C++：围绕原点旋转点，但输出点在一定程度上不正确

Question

第一次问。我想在 XY 平面中用 c++ 旋转 3d 中的一个点，并使用以下函数完成任务。

void rotateXY(double angle){
    //save the x and y and z coordinates in seperate variables
    double x = this->pos[0]; // value 1
    double y = this->pos[1]; // value 0
    double z = this->pos[2]; // value 0, but in the xy rotation it is not important
    double radian = angle*M_PI/180;

    this->pos[0] = cos(radian)*x - sin(radian)*y;
    this->pos[1] = sin(radian)*x + cos(radian)*y;
    this->pos[2] = 1*z;
};

我从 https://gamedevelopment.tutsplus.com/tutorials/lets-build-a-3d-graphics-engine-linear-transformations--gamedev-7716

得到了矩阵

在这里我直接操作点的坐标，因此 this->pos[0]

如果我调用另一个名为 rotateXYP 的函数，我首先从旋转点减去一个数学向量，然后在旋转后将相同的数学向量添加到它，我得到想要的结果。

void rotateXYP(double angle, eng::point originOfRotation){
    this->subVec(originOfRotation);
    this->rotateXY(angle);
    this->addVec(originOfRotation);
};

void rotateXY(double angle){
    //save x,y and z in seperate variables for manipulation
    double x = this->pos[0]; // value 1
    double y = this->pos[1]; // value 0
    double z = this->pos[2]; // value 0, but in the xy rotation it is not important
    //convert from degrees to radians because cmath requires it
    double radian = angle*M_PI/180;
    //apply the values according to a rotation matrix found on the internet
    this->pos[0] = cos(radian)*x - sin(radian)*y;
    this->pos[1] = sin(radian)*x + cos(radian)*y;
    this->pos[2] = 1*z;
};

我的问题

为什么我将点 (1|0|0) 作为函数 rotateXY(90) 的输入，然后将其作为输出。

(6.12323e-17|1|0)

而不是

(0|1|0)

如果我调用函数 rotateXYP(90, some point)，我会得到正确的点，没有 x 坐标上的小数字。我怀疑它与以下代码行中的 cos 和 sin 有关：

this->pos[0] = cos(radian)*x - sin(radian)*y;

由于我对 c++ 太缺乏经验，所以我寻求答案并希望这是一个不错的问题。

Answer 1

您的实施是正确的。这只是浮点运算的本质。所有数字都表示为近似值。翻译点时，您会获得更好的数字条件。

我可能会补充说，这种效果的发生与所使用的编程语言和硬件无关。

Answer 2

我通过添加一个名为 accuracy 的变量解决了我的问题，该变量控制 double 允许的小数位数。

void rotateXY(double angle){
                //Accuracy: a is the number of decimal places
                int a = 2;
                int acc = pow(10,a);
                //save x,y and z in seperate variables for manipulation
                double x = this->pos[0]; // value 1
                double y = this->pos[1]; // value 0
                double z = this->pos[2]; // value 0, but in the xy rotation it is not important
                //convert from degrees to radians because cmath requires it
                double radian = angle*M_PI/180;
                //apply the values according to a rotation matrix found on the internet
                this->pos[0] = round((cos(radian)*x - sin(radian)*y)*acc)/acc;
                this->pos[1] = round((sin(radian)*x + cos(radian)*y)*acc)/acc;
                this->pos[2] = round((1*z)*acc)/acc;
            };

C++：围绕原点旋转点，但输出点在一定程度上不正确

C++: Rotating point around origin, but output point is not correct by some margin

c++

3d

rotation

我的问题