推荐：用 NSDT编辑器 快速搭建可编程3D场景

在Three.js应用开发中，有时你可能需要为3D场景中的网格绘制2D的包围框，应该怎么做？

朴素的想法是把网格的3D包围框投影到屏幕空间，例如，下图中的绿色框 3D包围框， 当将其投影为 2D 时，得到的红色2D包围框，显然比想要的蓝色框大很多：

正确的做法是先将3D网格投影到屏幕空间，再计算2D包围框。

1、计算单个网格的2D包围框

只需将所有顶点转换为屏幕空间并从中创建一个 2d 边界框：

function computescreenspaceboundingbox(mesh, camera) {
  var vertices = mesh.geometry.vertices;
  var vertex = new three.vector3();
  var min = new three.vector3(1, 1, 1);
  var max = new three.vector3(-1, -1, -1);

  for (var i = 0; i < vertices.length; i++) {
    var vertexworldcoord = vertex.copy(vertices[i]).applymatrix4(mesh.matrixworld);
    var vertexscreenspace = vertexworldcoord.project(camera);
    min.min(vertexscreenspace);
    max.max(vertexscreenspace);
  }

  return new three.box2(min, max);
}

生成的 box2 位于标准化屏幕坐标 [-1, 1] 中， 可以通过乘以渲染器高度和宽度的一半来获得像素：

function normalizedtopixels(coord, renderwidthpixels, renderheightpixels) {
  var halfscreen = new three.vector2(renderwidthpixels/2, renderheightpixels/2)
  return coord.clone().multiply(halfscreen);
}

2、计算3DObject的2D包围框

更完善的实现需要考虑组、子节点等各种3DObject，其中可能包含多个网格，这需要一个递归实现，代码如下：

function computescreenspaceboundingbox(obj, camera) {
    var min;
    var max;

    // is this an array of objects?
    if(array.isarray(obj)) {
        for(var i = 0; i < obj.length; ++i) {
            let box2 = computescreenspaceboundingbox(obj[i], camera);
            if(min === undefined) {
                min = box2.min.clone();
                max = box2.max.clone();
            } else {
                min.min(box2.min);
                max.max(box2.max);
            }
        }
    }

    // does this object have geometry?
    if(obj.geometry !== undefined) {
        var vertices = obj.geometry.vertices;
        if(vertices === undefined
            && obj.geometry.attributes !== undefined
            && 'position' in obj.geometry.attributes) {
            // buffered geometry
            var vertex = new three.vector3();       
            var pos = obj.geometry.attributes.position;
            for(var i = 0; i < pos.count * pos.itemsize; i += pos.itemsize)
            {
                vertex.set(pos.array[i], pos.array[i + 1], pos.array[1 + 2]);
                var vertexworldcoord = vertex.applymatrix4(obj.matrixworld);
                var vertexscreenspace = vertexworldcoord.project(camera);
                if(min === undefined) {
                    min = vertexscreenspace.clone();
                    max = vertexscreenspace.clone();
                }
                min.min(vertexscreenspace);
                max.max(vertexscreenspace);
            }
        } else {
            // regular geometry
            var vertex = new three.vector3();       
            for(var i = 0; i < vertices.length; ++i) {
                var vertexworldcoord = vertex.copy(vertices[i]).applymatrix4(obj.matrixworld);
                var vertexscreenspace = vertexworldcoord.project(camera);
                if(min === undefined) {
                    min = vertexscreenspace.clone();
                    max = vertexscreenspace.clone();
                }
                min.min(vertexscreenspace);
                max.max(vertexscreenspace);
            }
        }
    }
    
    // does this object have children?
    if(obj.children !== undefined) {
        for(var i = 0; i < obj.children.length; ++i) {
            let box2 = computescreenspaceboundingbox(obj.children[i], camera);
            if(min === undefined) {
                min = box2.min.clone();
                max = box2.max.clone();
            } else {
                min.min(box2.min);
                max.max(box2.max);
            }
        }
    }
    
    return new three.box2(min, max);
}

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原文链接：计算3D对象的2D包围框 — BimAnt