0細分的體積計算錯誤

我最近提交了一個關於體積計算的問題，在this thread得到了一些很大的幫助，並開發了一個函數來計算Three JS中封閉網格的體積。對於Face3網格，變量face4是一個真/假，將臉分爲兩個三角形。我的幾何主要是自定義的Face4構造。0細分的體積計算錯誤

function volumeCalc(object, face4){ 

     if (face4 == false) { 

     for (var i=0; i<object.geometry.faces.length; i++) { 

    var pA = (object.geometry.faces[i].a); 
    var qA = (object.geometry.faces[i].b); 
    var rA = (object.geometry.faces[i].c); 

    var Px = object.geometry.vertices[pA].x; 
    var Py = object.geometry.vertices[pA].y; 
    var Pz = object.geometry.vertices[pA].z; 

    Pxlist.push(Px); 
    Pylist.push(Py); 
    Pzlist.push(Pz); 

    var Qx = object.geometry.vertices[qA].x; 
    var Qy = object.geometry.vertices[qA].y; 
    var Qz = object.geometry.vertices[qA].z; 

    Qxlist.push(Qx); 
    Qylist.push(Qy); 
    Qzlist.push(Qz); 

    var Rx = object.geometry.vertices[rA].x; 
    var Ry = object.geometry.vertices[rA].y; 
    var Rz = object.geometry.vertices[rA].z; 

    Rxlist.push(Rx); 
    Rxlist.push(Ry); 
    Rzlist.push(Rz); 
} 
    } else { 
     for (var i=0; i<object.geometry.faces.length; i++) { 

    var pA = (object.geometry.faces[i].b); 
    var qA = (object.geometry.faces[i].c); 
    var rA = (object.geometry.faces[i].d); 

    var Px = object.geometry.vertices[pA].x; 
    var Py = object.geometry.vertices[pA].y; 
    var Pz = object.geometry.vertices[pA].z; 

    Pxlist.push(Px); 
    Pylist.push(Py); 
    Pzlist.push(Pz); 

    var Qx = object.geometry.vertices[qA].x; 
    var Qy = object.geometry.vertices[qA].y; 
    var Qz = object.geometry.vertices[qA].z; 

    Qxlist.push(Qx); 
    Qylist.push(Qy); 
    Qzlist.push(Qz); 

    var Rx = object.geometry.vertices[rA].x; 
    var Ry = object.geometry.vertices[rA].y; 
    var Rz = object.geometry.vertices[rA].z; 

    Rxlist.push(Rx); 
    Rxlist.push(Ry); 
    Rzlist.push(Rz); 
    } 
} 
    for (i=0;i < Pxlist.length; i++){ 

    pv = Pxlist[i]*Qylist[i]*Rzlist[i]; + Pylist[i]*Qzlist[i]*Rxlist[i]; + Pzlist[i]*Qxlist[i]*Rylist[i]; - Pxlist[i]*Qzlist[i]*Rylist[i]; - Pylist[i]*Qxlist[i]*Rzlist[i]; -Pzlist[i]*Qylist[i]*Rxlist[i]; 
    pvlist.push(pv); 

} 

// calculate the total of these, I'm using _.js to add all values in the list. 

addUp = (_.reduce(pvlist, function(memo, num){ return memo + num; }, 0))/6;

這是基於下式

pv = Px*Qy*Rz + Py*Qz*Rx + Pz*Qx*Ry - Px*Qz*Ry - Py*Qx*Rz - Pz*Qy*Rx;

我創建網格之前執行對THREE.Geometry以下：

geom.mergeVertices(); 
geom.computeCentroids(); 
geom.computeFaceNormals(); 
geom.computeVertexNormals(); 

var modifier = new THREE.SubdivisionModifier(x); 

modifier.modify(geom);

體積計算是在所有的情況下正確細分其中x> 0。當x = 0或沒有細分時，它是不正確的，數量級。

任何想法？同時也會意識到如何清理功能以供其他人使用，這是我第一次嘗試開源貢獻。謝謝。

來源

2013-01-17 Michael S Bergin