A system for obtaining an orientation independent sensing coordinate frame ( ŵ, â, n̂) for characterizing cardiac conduction conditions, comprising: a high-density diagnostic catheter (10, 30, 50, 100) with closely spaced electrodes configured to measure a potential φ at each electrode at a plurality of measuring time points over a depolarization interval; an electronic control unit configured to: determine a depolarization wavefront φ (x, y, z, t) from the potentials φ over the depolarization interval; determine a local 3D electric field loop E (t) by using φ (x, y, z, t); create a zero mean version of E (t) over the depolarization interval; compute a d E /dt value E at each of the plurality of measuring time points; compute an initial estimate of the depolarization wavefront direction ŵ from a cross product of E and the Ė value for each of the plurality of measuring time points; average the initial estimate of ŵ from each of the plurality of measuring time points for a best estimate of ŵ; perform a search over angles Θ for propagation direction values â (Θ) of the depolarization wave travelling over a cardiac surface and the normal direction n̂ (Θ) of the cardiac surface by choosing a corresponding n̂ (Θ) value from the cross product â (Θ) x w for each â (Θ) value; compute a composite match score for how well dφ/dt matches an inner product E·â (Θ) and how well - φ matches the inner product E· n̂ (Θ); and choose at least one best value for â and a best value for n̂ providing closest match. a high-density diagnostic catheter (10, 30, 50, 100) with closely spaced electrodes configured to measure a potential φ at each electrode at a plurality of measuring time points over a depolarization interval; an electronic control unit configured to: determine a depolarization wavefront φ (x, y, z, t) from the potentials φ over the depolarization interval; determine a local 3D electric field loop E (t) by using φ (x, y, z, t); create a zero mean version of E (t) over the depolarization interval; compute a d E /dt value E at each of the plurality of measuring time points; compute an initial estimate of the depolarization wavefront direction ŵ from a cross product of E and the Ė value for each of the plurality of measuring time points; average the initial estimate of ŵ from each of the plurality of measuring time points for a best estimate of ŵ; perform a search over angles Θ for propagation direction values â (Θ) of the depolarization wave travelling over a cardiac surface and the normal direction n̂ (Θ) of the cardiac surface by choosing a corresponding n̂ (Θ) value from the cross product â (Θ) x w for each â (Θ) value; compute a composite match score for how well dφ/dt matches an inner product E·â (Θ) and how well - φ matches the inner product E· n̂ (Θ); and choose at least one best value for â and a best value for n̂ providing closest match. determine a depolarization wavefront φ (x, y, z, t) from the potentials φ over the depolarization interval; determine a local 3D electric field loop E (t) by using φ (x, y, z, t); create a zero mean version of E (t) over the depolarization interval; compute a d E /dt value E at each of the plurality of measuring time points; compute an initial estimate of the depolarization wavefront direction ŵ from a cross product of E and the Ė value for each of the plurality of measuring time points; average the initial estimate of ŵ from each of the plurality of measuring time points for a best estimate of ŵ; perform a search over angles Θ for propagation direction values â (Θ) of the depolarization wave travelling over a cardiac surface and the normal direction n̂ (Θ) of the cardiac surface by choosing a corresponding n̂ (Θ) value from the cross product â (Θ) x w for each â (Θ) value; compute a composite match score for how well dφ/dt matches an inner product E·â (Θ) and how well - φ matches the inner product E· n̂ (Θ); and choose at least one best value for â and a best value for n̂ providing closest match.