GraphicsComplex

WLJS

Execution environment

wljs-graphics3d-threejs

Package

Supports dynamics

GraphicsComplex[data_List, primitives_, opts___]

represents an efficient graphics structure for drawing complex 3D objects (or 2D - see GraphicsComplex) storing vertices data in data variable. It replaces indexes found in primitives (can be nested) with a corresponding vertices and colors (if specified)

Most plotting functions such as ListPlot3D and others use this way showing 3D graphics.

The implementation of GraphicsComplex is based on a low-level THREE.js buffer position attribute directly written to a GPU memory.

Supported primitives

Line

No restrictions

v = PolyhedronData["Dodecahedron", "Vertices"] // N;
i = PolyhedronData["Dodecahedron", "FaceIndices"];

GraphicsComplex[v, {Black, Line[i]}] // Graphics3D 

Polygon

Triangles works faster than quads or pentagons

GraphicsComplex[v, Polygon[i]] // Graphics3D 

Point

Options

"VertexColors"

Defines sets of colors used for shading vertices

info

"VertexColors" is a plain list which must have the following form

"VertexColors" ->{{r1,g1,b1}, {r2,g2,b2}, ...}

Dynamic updates

It does support dynamic updates for vertices data and colors. Use Offload wrapper.

warning

Number of points in a mesh cannot be changed

cell 1

(* generate mesh *)
proc = HardcorePointProcess[50, 0.5, 2];
reg = Rectangle[{-10, -10}, {10, 10}];
samples = RandomPointConfiguration[proc, reg]["Points"];

(* triangulate *)
Needs["ComputationalGeometry`"];
triangles2[points_] := Module[{tr, triples},
  tr = DelaunayTriangulation[points];
  triples = Flatten[Function[{v, list},
      Switch[Length[list],
        (* account for nodes with connectivity 2 or less *)
        1, {},
        2, {Flatten[{v, list}]}, 
        _, {v, ##} & @@@ Partition[list, 2, 1, {1, 1}]
      ]
    ] @@@ tr, 1];
  Cases[GatherBy[triples, Sort], a_ /; Length[a] == 3 :> a[[1]]]]

triangles = triangles2[samples];

(* sample function *)
f[p_, {x_,y_,z_}] := z Exp[-(*FB[*)(((*SpB[*)Power[Norm[p - {x,y}](*|*),(*|*)2](*]SpB*))(*,*)/(*,*)(2.))(*]FB*)]

(* initial data *)
probe = {#[[1]], #[[2]], f[#, {10, 0, 0}]} &/@ samples // Chop;
colors = With[{mm = MinMax[probe[[All,3]]]},
      (Blend[{{mm[[1]], Blue}, {mm[[2]], Red}}, #[[3]]] )&/@ probe /. {RGBColor -> List} // Chop];

cell 2

Graphics3D[{
  GraphicsComplex[probe // Offload, {Polygon[triangles]}, "VertexColors"->Offload[colors]],

  EventHandler[Sphere[{0,0,0}, 0.1], {"transform"->Function[data, With[{pos = data["position"]},
    probe = {#[[1]], #[[2]], f[#, pos]} &/@ samples // Chop;
    colors = With[{mm = MinMax[probe[[All,3]]]},
      (Blend[{{mm[[1]], Blue}, {mm[[2]], Red}}, #[[3]]] )&/@ probe /. {RGBColor -> List} // Chop];
  ]]}]
}]

The result is interactive 3D plot

Or the variation of it, if we add a point light source

light = {0,0,0};
Graphics3D[{
  GraphicsComplex[probe // Offload, {Polygon[triangles]}],
  PointLight[Red, light // Offload],

  EventHandler[Sphere[{0,0,0}, 0.1], {"transform"->Function[data, With[{pos = data["position"]},
    probe = {#[[1]], #[[2]], f[#, pos]} &/@ samples // Chop;
    light = pos;
  ]]}]
}]