//
// Vector getRelationship(f, r, c, theta)
// Last modified: 28Aug2006
//
// Uses the secant method to calculate the intersection of the function
// and a circle centered at the parameterized vector position c with
// the appropriate radius, returning a vector from c to this intersection.
//
// The secant method is defined by the following recurrence relation:
//
// x_(n + 1) = x_n - f(x_n) * (x_n - x_(n - 1)) / (f(x_n) - f(x_(n - 1))).
//
// Returns: vector from the parameterized vector position c
// to the intersection of the function and appropriate circle
// Parameters:
// f in the intersecting function
// r in the radius of the intersecting circle
// c in the position to be centered at
// theta in the rotation of the relationship (default 0)
//
Vector Formation::getRelationship(const Function f,
const GLfloat r,
const Vector c,
const GLfloat theta)
{
if (f == NULL) return Vector();
GLfloat xn = c.x + r + X_ROOT_THRESHOLD,
xn_1 = c.x + r - X_ROOT_THRESHOLD,
intersect = 0.0f, error = 0.0f;
for (int i = 0; i < X_N_ITERATIONS; ++i)
{
intersect = fIntersect(f, r, c, xn);
error = intersect * (xn - xn_1) /
(intersect - fIntersect(f, r, c, xn_1));
if (abs(error) <= X_ROOT_THRESHOLD) break;
xn_1 = xn;
xn -= error;
}
Vector rel = Vector(xn, f(xn)) - c;
rel.rotateRelative(-theta);
return rel;
} // getRelationship(const..{Function, GLfloat, Vector, GLfloat})
// Uses the secant method to calculate the intersection of the function
// and a circle centered at the parameterized vector position c with
// the appropriate radius, returning a vector from c to this intersection.
//
// The secant method is defined by the following recurrence relation:
//
// x_(n + 1) = x_n - f(x_n) * (x_n - x_(n - 1)) / (f(x_n) - f(x_(n - 1))).
//
// Returns: vector from the parameterized vector position c
// to the intersection of the function and appropriate circle
// Parameters:
// f in the intersecting function
// r in the radius of the intersecting circle
// c in the position to be centered at
// theta in the rotation of the relationship (default 0)
//
Vector Formation::calculateDesiredRelationship(const Function f,
const float r,
const Vector c,
const float theta)
{
// TODO: HERE IS THE GOOFY ONE
if (f == NULL) return Vector();
float xn = c.x + r + X_ROOT_THRESHOLD,
xn_1 = c.x + r - X_ROOT_THRESHOLD,
intersect = 0.0f, error = 0.0f;
for (int i = 0; i < X_N_ITERATIONS; ++i)
{
intersect = fIntersect(f, r, c, xn);
error = intersect * (xn - xn_1) /
(intersect - fIntersect(f, r, c, xn_1));
if (abs(error) <= X_ROOT_THRESHOLD) break;
xn_1 = xn;
xn -= error;
}
Vector rel = Vector(xn, f(xn)) - c;
rel.rotateRelative(-theta);
return rel;
}
