Control point manipulation techniques in haptic systems
A method for blending new control points into the field is described. A more costly but conceptually simpler method, measuring the extant field and recreating a copy of that field interpolated with the actually desired value at a new control point is first described. Further, traditionally predicting the output of phased array systems involves taking each element and evaluating its contribution to the field. When focusing phased arrays, predicting the output and the fringing field is necessary for multipoint focusing and acoustic cloaking applications. In the limit of a large enough number of discrete transducer elements, the evaluation of a single approximation will inevitably outperform even a linear summation over the linear acoustic properties of the elements. Further, to resolve the misalignment of expected and realized output of the mid-air haptic array, interactable objects are subdivided into customizable, uniform, intersection “regions” that are then used to compute a volume of 3D positions in which the haptic focal point is then moved between. Positions can be produced and assigned in different ways, and volumes can be produced from any object as long as they have their regions pre-computed. Rather than directly targeting the hand of the user, the virtual intersection of the hand are used and these regions create a generally larger volume in which mid-air haptics can be produced.
1 . A system comprising:
an acoustic field controlled via a plurality of control points in mid-air, wherein each of the plurality of control points is assigned a value equating to a desired amplitude at the control point;
a plurality of transducer elements having a transducer output for creating the acoustic field exhibiting the desired amplitudes at the plurality of control points;
a new control point having a new degree of freedom incrementally added to the acoustic field smoothing its effect on the transducer output via introduction of a blending coefficient so that the new degree of freedom is incrementally added to the acoustic field;
wherein the new control point is incrementally added to the acoustic field by creating an interpolation between a matrix that allows interaction between the plurality of control points and a matrix that prevents interactions between the plurality of control points;
wherein the interpolation is described as
( PCP H +( I−PP H ) C diag) z′=b,
wherein I is an identity matrix;
wherein PP H is an m×m matrix where diagonal elements are squares of corresponding control point blending coefficients;
wherein PCP H is a modified C matrix with the blending coefficient corresponding to the control point of the row and the blending coefficient corresponding to the control point of the column both multiplying each of the C matrix elements;
wherein (I−PP H )Cdiag is a matrix that cancels the modified diagonal of PCP H having a diagonal modified by the blending coefficient of both the row and column which is the same such that a corresponding diagonal element is a square;
wherein the portion of (I−PP H )Cdiag, ICdiag then replaces the modified diagonal of PCP H with the original diagonal of the C matrix Cdiag leaving it unmodified by application of the blending coefficients;
wherein z′ is a solution vector whose j th component describes a proportion of each of a set of complex-valued basis vectors whose components respectively describe a scalable portion of a drive of each transducer that is applicable to the j th control point; and
wherein b is the vector of the desired complex-valued acoustic quantities at each of the defined control points.
2 . The system as in claim 1 , further comprising: a number of the plurality of control points fewer than a number of the plurality of transducers elements placed into a complex-valued linear system with the sample vector b={α 1 (y1), . . . , α m (X m )} representing a desired total linear scalar complex-valued acoustic quantity; wherein amplitudes are desired amplitudes of an acoustic quantity and phases are taken from a phase oracle; and wherein α m (X m ) represents a complex-valued component associated with the m th defined control point.
3 . The system as in claim 2 , wherein at least one component of the sample vector b comprises an interpolation between a complex-valued simulated measurement of the acoustic field at a required location and the desired complex-valued acoustic quantity at the required location.
4 . The system as in claim 3 , wherein if the desired complex-valued linear system is described as Ax=b, an x vector comprises field coefficients for each of the plurality of transducer elements;
wherein A represents the modelled transducer output given an input with unit amplitude and zero phase.
5 . The system as in claim 3 , wherein the desired complex-valued linear system is used to drive the plurality of transducers elements in a loop.