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javavectordoublepointangle

Calculate angle between 3 points with vector, more precision needed (java)

I need to calculate the angle between 3 points. I've done that using vectors, it looks like it's working, but sometimes I get NaN as a result. To calculate the angle I used the arcos(dot(v1,v2)/(length(v1)*length(v2))) formula. Here's the code:

private static double angleBetween(Point previous, Point center, Point next) {
        Vector2D vCenter = new Vector2D(center.x, center.y );
        Vector2D vPrev = new Vector2D(previous.x, previous.y );
        Vector2D vNext = new Vector2D(next.x, next.y );

        Vector2D a = vCenter.minus(vPrev);
        Vector2D b = vCenter.minus(vNext);

        double dot = Vector2D.dot(a, b);

        double la = a.length();

        double lb = b.length();

        double l = la*lb;

        double acos = Math.acos(dot/l);

        double deg = Math.toDegrees(acos);

        return deg;

        }

Vector2D class:

public double length() {
        return Math.sqrt(x * x + y * y);
    };

public static double dot(Vector2D v1, Vector2D v2) {
        return v1.x * v2.x + v1.y * v2.y;
    };

public Vector2D minus(Vector2D v) {
        return new Vector2D(x - v.x, y - v.y);
    };

Debugging the program I've discovered why this happens. for example let be:

center = (127,356)
previous = (117,358)
next = (137,354)

//calculating the vectors
a = (-10,2) //center - prev
b = (10,-2) //center - next

dot = -10*10 + 2*-2 = 104

la = sqrt(-10*-10 + 2*2) = sqrt(104) = see attachment
lb = sqrt(10*10 + -2*-2) = sqrt(104) = see attachment

l = la * lb = see attachment

acos = NaN because dot/l>1 because I lost precision because of sqrt() which didn't give me the exact value therefore la*lb isn't 104.

now as far as I know double is the most precise number type in java. How can I solve this problem?

attchment: la,lb,l values

PS It may looks like a very rare situation, but I'm experiencing quite a lot of them, so I can't just ignore it.

Solution

  • The best way to solve this problem is to use an appropriate data type like java.math.BigDecimal and define a precision for you computation using an instance of type java.math.MathContext. For instance:

    double l = la*lb;
BigDecimal lWrapper = new BigDecimal(l, new MathContext(5));
l = lWrapper.doubleValue();

    There is an other way to work around this problem. Use the following formula:

    angle = atan(length(crossProduct(a, b)) / dotProduct(a, b)) // Because the domain of definition of the tan function is R

    Derivation of the formula:

      cos(angle) = dotProduct(a, b)   / (length(a) * length(b)) and
  sin(angle) = length(crossProduct(a, b)) / (length(a) * length(b))

    One has

     tan(angle) = sin(angle) / cos(angle)

    so

    tan(angle) = length(crossProduct(a, b)) / (length(a) * length(b)) / dotProduct(a, b)   / (length(a) * length(b))
tan(angle) = length(crossProduct(a, b)) / dotProduct(a, b)

    Applying the invert function of tan:

    angle = atan(length(crossProduct(a, b)) / dotProduct(a, b))

    The cross product of A, B ∈ ℜ2:

    || A x B || = det(A,B) = ((A.x * B.y) - (A.y * B.x))

    Remarks:

    1. ||x|| is the length of the vector x ⇔ length(a)
    2. ∀ A, B ∈ ℜ2: || A x B || equal the determinant of A, B
    3. You can use the sign(|| A x B ||) to find out the orientation