Software (TOMS)
Sampling with Hammersley and Halton points
Journal of Graphics Tools
The direct simulation Monte Carlo method
Computers in Physics
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Fast primitive distribution for illustration
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Computing Volume Properties Using Low-Discrepancy Sequences
Geometric Modelling
Alternative Algorithm for Hilbert's Space-Filling Curve
IEEE Transactions on Computers
A survey of point-based techniques in computer graphics
Computers and Graphics
On the metric properties of discrete space-filling curves
IEEE Transactions on Image Processing
Point sampling with uniformly distributed lines
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
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Low-discrepancy point distributions exhibit excellent uniformity properties for sampling in applications such as rendering and measurement. We present an algorithm for generating low-discrepancy point distributions on arbitrary parametric surfaces using the idea of converting the 2D sampling problem into a 1D problem by adaptively mapping a space-filling curve onto the surface. The 1D distribution takes into account the parametric mapping by employing a corrective approach similar to histogram equalisation to ensure that it gives a 2D low-discrepancy point distribution on the surface. This also allows for control over the local density of the distribution, e.g. to place points more densely in regions of higher curvature. To allow for parametric distortion, the space-filling curve is generated adaptively to cover the surface evenly. Experiments show that this approach efficiently generates low-discrepancy distributions on arbitrary parametric surfaces and creates nearly as good results as well-known low-discrepancy sampling methods designed for particular surfaces like planes and spheres. However, we also show that machine-precision limitations may require surface reparameterisation in addition to adaptive sampling.