float OpenNaturalCubicSpline::inverse( float x, float tGuess, float epsilon, int maxIterations )
{
float result = tGuess;
float xResult = evaluateAt( result );
float error = x - xResult;
float absError = fabs( error );
int n = 0;
while( ( absError > epsilon ) && ( n < maxIterations ) )
{
float dxdt = derivativeAt( result );
result += error / dxdt;
xResult = evaluateAt( result );
error = x - xResult;
absError = fabs( error );
++n;
}
#if _DEBUG
if( n == maxIterations )
{
printf( "max iterations reached! " );
}
printf( "error = %f\n", absError );
#endif
return result;
}
float Spline2f::computeHalfSpace( const Vector2f& p, float* closestT, float* closestDistance )
{
float t;
Vector2f closestPoint = closestPointOnSpline( p, &t, closestDistance );
Vector2f tangent = derivativeAt( t );
Vector2f pointToClosestPoint = p - closestPoint;
if( closestT != NULL )
{
*closestT = t;
}
return Vector2f::cross( tangent, pointToClosestPoint ).z;
}
Vector2f Spline2f::normalAt( float t )
{
return derivativeAt( t ).normal();
}
