3D空间中两个盒子之间的相交 [英] Intersection between two boxes in 3D space

问题描述

我想为我的图形引擎实现一个碰撞检测系统.

I want to implement a collision detection system for my graphic engine.

我不知道这是否是常用的方法，但我的想法是在3D框中绑定任何固体对象(例如网格或相机)，这将给我比球体更准确的结果

I don't know if it is the common way to do it but my idea was to bound any solid object (like a mesh or the camera) within a 3D box, which would give me much more accurate results than a sphere.

此框由八个顶点定义

    x0 = min(vertices.x)-off   // parsing mesh's vertices for the minimum x
    y0 = min(vertices.y)-off
    z0 = min(vertices.z)-off
    x1 = max(vertices.x)+off   // off avoids 2D bounding on 2D objects
    y1 = max(vertices.y)+off
    z1 = max(vertices.z)+off
    boundingBox[0] = vec3(x0, y0, z0);
    boundingBox[1] = vec3(x0, y1, z0);
    boundingBox[2] = vec3(x1, y0, z0);
    boundingBox[3] = vec3(x1, y1, z0);
    boundingBox[4] = vec3(x0, y0, z1);
    boundingBox[5] = vec3(x0, y1, z1);
    boundingBox[6] = vec3(x1, y0, z1);
    boundingBox[7] = vec3(x1, y1, z1);

在将边界框转换为世界坐标之后，我正在寻找一种方法来检查两个坐标之间是否存在交集，但是我不知道如何使用线性代数.

After having transformed the bounding box to world coordinates, I'm looking for a way to check if there is an intersection between two of them, but I don't know how to do it with linear algebra.

我认为，如果可以确定所有框都与XZ平面平行，则可以简单地将box1的所有顶点与box2的最小/最大坐标进行比较，如下所示:

I thought that if I was sure that all the boxes were parallel to XZ plane I could simply check all the vertices of box1 against min/max coordinates of box2, like this:

for(int i = 0; i < 8; i++) {
    if(box1[i].x >= box2.minX && box1[i].x <= box2.maxX) &&
      (box1[i].y >= box2.minY && box1[i].y <= box2.maxY) &&
      (box1[i].z >= box2.minZ && box1[i].z <= box2.maxZ) {
        // collision here
    }
}

但是，由于网格可能已经旋转，因此这行不通.我可以使用数学公式吗?

But this is not going to work since meshes could have been rotated. Is there a mathematical formula that I can use?

推荐答案

可以通过分隔轴定理(此处和此处).

Intersections between two oriented bounding boxes (or more general between two objects) can be done by the separating axis theorem (here, here and here).

对于对象之间的一般相交测试，一个对象正在搜索一个平面，以使两个对象位于不同的半空间中，并且该平面不与其中一个对象相交.例如，可以在此 Gamasutra文章

For a general intersection tests between objects, one is searching for a plane such that the two objects lie in different halfspaces and the plane does not intersect one of the objects. An implementation of this can for example be found in this Gamasutra article.

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