如何围绕任意轴旋转一个点？

Question

我想围绕任意轴旋转 OpenGL 中的一个点。 我想利用它来旋转一个球体。

这是我到目前为止得到的：

float degreeBetweenTwoVec(glm::vec3 &a, glm::vec3 b)
{
    float prod = b.x * a.x + b.y * a.y + b.z * a.z;
    float mag_axis = sqrt((b.x * b.x) + (b.y * b.y) + (b.z * b.z));
    float mag_vec = sqrt((a.x * a.x) + (a.y * a.y) + (a.z * a.z));
    float degree = prod / (mag_axis * mag_vec);

    return acos(degree) * 180.0 / PI;;
}

void rotAroundZ(glm::vec3 &point, float degree) 
{
    glm::vec3 n_point;

    n_point.x = (point.x * cos(degree * PI / 180.0)) - (point.y * sin(degree * PI / 180.0));
    n_point.y = (point.x * sin(degree * PI / 180.0)) + (point.y * cos(degree * PI / 180.0));
    n_point.z = point.z;

    point.x = n_point.x;
    point.y = n_point.y;
    point.z = n_point.z;
}

void rotAroundY(glm::vec3& point, float degree)
{
    glm::vec3 n_point;

    n_point.x = (point.x * cos(degree * PI / 180.0)) + (point.z * sin(degree * PI / 180.0));
    n_point.y = point.y;
    n_point.z = ((point.x * -1.0f) * sin(degree * PI / 180.0)) + (point.z * cos(degree * PI / 180.0));;

    point.x = n_point.x;
    point.y = n_point.y;
    point.z = n_point.z;
}

void rotAroundA(glm::vec3& point, glm::vec3 &axis, float zdegree)
{
    float xdegree = degreeBetweenTwoVec(axis, glm::vec3{ 1.0f, 0.0f, 0.0f });
    float ydegree = degreeBetweenTwoVec(axis, glm::vec3{ 0.0f, 1.0f, 0.0f });

    rotAroundZ(point,  xdegree);
    rotAroundY(point,  ydegree);
    rotAroundZ(point,  zdegree);
    rotAroundY(point, -ydegree);
    rotAroundZ(point, -xdegree);
}

void rotAObject(Object& obj, glm::vec3 &axis, float degree)
{
    axis = glm::normalize(axis);
    translate(axis, glm::vec3{ axis.x, axis.y, axis.z });
    for (int i = 0; i < obj.vertices.size(); i++)
    {
        rotAroundA(obj.vertices[i], axis, degree);
    }
    rotAroundA(obj.mp, axis, degree);
    translate(axis, glm::vec3{ axis.x * -1.0f, axis.y * -1.0f, axis.z * -1.0f });
}

如果给定轴恰好位于全局轴之一上，则此方法工作得很好。 但是，如果不是，并且给定的轴基本上是围绕其他东西旋转。 它正在围绕某种轴旋转，但是一旦改变给定的轴，例如围绕 z 轴旋转它，它就会围绕与以前完全不同的轴旋转。 看起来对于每个 position 给定的轴可以采用 object 实际上在旋转的其他轴。

任何帮助表示赞赏！

Answer 1

我建议使用旋转矩阵。 使用glm::rotate() ，通过轴和角度设置旋转矩阵。
将点转换为glm::vec4并通过旋转矩阵对其进行变换：

#include <glm/glm.hpp>
#include <glm/gtc/matrix_transform.hpp>

glm::mat4 rot_mat = glm::rotate(glm::mat4(1.0f), glm::radians(degree), axis);
glm::vec3 n_point = glm::vec3(glm::vec4(point, 1.0f) * rot_mat);