OpenGL Rotation of an object around a line

Question

I am programming in OpenGL and C++. I know 2 points on 1 line (a diagonal line) and wish to rotate an object around that diagonal line. How can I go about doing this? I know

Answer 1

Hey, how about doing some quaternions / vector maths? =) I've done that using small "patch" on my Vector class:

double NumBounds(double value)
{
    if (fabs(value) < (1 / 1000000.0f))
        return 0; else
            return value;
}

class Vector
{
    private:
        double x, y, z;

    public:
        Vector(const Vector &v)
        {
            x = NumBounds(v.x); y = NumBounds(v.y); z = NumBounds(v.z);
        }

        Vector(double _x, double _y, double _z)
        {
            x = NumBounds(_x); y = NumBounds(_y); z = NumBounds(_z);
        }

        Vector Normalize()
        {
            if (Length() != 0)
                return Vector(x / Length(), y / Length(), z / Length()); else
                    return *this;
        }

        double operator[](unsigned int index) const
        {
            if (index == 0)
                return NumBounds(x); else
            if (index == 1)
                return NumBounds(y); else
            if (index == 2)
                return NumBounds(z); else
                    return 0;
        }

        void operator=(const Vector &v)
        {
            x = NumBounds(v.x); y = NumBounds(v.y); z = NumBounds(v.z);
        }

        Vector operator+(const Vector &v)
        {
            return Vector(x + v.x, y + v.y, z + v.z);
        }

        Vector operator-(const Vector &v)
        {
            return Vector(x - v.x, y - v.y, z - v.z);
        }

        double operator*(const Vector &v)
        {
            return NumBounds((x * v.x) + (y * v.y) + (z * v.z));
        }

        Vector operator*(double s)
        {
            return Vector(x * s, y * s, z * s);
        }

        Vector DotProduct(const Vector &v)
        {
            double k1 = (y * v.z) - (z * v.y);
            double k2 = (z * v.x) - (x * v.z);
            double k3 = (x * v.y) - (y * v.x);

            return Vector(NumBounds(k1), NumBounds(k2), NumBounds(k3));
        }

        Vector Rotate(Vector &axis, double Angle)
        {
            Vector v = *this;

            return ((v - axis * (axis * v)) * cos(angle)) + (axis.DotProduct(v) * sin(angle)) + (axis * (axis * v));
        }
};

Using this class you can easily rotate any vector around any other one:

Vector a(1.0f, 0.0f, 0.0f), b(0.0f, 1.0f, 0.0f), c(0.0f, 0.0f, 0.0f);

c = a.Rotate(b, M_PI / 2.0f); // rotate vector a around vector b for 90 degrees (PI / 2 radians): should be Vector(0, 0, 1);