如何从凸包中找到 OBB 顶点？

编程问答 2022-05-23

问题描述

我有凸包顶点（只有那些形成包边界的顶点），并且根据 codepen 上发布的答案改编了这个函数（如果我能找到它，我会尝试链接源）。

框大小坐标似乎有问题。你能帮我解决我出错的地方吗？我需要 3d 边界框的 8 个角，我可以用它来渲染对象周围的定向框。

这是修改后的函数：

function dot(v1,v2) {
    return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}

function findobB(vertices) {
    // copy the [x,y,z] array
    // input: vertices is convex hull vertices
    
    var xyzArray = [];
    for (var i = 0; i < vertices.length; i++) {
        xyzArray.push([vertices[i].x,vertices[i].y,vertices[i].z]);
    }
    
    // find mean
    var xbar = 0;
    var ybar = 0;
    var zbar = 0;
    for (var i = 0; i < xyzArray.length; i++) {
        xbar += xyzArray[i][0];
        ybar += xyzArray[i][1];
        zbar += xyzArray[i][2];
    }

    xbar /= xyzArray.length;
    ybar /= xyzArray.length;
    zbar /= xyzArray.length;
    
    // adjust data
    for (var i = 0; i < xyzArray.length; i++) {
        xyzArray[i][0] -= xbar;
        xyzArray[i][1] -= ybar;
        xyzArray[i][2] -= zbar;
    }
    
    // covariance matrix
    var xx = xy = xz = yy = yz = zz = 0;
    for (var i = 0; i < xyzArray.length; i++) {
        xx += xyzArray[i][0] * xyzArray[i][0];
        xy += xyzArray[i][0] * xyzArray[i][1];
        xz += xyzArray[i][0] * xyzArray[i][2];
        yy += xyzArray[i][1] * xyzArray[i][1];
        yz += xyzArray[i][1] * xyzArray[i][2];
        zz += xyzArray[i][2] * xyzArray[i][2];
    }
    
    var cM = [
        [xx,xy,xz],[xy,yy,yz],[xz,yz,zz]
    ];

    // Eigen vector
    var ev = numeric.eig(cM);
    // console.log("eigen:",ev)

    // pick PC1 as +y
    var PC1 = [ev.E.x[0][1],ev.E.x[1][1],ev.E.x[2][1]];

    // rotate 90 ccw as +z}
    var PC2 = [-PC1[2],PC1[1],PC1[0]];

    // +x
    var PC3 = [PC1[0],PC1[2]];

    // change basis
    for (var i = 0; i < xyzArray.length; i++) {
        var xp = dot(xyzArray[i],PC3);
        var yp = dot(xyzArray[i],PC1);
        var zp = dot(xyzArray[i],PC2);
        xyzArray[i][0] = xp;
        xyzArray[i][1] = yp;
        xyzArray[i][2] = zp;
    }

    // find xyz extreme values
    var xMin,xMax,yMin,yMax,zMin,zMax;
    xMin = yMin = zMin = 1e10;
    xMax = yMax = zMax = -1e10;

    for (var i = 0; i < xyzArray.length; i++) {
        if (xyzArray[i][0] < xMin) xMin = xyzArray[i][0];
        if (xyzArray[i][0] > xMax) xMax = xyzArray[i][0];
        if (xyzArray[i][1] < yMin) yMin = xyzArray[i][1];
        if (xyzArray[i][1] > yMax) yMax = xyzArray[i][1];
        if (xyzArray[i][2] < zMin) zMin = xyzArray[i][2];
        if (xyzArray[i][2] > zMax) zMax = xyzArray[i][2];
    }

    // get 8 corners
    // need help here too in getting all 8 corners from min and max values
    return {
        center: [xbar,ybar,zbar],axes: [PC3,PC1,PC2],size: [
            [xMin,xMax],[yMin,yMax],[zMin,zMax]
        ]
    };
}


let convexHullVertices = [
  new THREE.Vector3(5.741938591003418,3.3484504222869873,0.23263418674468994),new THREE.Vector3(4.082177639007568,1.096161961555481,0.2243420034646988),new THREE.Vector3(7.95594596862793,2.680605173110962,0.07928863912820816),new THREE.Vector3(5.741938591003418,new THREE.Vector3(4.862088680267334,6.645958423614502,0.2927774488925934),new THREE.Vector3(2.20054030418396,4.291943550109863,0.35655561089515686),0.35655561089515686)
]

let OBB = findobB(convexHullVertices)
console.log("OBB:",OBB)
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r99/three.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/numeric/1.2.6/numeric.min.js"></script>

解决方法

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