discretize function

Discretization grid builder.

Builds a discretization grid covering the two-dimensional unit simplex, with specified number of points and minimal distance from the boundary.

discretize(npoints = 40, eps = 0.001, equi = FALSE)

Arguments

• npoints: The number of grid nodes on the squared grid containing the desired triangle.
• eps: Positive number: minimum distance from any node inside the simplex to the simplex boundary
• equi: logical. Is the simplex represented as an equilateral triangle (if TRUE) or a right triangle (if FALSE) ?

Returns

A list containing two elements: X and Y, vectors of size npoints, the Cartesian coordinates of the grid nodes.

Details

The npoints*npoints grid covers either the equilateral representation of the simplex, or the right angled one. In any case, the grid is rectangular: some nodes lie outside the triangle. Density computations on such a grid should handle the case when the point passed as argument is outside the simplex (typically, the function should return zero in such a case).

Note

In case equi==TRUE, epsilon is the minimum distance from any node inside the simplex to the simplex boundary, after transformation to the right-angled representation.