javascript - 朴素表面网络算法的工作流程

Question

我目前正在研究等值面提取算法。我找到了introduction在这里使用有效的 Javascript 代码。我必须注意，我不是 Javascript 编码员。我主要使用 Java 和 F#，但我能够将代码移植到 F#。

毕竟我目前的问题是理解表面网络算法的实现原理。 (下面提供了链接)。它是由博客/简介的作者制作的。

197 行(169 sloc)6.38 KB，来自 here

// The MIT License (MIT)
//
// Copyright (c) 2012-2013 Mikola Lysenko
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

/**
 * SurfaceNets in JavaScript
 *
 * Written by Mikola Lysenko (C) 2012
 *
 * MIT License
 *
 * Based on: S.F. Gibson, "Constrained Elastic Surface Nets". (1998) MERL Tech Report.
 */
var SurfaceNets = (function() {
"use strict";

//Precompute edge table, like Paul Bourke does.
// This saves a bit of time when computing the centroid of each boundary cell
var cube_edges = new Int32Array(24)
  , edge_table = new Int32Array(256);
(function() {

  //Initialize the cube_edges table
  // This is just the vertex number of each cube
  var k = 0;
  for(var i=0; i<8; ++i) {
    for(var j=1; j<=4; j<<=1) {
      var p = i^j;
      if(i <= p) {
        cube_edges[k++] = i;
        cube_edges[k++] = p;
      }
    }
  }

  //Initialize the intersection table.
  //  This is a 2^(cube configuration) ->  2^(edge configuration) map
  //  There is one entry for each possible cube configuration, and the output is a 12-bit vector enumerating all edges crossing the 0-level.
  for(var i=0; i<256; ++i) {
    var em = 0;
    for(var j=0; j<24; j+=2) {
      var a = !!(i & (1<<cube_edges[j]))
        , b = !!(i & (1<<cube_edges[j+1]));
      em |= a !== b ? (1 << (j >> 1)) : 0;
    }
    edge_table[i] = em;
  }
})();

//Internal buffer, this may get resized at run time
var buffer = new Int32Array(4096);

return function(data, dims) {

  var vertices = []
    , faces = []
    , n = 0
    , x = new Int32Array(3)
    , R = new Int32Array([1, (dims[0]+1), (dims[0]+1)*(dims[1]+1)])
    , grid = new Float32Array(8)
    , buf_no = 1;

  //Resize buffer if necessary 
  if(R[2] * 2 > buffer.length) {
    buffer = new Int32Array(R[2] * 2);
  }

  //March over the voxel grid
  for(x[2]=0; x[2]<dims[2]-1; ++x[2], n+=dims[0], buf_no ^= 1, R[2]=-R[2]) {

    //m is the pointer into the buffer we are going to use.  
    //This is slightly obtuse because javascript does not have good support for packed data structures, so we must use typed arrays :(
    //The contents of the buffer will be the indices of the vertices on the previous x/y slice of the volume
    var m = 1 + (dims[0]+1) * (1 + buf_no * (dims[1]+1));

    for(x[1]=0; x[1]<dims[1]-1; ++x[1], ++n, m+=2)
    for(x[0]=0; x[0]<dims[0]-1; ++x[0], ++n, ++m) {

      //Read in 8 field values around this vertex and store them in an array
      //Also calculate 8-bit mask, like in marching cubes, so we can speed up sign checks later
      var mask = 0, g = 0, idx = n;
      for(var k=0; k<2; ++k, idx += dims[0]*(dims[1]-2))
      for(var j=0; j<2; ++j, idx += dims[0]-2)      
      for(var i=0; i<2; ++i, ++g, ++idx) {
        var p = data[idx];
        grid[g] = p;
        mask |= (p < 0) ? (1<<g) : 0;
      }

      //Check for early termination if cell does not intersect boundary
      if(mask === 0 || mask === 0xff) {
        continue;
      }

      //Sum up edge intersections
      var edge_mask = edge_table[mask]
        , v = [0.0,0.0,0.0]
        , e_count = 0;

      //For every edge of the cube...
      for(var i=0; i<12; ++i) {

        //Use edge mask to check if it is crossed
        if(!(edge_mask & (1<<i))) {
          continue;
        }

        //If it did, increment number of edge crossings
        ++e_count;

        //Now find the point of intersection
        var e0 = cube_edges[ i<<1 ]       //Unpack vertices
          , e1 = cube_edges[(i<<1)+1]
          , g0 = grid[e0]                 //Unpack grid values
          , g1 = grid[e1]
          , t  = g0 - g1;                 //Compute point of intersection
        if(Math.abs(t) > 1e-6) {
          t = g0 / t;
        } else {
          continue;
        }

        //Interpolate vertices and add up intersections (this can be done without multiplying)
        for(var j=0, k=1; j<3; ++j, k<<=1) {
          var a = e0 & k
            , b = e1 & k;
          if(a !== b) {
            v[j] += a ? 1.0 - t : t;
          } else {
            v[j] += a ? 1.0 : 0;
          }
        }
      }

      //Now we just average the edge intersections and add them to coordinate
      var s = 1.0 / e_count;
      for(var i=0; i<3; ++i) {
        v[i] = x[i] + s * v[i];
      }

      //Add vertex to buffer, store pointer to vertex index in buffer
      buffer[m] = vertices.length;
      vertices.push(v);

      //Now we need to add faces together, to do this we just loop over 3 basis components
      for(var i=0; i<3; ++i) {
        //The first three entries of the edge_mask count the crossings along the edge
        if(!(edge_mask & (1<<i)) ) {
          continue;
        }

        // i = axes we are point along.  iu, iv = orthogonal axes
        var iu = (i+1)%3
          , iv = (i+2)%3;

        //If we are on a boundary, skip it
        if(x[iu] === 0 || x[iv] === 0) {
          continue;
        }

        //Otherwise, look up adjacent edges in buffer
        var du = R[iu]
          , dv = R[iv];

        //Remember to flip orientation depending on the sign of the corner.
        if(mask & 1) {
          faces.push([buffer[m], buffer[m-du], buffer[m-du-dv], buffer[m-dv]]);
        } else {
          faces.push([buffer[m], buffer[m-dv], buffer[m-du-dv], buffer[m-du]]);
        }
      }
    }
  }

  //All done!  Return the result
  return { vertices: vertices, faces: faces };
};
})();

我将在这里写下我所理解和不清楚的内容:

我如何理解算法:

1. 制作一个cube_edges(或者更确切地说是顶点列表)组合列表和一个边列表(查找表)

2. 迭代整个网格，根据当前单元/立方体中每个顶点的拓扑(依赖于边列表)插入浮点值。

3. 推回顶点并设置面。

我不清楚的是:

1. 我已经在互联网上搜索了生成edges_table的算法，但我还没有找到。有人能给我解释一下吗？
2. 这些面是如何相互连接的。最后一个片段中的面孔发生了什么？

我愿意改进我的问题以符合规则。

Answer 1

我没有阅读您引用的代码，但回答您的问题:

1. Edges_table 算法非常简单，它遵循将立方体的顶点和边映射到特定数字的约定。请参阅Paul Bourke's Implementation了解详情。

2. 在匹配框算法中，交点通常是通过每个顶点值的线性插值来计算的:

P = P1 + (isovalue - V1) (P2 - P1) / (V2 - V1)

相邻立方体的共享边将始终在相同位置具有交点，因此相邻立方体的生成面将始终完美契合。