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

struct Point {
    float x, y, z;
};

struct Vector {
    float x, y, z;
};

2. 计算物体的中心点

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

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

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

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

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。