[Java-matematika] Računanje relativnega horizontalnega in vertikalnega kota v 3D

Imam bolj matematični problem.
Rad bi izračunal horizontalen in vertikalen kot med dvema točkama v 3D prostoru, ampak ne znam matematike .

To imam sedaj, vendar ne deluje pravilno (v nekaterih primerih je prav):

public class Position
{
    public double X; // meters
    public double Y; // meters
    public double Z; // meters
    public double HorizontalAngle; // -180 > 180
    public double VerticalAngle; // -180 > 180
    
    public Position(double x, double y, double z)
    {
        X = x;
        Y = y;
        Z = z;
    }
    
    public Position(double x, double y, double z, double horizontalAngle, double verticalAngle)
    {
        X = x;
        Y = y;
        Z = z;
        HorizontalAngle = horizontalAngle;
        VerticalAngle = verticalAngle;
    }
    
    public double horizontalAngle(Position p)
    {
        return Math.toDegrees(Math.atan2(p.X - X, (p.Y - Y) + (p.Z - Z) * Math.sin(VerticalAngle))) - HorizontalAngle;
    }
    
    public double verticalAngle(Position p)
    {
        return Math.toDegrees(Math.atan2(p.Z - Z, (p.Y - Y) + (p.X - X) * Math.sin(HorizontalAngle))) - VerticalAngle;
    }
}

Testi (pričakovano delovanje):

import org.junit.Test;
import static org.junit.Assert.*;

public class PositionTest
{
    @Test
    public void horizontalAngle_1()
    {
        Position a = new Position(1, 1, 1, 0, 0);
        Position b = new Position(1, 2, 1);
        assertEquals(0, a.horizontalAngle(b), 0);
    }
    
    @Test
    public void horizontalAngle_2()
    {
        Position a = new Position(1, 1, 1, 0, 45);
        Position b = new Position(1, 2, 2);
        assertEquals(0, a.horizontalAngle(b), 0);
    }
    
    @Test
    public void horizontalAngle_3()
    {
        Position a = new Position(1, 1, 1, 0, 90);
        Position b = new Position(1, 1, 2);
        assertEquals(0, a.horizontalAngle(b), 0);
    }
    
    @Test
    public void horizontalAngle_4()
    {
        Position a = new Position(1, 1, 1, 0, 180);
        Position b = new Position(1, 0, 1);
        assertEquals(0, a.horizontalAngle(b), 0);
    }
    
    @Test
    public void horizontalAngle_5()
    {
        Position a = new Position(1, 1, 1, 0, -45);
        Position b = new Position(1, 0, 0);
        assertEquals(0, a.horizontalAngle(b), 0);
    }
    
    @Test
    public void horizontalAngle_6()
    {
        Position a = new Position(1, 1, 1, 0, -90);
        Position b = new Position(1, 1, 0);
        assertEquals(0, a.horizontalAngle(b), 0);
    }
    
    @Test
    public void horizontalAngle_7()
    {
        Position a = new Position(1, 1, 1, 0, -180);
        Position b = new Position(1, 0, 1);
        assertEquals(0, a.horizontalAngle(b), 0);
    }

    @Test
    public void horizontalAngle_8()
    {
        Position a = new Position(1, 1, 1, 0, -180);
        Position b = new Position(1, 2, 1);
        assertEquals(-180, a.horizontalAngle(b), 0);
    }

    @Test
    public void verticalAngle_1()
    {
        Position a = new Position(1, 1, 1, 0, 0);
        Position b = new Position(1, 2, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }
    
    @Test
    public void verticalAngle_2()
    {
        Position a = new Position(1, 1, 1, 45, 0);
        Position b = new Position(2, 2, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }
    
    @Test
    public void verticalAngle_3()
    {
        Position a = new Position(1, 1, 1, 90, 0);
        Position b = new Position(1, 2, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }
    
    @Test
    public void verticalAngle_4()
    {
        Position a = new Position(1, 1, 1, 180, 0);
        Position b = new Position(1, 0, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }
    
    @Test
    public void verticalAngle_5()
    {
        Position a = new Position(1, 1, 1, -45, 0);
        Position b = new Position(0, 0, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }
    
    @Test
    public void verticalAngle_6()
    {
        Position a = new Position(1, 1, 1, -90, 0);
        Position b = new Position(0, 1, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }
    
    @Test
    public void verticalAngle_7()
    {
        Position a = new Position(1, 1, 1, -180, 0);
        Position b = new Position(1, 0, 1);
        assertEquals(0, a.verticalAngle(b), 0);
    }

    @Test
    public void verticalAngle_8()
    {
        Position a = new Position(1, 1, 1, 180, 0);
        Position b = new Position(1, 2, 1);
        assertEquals(180, a.verticalAngle(b), 0);
    }
}

PositionTest.verticalAngle_4:117 expected:0.0 but was:180.0
PositionTest.verticalAngle_5:125 expected:0.0 but was:180.0
PositionTest.verticalAngle_7:141 expected:0.0 but was:180.0
PositionTest.verticalAngle_8:149 expected:180.0 but was:0.0
PositionTest.horizontalAngle_4:53 expected:0.0 but was:180.0
PositionTest.horizontalAngle_5:61 expected:0.0 but was:180.0
PositionTest.horizontalAngle_7:77 expected:0.0 but was:180.0
PositionTest.horizontalAngle_8:85 expected:-180.0 but was:0.0

Lahko izracunas kot med koordinatnim sistemom (3-2-1, Bezugssystem) in 3D tocko, oz. razliko med koti.

otago je 13. jul 2019 ob 13:52 izjavil:

Lahko izracunas kot med koordinatnim sistemom (3-2-1, Bezugssystem) in 3D tocko, oz. razliko med koti.

Ali dobim lahko posamezno horizontalni in vertikalni kot?
Za skupen kot sem našel.