jonarya - 1 month ago 10

C++ Question

I have converted a c++ code into javascript which calculates angle between 3 points. Though it is working properly I do not understand math behind it.

`function angle(a, b, c) {`

var ab = { x: b.x - a.x, y: b.y - a.y };

var cb = { x: b.x - c.x, y: b.y - c.y };

var dot = (ab.x * cb.x + ab.y * cb.y); // dot product

var cross = (ab.x * cb.y - ab.y * cb.x); // cross product

var alpha = -Math.atan2(cross, dot);

if (alpha < 0) alpha += 2 * Math.PI;

return alpha;

}

What is the use of dot and cross product here? How does atan2 use cross and dot products to calculate angle?

Answer Source

```
var ab = { x: b.x - a.x, y: b.y - a.y };
var cb = { x: b.x - c.x, y: b.y - c.y };
```

these points represent the lines AB and BC. Now dot product of 2 lines is

```
dot = |AB|.|BC|.cos(theta)
cross = |AB|.|BC|.sin(theta)
```

their division would get

```
cross/dot = tan(theta)
```

so

```
theta = atan(cross, dot)
```

we know the value of dot and cross from

```
dot = (ab.x * cb.x + ab.y * cb.y);
cross = (ab.x * cb.y - ab.y * cb.x);
```

hence we can find the angle using the above information