Piecewise-Linear and Piecewise-Affine Subspace Transformations for Finger-Angle and Spatial Measurement Decoupling and Correction in Single-Touch and Multi-Touch Touchpad and Touchscreen Systems

Methods for piecewise-linear and piecewise-affine transformations for finger-angle and spatial measurement decoupling in user touch and gesture interfaces including those with multitouch capabilities are described. A calculation chain provides a first-order calculation of up to six touch parameters (left-right, front-back, downward pressure, roll angle, pitch angle, yaw angle) responsive in real-time to user touch on a touch-responsive sensor array. A piecewise-affine transformation is applied to these first-order calculations to produce parameter decoupling. The piecewise-affine transformation can be structured to depend only on current numerical values from the first-order calculation. Alternatively, the piecewise-affine transformation can be structured to additionally depend on the positive or negative direction of change over time of at least one numerical value from the first-order calculation, thereby providing a correction for hysteresis effects.