Included angle of 3D vector

Project scenario ：

Calculate the included angle of three-dimensional coordinates

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The included angle of three-dimensional vector

Reference resources ：[ Online calculation of three-dimensional vector angle ](https://www.23bei.com/tool/300.html)

The formula ：
The formula for calculating the included angle of three-dimensional vector is as follows ：

Suppose that the two three-dimensional vectors are ：a=(x1,y1,z1),b=(x2,y2,z2).
vector a The mold ：|a|=√(x1^2+y12+z1^2).
vector b The mold ：|b|=√(x2^2+y22+z2^2).
Dot multiplication of two vectors ：a·b=(x1x2+y1y2+z1z2).
Let the angle between two vectors be θ, Then there are ：cosθ=(x1x2+y1y2+z1z2)/[√(x1^2+y12+z1^2)*√(x22+y2^2+z22)].

The above formulas are given in three-dimensional coordinates , If you let the coordinate in z=0, Then we get the calculation formula of the plane vector .
Angle between two vectors θ The range of phi is zero ：[0,π]. When the included angle is an acute angle ,cosθ>0; When the included angle is an obtuse angle ,cosθ<0.

Three dimensional point coordinates

public class Point {
    
    public float x;
    public float y;
    public float z;

    public Point (float x, float y, float z) {
    
        this.x = x;
        this.y = y;
        this.z = z;
    }
}

Calculation formula

/** *  Get the included angle of the three-dimensional vector . * * @param center  Included angle center point  * @param start  The starting point  * @param end  The end point  * @return  Return included angle  */
    public static float getTdAngle(Point center, Point start, Point end) {
    
        //  vector 1
        float x1 = start.x - center.x, y1 = start.y - center.y, z1 = start.z - center.z;
        //  vector 2
        float x2 = end.x - center.x, y2 = end.y - center.y, z2 = end.z - center.z;
        System.out.println("x1/y1/z1=" + x1 + "/" + y1 + "/" + z1);
        System.out.println("x2/y2/z2=" + x2 + "/" + y2 + "/" + z2);
        //  Dot product of vector 
        float vectorDot = x1*x2 + y1*y2 + z1*z2;
        //  vector 1 The mold 
        double vectorMold1 = Math.sqrt(Math.pow(x1, 2) + Math.pow(y1, 2) + Math.pow(z1, 2));
        //  vector 2 The mold 
        double vectorMold2 = Math.sqrt(Math.pow(x2, 2) + Math.pow(y2, 2) + Math.pow(z2, 2));
        //  The angle of the vector [0, PI], When the included angle is an acute angle ,cosθ>0; When the included angle is an obtuse angle ,cosθ<0
        double cosAngle = vectorDot / (vectorMold1 * vectorMold2);
        double radian = Math.acos(cosAngle);
        return (float) (180 / Math.PI * radian);
    }

test result

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