Grid

The grid constructor.

Test:

• Grid [ unit tests ] constructor

field_size array of field size in each dimension. E.g. [100,200] for a grid that is 100 pixels wide and 200 pixels high. Entries must be positive integer numbers.

Array coordinates to the middle pixel on the grid.

Number of dimensions of the grid.

Should the borders of the grid be linked, so that a cell moving out on the left reappears on the right? Warning: setting to false can give artifacts if done incorrectly. If torus is set to false, artifacts arise because cells at the border have fewer neighbors. Cells will then stick to the grid borders where they have fewer neighbors to get adhesion and/or perimeter penalties from. You will need to specify how to handle the borders explicitly; see the examples/ folder for details on how to do this. Torus can be specified for each dimension separately.

Array with values for each pixel stored at the position of its IndexCoordinate. E.g. the value of pixel with coordinate i is stored as this._pixels[i]. This should be implemented in the grid subclass; see e.g. Grid2D#_pixelArray. Note that this array is accessed indirectly via the _pixels set- and get methods.

Return the array this._pixelArray, which should be set in the grid subclass.

Test:

• Grid [ class extension ] should throw an error when _pixelArray is not set in subclass

Set or update the private this._pixelArray.

For storing a copy of all pixel values; eg for synchronous updating of some sort.

Apply a function to all pixel values on the grid. It acts on this._pixels, which is implemented in the grid subclass.

Method to check if a given ArrayCoordinate falls within the bounds of this grid. Returns an error if this is not the case.

Method to correct an ArrayCoordinate outside the grid dimensions when the grid is wrapped (torus = true). If the coordinate falls inside the grid, it is returned unchanged. If it falls outside the grid and the grid is periodic in that dimension, a corrected coordinate is returned. If the pixel falls outside the grid which is not periodic in that dimension, the function returns 'undefined'.

Perform a diffusion step on the grid, updating the values of all pixels according to Fick's second law of diffusion.

Test:

• Grid [ unit tests ] diffusion method

See:

• https://en.wikipedia.org/wiki/Diffusion#Fick's_law_and_equations
• https://en.wikipedia.org/wiki/Discrete_Laplace_operator#Mesh_Laplacians

Method to compute the gradient at location p on the grid (location given in array coordinates). It internally calls the gradienti method using index coordinates, which should be implemented in the grid subclass.

Test:

• Grid [ class extension ] should throw error when gradienti not implemented
• Grid [ class extension ] gradient should work as soon as gradienti and p2i are implemented.

See:

• https://en.wikipedia.org/wiki/Gradient

Template method to compute the gradient at location i on the grid (location given in index coordinates). This method throws an error, which is overwritten when a subclass implements a gradienti method.

See:

• https://en.wikipedia.org/wiki/Gradient

Method for conversion from an IndexCoordinate to an ArrayCoordinate. This method should be implemented in the subclass, see Grid2D#i2p for an example.

Test:

• Grid [ class extension ] superclass should throw error when p2i/i2p not implemented

Method to compute the laplacian at location p on the grid (location given in array coordinates). It internally calls the laplaciani method that does the same but uses index coordinates.

Test:

• Grid [ class extension ] laplaciani should throw error when neighNeumanni not implemented
• Grid [ class extension ] laplacian should throw error when p2i/neighNeumanni not implemented
• Grid [ class extension ] laplacian(i) should work if p2i, neighNeumanni, and _pixelArray exist

See:

• https://en.wikipedia.org/wiki/Laplace_operator#Coordinate_expressions

Method to compute the laplacian at location i on the grid (location given in index coordinates). It internally uses the neighNeumanni method to compute a Neumann neighborhood, which should be implemented in the grid subclass. It then uses the finite difference method (see link) with h = 1.

Test:

• Grid [ unit tests ] laplacian(i) method
• Grid [ class extension ] laplaciani should throw error when neighNeumanni not implemented
• Grid [ class extension ] laplacian should throw error when p2i/neighNeumanni not implemented
• Grid [ class extension ] laplacian(i) should work if p2i, neighNeumanni, and _pixelArray exist

See:

• https://en.wikipedia.org/wiki/Laplace_operator#Coordinate_expressions
• https://en.wikipedia.org/wiki/Discrete_Laplace_operator#Finite_differences

Multiply all pixel values on the grid with a constant factor r. This method acts on this._pixels, which is implemented in the grid subclass.

The neigh method returns the neighborhood of a pixel p. This function uses array coordinates as input and output arguments, but internally calls a method 'neighi' which computes neighborhoods using index- coordinates. Since neighborhoods depend on the coordinate system, the 'neighi' method is defined in the extension class for that specific coordinate system.

Test:

• Grid [ unit tests ] neigh method
• Grid [ class extension ] should throw error when neighi not implemented

A method to compute the Neumann neighborhood should be implemented in the Grid subclass if the laplacian (see below) is used. This mock function ensures that an error is thrown when there is no method called neighNeumanni in the grid subclass.

See:

• https://en.wikipedia.org/wiki/Von_Neumann_neighborhood

Method returning the (Moore) neighborhood of a pixel based on its IndexCoordinate. This method should be implemented in the subclass, see Grid2D#neighi for an example.

Method for conversion from an ArrayCoordinate to an IndexCoordinate. This method should be implemented in the subclass, see Grid2D#p2i for an example.

Test:

• Grid [ class extension ] superclass should throw error when p2i/i2p not implemented

This iterator returns locations and values of all non-zero pixels. This method isn't actually called because the subclasses implement it themselves due to efficiency reasons. It serves as a template to document the functionality.

Test:

• Grid [ class extension ] should throw error when pixels/pixelsi not implemented

This method pre-allocates an array of the correct datatype to make a copy of the current pixel values. Values are not actually copied yet.

Test:

• Grid [ unit tests ] pixelsBuffer method

This iterator returns locations all pixels including background. This method isn't actually called because the subclasses implement it themselves due to efficiency reasons. It serves as a template to document the functionality.

The pixt method finds the current value of a pixel p on the grid.

Test:

• Grid [ unit tests ] pixt(i) methods
• Grid [ unit tests ] pixt(i) methods pixt(i) can show types on the grid.

The pixti method finds the current value of a pixel i on the grid.

Test:

• Grid [ unit tests ] pixt(i) methods
• Grid [ unit tests ] pixt(i) methods pixt(i) can show types on the grid.

The setpix method changes the value of a pixel p on the grid to t.

Test:

• Grid [ unit tests ] setpix(i) methods
• Grid [ unit tests ] setpix(i) methods can be called
• Grid [ unit tests ] setpix(i) methods should prohibit setting an invalid type on the grid to avoid bugs
• Grid [ unit tests ] setpix(i) methods store values in the Grid correctly

The setpixi method changes the value of a pixel i on the grid to t.

Test:

• Grid [ unit tests ] setpix(i) methods
• Grid [ unit tests ] setpix(i) methods can be called
• Grid [ unit tests ] setpix(i) methods should prohibit setting an invalid type on the grid to avoid bugs
• Grid [ unit tests ] setpix(i) methods store values in the Grid correctly

Check if a value is valid on this type of grid. This function forbids trying to set forbidden (negative/float) values on an integer grid, which could cause bugs if the setpix(i) methods try to set such a value unnoticed.

Test:

• Grid [ unit tests ] setpix(i) methods should prohibit setting an invalid type on the grid to avoid bugs