A system and method for generating a curve, such as a Low Discrepancy Curve,
on
a surface, such as an abstract surface with a Riemannian metric. The system may
comprise a computer which includes a CPU and a memory medium which is operable
to store one or more programs executable by the CPU to perform the method. The
method may: 1) parameterize the surface; 2) select a curve, such as a Low Discrepancy
Curve, in a parameter space, for example, a simple space such as a unit square;
3) re-parameterize the surface, for example, re-parameterize the surface such that
a ratio of line and area elements of the surface based on a Riemannian metric is
constant; and 4) map the curve onto the surface using the re-parameterization.
The method may also generate output comprising information regarding the mapped
curve, for example, displaying the mapped curve on a display device.
