NX二次开发,用C++ 写一个OBB算法来创建实体的最小包容盒

OBB（oriented bounding box）算法是一种用于计算三维物体包围盒的算法，它可以创建一个最小的、能够完全包含物体的矩形盒子。以下是使用C++语言编写OBB算法的基本步骤： 1. 定义点和向量结构体 ```c++ struct Point { float x, y, z; }; struct Vector { float x, y, z; }; ``` 2. 计算物体的中心点 ```c++ Point computeCenterPoint(Point* points, int numPoints) { Point center = { 0.0f, 0.0f, 0.0f }; for (int i = 0; i < numPoints; i++) { center.x += points[i].x; center.y += points[i].y; center.z += points[i].z; } center.x /= numPoints; center.y /= numPoints; center.z /= numPoints; return center; } ``` 3. 计算物体的协方差矩阵 ```c++ Matrix3x3 computeCovarianceMatrix(Point* points, int numPoints) { Point center = computeCenterPoint(points, numPoints); Matrix3x3 covarianceMatrix = { 0.0f }; for (int i = 0; i < numPoints; i++) { Vector v = { points[i].x - center.x, points[i].y - center.y, points[i].z - center.z }; covarianceMatrix.m11 += v.x * v.x; covarianceMatrix.m12 += v.x * v.y; covarianceMatrix.m13 += v.x * v.z; covarianceMatrix.m21 += v.y * v.x; covarianceMatrix.m22 += v.y * v.y; covarianceMatrix.m23 += v.y * v.z; covarianceMatrix.m31 += v.z * v.x; covarianceMatrix.m32 += v.z * v.y; covarianceMatrix.m33 += v.z * v.z; } covarianceMatrix.m11 /= numPoints; covarianceMatrix.m12 /= numPoints; covarianceMatrix.m13 /= numPoints; covarianceMatrix.m21 = covarianceMatrix.m12; covarianceMatrix.m22 /= numPoints; covarianceMatrix.m23 /= numPoints; covarianceMatrix.m31 = covarianceMatrix.m13; covarianceMatrix.m32 = covarianceMatrix.m23; covarianceMatrix.m33 /= numPoints; return covarianceMatrix; } ``` 4. 计算物体的主轴 ```c++ void computePrincipalAxis(Matrix3x3 covarianceMatrix, Vector* axis) { float eigenvalues[3]; Vector eigenvectors[3]; diagonalize(covarianceMatrix, eigenvalues, eigenvectors); int maxEigenvalueIndex = 0; float maxEigenvalue = eigenvalues[0]; for (int i = 1; i < 3; i++) { if (eigenvalues[i] > maxEigenvalue) { maxEigenvalueIndex = i; maxEigenvalue = eigenvalues[i]; } } axis->x = eigenvectors[maxEigenvalueIndex].x; axis->y = eigenvectors[maxEigenvalueIndex].y; axis->z = eigenvectors[maxEigenvalueIndex].z; } ``` 5. 计算物体的OBB ```c++ void computeOBB(Point* points, int numPoints, Point* obbCenter, Vector* obbAxis, Vector* obbExtent) { Matrix3x3 covarianceMatrix = computeCovarianceMatrix(points, numPoints); computePrincipalAxis(covarianceMatrix, obbAxis); Point center = computeCenterPoint(points, numPoints); obbCenter->x = center.x + obbAxis->x * dotProduct(points[0], *obbAxis); obbCenter->y = center.y + obbAxis->y * dotProduct(points[0], *obbAxis); obbCenter->z = center.z + obbAxis->z * dotProduct(points[0], *obbAxis); float minX, minY, minZ, maxX, maxY, maxZ; minX = minY = minZ = FLT_MAX; maxX = maxY = maxZ = -FLT_MAX; for (int i = 0; i < numPoints; i++) { Vector p = { points[i].x - obbCenter->x, points[i].y - obbCenter->y, points[i].z - obbCenter->z }; Vector e = { obbAxis->x * dotProduct(p, *obbAxis), obbAxis->y * dotProduct(p, *obbAxis), obbAxis->z * dotProduct(p, *obbAxis) }; if (e.x < minX) minX = e.x; if (e.y < minY) minY = e.y; if (e.z < minZ) minZ = e.z; if (e.x > maxX) maxX = e.x; if (e.y > maxY) maxY = e.y; if (e.z > maxZ) maxZ = e.z; } obbExtent->x = (maxX - minX) * 0.5f; obbExtent->y = (maxY - minY) * 0.5f; obbExtent->z = (maxZ - minZ) * 0.5f; } ``` 6. 计算两个OBB之间的距离 ```c++ float computeOBBDistance(Point* obb1Center, Vector* obb1Axis, Vector* obb1Extent, Point* obb2Center, Vector* obb2Axis, Vector* obb2Extent) { Vector d = { obb2Center->x - obb1Center->x, obb2Center->y - obb1Center->y, obb2Center->z - obb1Center->z }; float distance = fabs(dotProduct(d, *obb1Axis)); distance -= fabs(dotProduct(d, *obb2Axis)); Vector crossProduct = cross(*obb1Axis, *obb2Axis); distance += fabs(dotProduct(d, crossProduct)); for (int i = 0; i < 3; i++) { distance -= fabs(dotProduct(crossProduct, Vector{ obb2Extent->x * obb2Axis->x, obb2Extent->y * obb2Axis->y, obb2Extent->z * obb2Axis->z })); crossProduct = cross(*obb1Axis, Vector{ obb2Axis->x, obb2Axis->y, obb2Axis->z }); distance += fabs(dotProduct(d, crossProduct)); } return distance; } ``` 以上是使用C++语言编写OBB算法的基本步骤，你可以根据自己的需求进行调整。