SurfacePlotMesh (FXyz) constructor arguments

Question

I would like to know if I am correct with understanding the constructor argument as a Function<Point2D, Number> function. My function which I have used for 1D charts based on the applying the variables after every step on the x axis, but there is as a parametr Point2D which contain 2 variables : x and y, if i am correct the x varriable is step which increase "0.5" for every calculations after apply the function of y. Then what is the second parametr of generic type, the Number ? How could I implement other functions, using the SurfacePlotMesh class. Could someone explain me a little bit how it works ? Or link the documenations ( If it exist ) ?

Answer 1

If you have a look at the code for SurfacePlotMesh in the FXyz library, you'll find createPlotMesh(), a method that creates the mesh for the surface, based on two coordinates on a plane grid (x, y), taken from the Point2D coordinates, and a function value (z), given by the function applied on that point.

If you have a look at the default parameters:

private static final Function<Point2D, Number> DEFAULT_FUNCTION = 
    p -> Math.sin(p.magnitude()) / p.magnitude();

private static final double DEFAULT_X_RANGE = 10; // -5 +5
private static final double DEFAULT_Y_RANGE = 10; // -5 +5
private static final int DEFAULT_X_DIVISIONS = 64;
private static final int DEFAULT_Y_DIVISIONS = 64;
private static final double DEFAULT_FUNCTION_SCALE = 1.0D;

what it means it that there will be a grid of 10x10 units, with 64x64 divisions. In each and every vertex (x,y) of the total 65x65 vertices, we will evaluate the function to get the value z = f(x, y), with a default scale of 1.

I.e., for the top left 2D point at (-5, -5) -> f(-5, -5) = 1.0025, so the 3D point for the mesh will be (-5, -5, 1.0025), and so on.

This picture shows a grid of 10x10 range with 20x20 divisions, and the mesh with a scale of 4 for that function.

You can change the function at any time, like:

• p -> p.getX()
• p -> p.getX() * p.getY()
• p -> Math.cos(p.getX()) * Math.sin(p.getY())
• ...

as well as the other parameters (range, divisions, scale).

For the moment there is no documentation, but the code is fully available.

Also there is a sampler to run most of the samples and modify the parameters to easily check the result without recompiling all over again here.

EDIT

Based on the OP comment, for a function where there is no y dependency, a ribbon type of surface can be created by setting a very low value on y:

private void createSurface(double time) {
    surface = new SurfacePlotMesh(
        p-> Math.sqrt(Math.pow(Math.exp(-(Math.pow((p.getX() - time), 2))) * 
            (Math.cos((2 * Math.PI * (p.getX() - time)))), 2) + 
            Math.pow(Math.exp(-(Math.pow((p.getX() - time), 2))) * 
            (Math.sin((2 * Math.PI * (p.getX() - time)))), 2)),
            10, 0.1, 64, 2, 2);
}

where the time parameter will be set to a fixed value or in an animation.