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PLaSM.js domain mapping

Domain mapping

Map

DOMAIN(dims)(divs)

Create a domain.

I/O

⇒ Array dims: dimensions [dx, dy, dz, ...].

Array dx: intervals [start_x, end_x]

Number start_x: x min Number end_x: x max

Array dy: intervals [start_y, end_y]

Number start_y: y min Number end_y: y max

Array dz: intervals [start_z, end_z]

Number start_z: z min Number end_z: z max

⇐ Function: an anonymous function.

⇒ Array divs: divisions [nx, ny, nz, ...].

Number nx: division along x axes. Number ny: division along y axes. Number nz: division along z axes.

⇐ plasm.Model: a domain.

Example

var domain1 = DOMAIN([[0, PI])([32]);
DRAW(domain1);
var domain2 = DOMAIN([[0, PI], [0,1]])([32, 2]);
DRAW(domain2);
var domain3 = DOMAIN([[0, PI], [0,1], [0, 0.5]])([32, 2, 5]);
DRAW(domain3);

Domain mapping

Map

MAP(mapping)(domain)

Map a domain by a mapping function.

I/O

⇒ Function or Array<Function> mapping: the mapping function or an array of mapping functions

⇒ Array v: point of the domain to map

⇐ Array: the mapped point.

⇐ Function: an anonymous function.

⇒ plasm.Model domain: the domain to map.

⇒ plasm.Model: the mapped domain.

Example

var domain = DOMAIN([[0, 2*PI]])([32]);
var mapping = function (v) { return [SIN(v[0]), COS(v[1])]; });
var model = MAP(mapping)(domain);
DRAW(model);
var domain = DOMAIN([[0, 2*PI]])([32]);
var mapping = [
  function (v) { return [SIN(v[0])]; },
  function (v) { return [COS(v[1])]; }
];
var model = MAP(mapping)(domain);
DRAW(model);

Domain mapping

Mappings

Bisector

var domain = DOMAIN([[0, 5]])([10]);
var mapping = function (v) { return [v[0], v[0]] };
var model = MAP(mapping)(domain);
DRAW(model);
var domain = DOMAIN([[0, 5]])([10]);
var fx = function (v) { return [v[0]]; };
var fy = function (v) { return [v[0]]; };
mappings = [fx, fy];
var model = MAP(mappings)(domain);
DRAW(model);

Domain mapping

Mappings

sin

var domain = DOMAIN([[0, 2*PI]])([36]);
var mapping = function (v) { return [v[0], SIN(V[0])]; };
var model = MAP(mapping)(domain);
DRAW(model1);
var fx = function (v) { return [v[0]]; };
var fy = function (v) { return [SIN(V[0])]; };
var mappings = [fx, fy];
var model = MAP(mappings)(domain);
DRAW(model);

cos

var domain = DOMAIN([[0, 2*PI]])([36]);
var mapping = function (v) { return [v[0], COS(V[0])]; };
var model = MAP(mapping)(domain);
DRAW(model1);
var fx = function (v) { return [v[0]]; };
var fy = function (v) { return [COS(V[0])]; };
var mappings = [fx, fy];
var model = MAP(mappings)(domain);
DRAW(model);

Domain mapping

Mappings

Circle

var domain = DOMAIN([[0, 2*PI]])([36]);
var mapping = function (v) { return [COS(V[0]), SIN(V[0])]; };
var model = MAP(mapping)(domain);
DRAW(model);
var domain = DOMAIN([[0, 2*PI]])([36]);
var circle = function (r) {
  return  function (v) {
    return [r * COS(V[0]), r * SIN(V[0])];
  };
};
var mapping = circle(3);
var model = MAP(mapping)(domain);
DRAW(model);

Domain mapping

Mappings

Sphere

var domain = DOMAIN([[0, PI], [0, 2*PI]])([24,36]);
var mapping = function (v) {
  var a = v[0];
  var b = v[1];
  return [SIN(a)*COS(b), SIN(a)*SIN(b), COS(a)];
};
var model = MAP(mapping)(domain);
DRAW(model);
var domain = DOMAIN([[0, PI], [0, 2*PI]])([24,36]);
var sphere = function (r) {
  return function (v) {
    var a = v[0];
    var b = v[1];
    return [r*SIN(a)*COS(b), r*SIN(a)*SIN(b), r*COS(a)];
  };
};
var mapping = sphere(2);
var model = MAP(mapping)(domain);
DRAW(model);

Domain mapping

Mappings

Torus

var domain = DOMAIN([[0, 2*PI],[0, 2*PI]])([36,72]);
var torus = function (R, r) {
  return function (v) {
    var a = v[0];
    var b = v[1];

    var u = (r * COS(a) + R) * COS(b);
    var v = (r * COS(a) + R) * SIN(b);
    var w = (r * SIN(a));

    return [u,v,w];
  };
};
var mapping = torus(3,1);
var model = MAP(mapping)(domain);
DRAW(model);