Tiling

Methods

Own

(static) rectangulation(el, rg_u, rg_v, stepsU, stepsV)

Rectangulate (partition it into rectangles) a given two dimensional domain. The number of rectangles the original rectangle is divided into depends on the parameters stepsU and stepsV. Input are the ranges of u and v, as well as stepsU and stepsV which are static.

Example

var rg = board.create('slider', [[-7, -7], [3, -7], [1, 4, 5]], { name: 'rg' });

var box = [-5, 5];
var view = board.create('view3d',
    [[-5, -3], [8, 8],
    [box, box, box]],
    {
        projection: 'central',
        // axesPosition: 'center',
        xPlaneRear: { visible: false },
        yPlaneRear: { visible: false },
        zPlaneRear: { visible: false }
    });

var range = [() => -rg.Value(), () => rg.Value()],
    stepsU = 15,
    stepsV = 5,
    F = (x, y) => [x, y, 3 * Math.sin(Math.sqrt(x ** 2 + y ** 2))];

view.setView(0, Math.PI / 2);  // Set view from above

var el = { F: F }; // Fake surface3d element

var surface = JXG.Math.Tiling.rectangulation(el, range, range, stepsU, stepsV);
var pol = view.create('polyhedron3d', surface, {
    shader: {
        enabled: true,
        light: {
            dir: 0
        }
    },
    fillColorArray: ['white'],
    fillOpacity: 0.9,
    strokeWidth: 0.2
});

Parameters

Name	Type	Description
`el`	JXG.ParametricSurface3D \| JXG.Plane3D	element which is displayed using a polyhedron3d. From this element its function F is used.
`rg_u`	Array	Begin and end of first direction (numbers or functions)
`rg_v`	Array	Begin and end of second direction (numbers or functions)
`stepsU`	Number	Immutable
`stepsV`	Number	Immutable

Returns

[coords,faces]

Details

Source: math/tiling.js, line 304

(static) triangulation(el, rg_u, rg_v, stepsU, stepsVopt)

Triangulate (partition it into triangles) a given two dimensional domain. The number of triangles the original rectangle is divided into depends on the parameters stepsU and stepsV. Input are the ranges of u and v, as well as stepsU and stepsV which are static. If the optional parameter stepsV is not given or is equal to 0, the rectangle is partitioned into nearly equilateral triangles. Otherwise, the shape of the triangles depends on the ratio of stepsU / stepsV.

Example

var rg = board.create('slider', [[-7, -7], [3, -7], [1, 4, 5]], { name: 'rg' }); // range

var box = [-5, 5];
var view = board.create('view3d',
    [[-5, -3], [8, 8],
    [box, box, box]],
    {
        projection: 'central',
        xPlaneRear: { visible: false },
        yPlaneRear: { visible: false },
        zPlaneRear: { visible: false }
    });

var range = [() => -rg.Value(), () => rg.Value()],
    stepsU = 25,
    // stepsV = 25,
    F = (x, y) => [x, y, 3 * Math.sin(Math.sqrt(x ** 2 + y ** 2))];

view.setView(0, Math.PI / 2); // Set view from above

var el = { F: F }; // Fake surface3d element

// stepsV not supplied -> approx. equilater triangles
var surface = JXG.Math.Tiling.triangulation(el, range, range, stepsU);
var pol = view.create('polyhedron3d', surface, {
    shader: {
        enabled: true,
        light: {
            dir: 0
        }
    },
    fillColorArray: ['white'],
    fillOpacity: 0.9,
    strokeWidth: 0.2
});

Parameters

Name	Type	Attributes	Default	Description
`el`	JXG.ParametricSurface3D \| JXG.Plane3D			element which is displayed using a polyhedron3d. From this element its function F is used.
`rg_u`	Array			Begin and end of first direction (numbers or functions)
`rg_v`	Array			Begin and end of second direction (numbers or functions)
`stepsU`	Number			Immutable
`stepsV`	Number	<optional>	`0`	Immutable

Returns

[coords,faces]

Details

Source: math/tiling.js, line 145

Inherited

none

Details

Source: math/tiling.js, line 40