HYPERSPHERE_SURFACE
Estimate Hypersurface Location

HYPERSPHERE_SURFACE, a MATLAB library which investigates a procedure for estimating the location of points on a hypersurface implicitly defined by a characteristic function or by a signed function.

In M dimensions, a characteristic function F for a region of points S has the property that F(X) is 1 for points inside S, and 0 otherwise. A characteristic function is thus discontinous. The set of discontinuity points for F is the boundary of S.

In M dimensions, suppose that the function F, presumably continuous, takes on both positive and negative values. Then we may be interested in the set of points X such that F(X) = 0, which we regard as the boundary between the sets where F is negative or positive. Assuming that F is continuous, or better yet, differentiable, then this boundary may be substantially easier to locate than in the characteristic function case.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

HYPERSPHERE_SURFACE is available in a MATLAB version.

Related Data and Programs:

EDGE, a MATLAB library which defines some test functions in 1D, 2D and 3D for the detection of edges.

HYPERSPHERE_PROPERTIES, a MATLAB library which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.

hypersphere_surface_test

LEVELS, a MATLAB library which makes a contour plot, choosing the contour levels using random sampling.

SHORELINE, a MATLAB program which tries to identify and triangulate the 2D domain over which some function f(x,y) is nonnegative.

SHORELINE2, a MATLAB program which tries to identify and triangulate the 2D domain over which some function f(x,y) is roughly zero.

Source Code:

• bisect_characteristic.m, uses bisection to outline the transition surface for a given characteristic function.
• cartesian_to_hypersphere.m, converts from a cartesian to a hypersphere coordinate system.
• exterior_point_characteristic.m, searches for a point that is outside a surface defined by a characteristic, and for which a base point inside the surface is given, as well as the desired hypersphere angles of the exterior point.
• hypersphere_to_cartesian.m, converts from a hypersphere to a cartesian coordinate system.
• interior_point.m seeks a point X such that F(X) < 0.
• interior_point_characteristic.m searches a hyperrectangle for a point that is inside a surface defined by a characteristic.
• r8vec_print.m prints an R8VEC.
• timestamp.m prints the YMDHMS date as a timestamp.