A method and apparatus for creating a curve to be displayed on an output device operates to interactively and directly specify the curve from input signals generated by an input device in response to control by a user. An apparatus may include an input device having a pointer for inputting points along a path-defined curve specified directly (using actual input points intended to be approximately on the curve) by a user. A processor outputs to an output device certain rendering data for rendering an image of the curve in real time for feeding back to a user. The user may augment (edit, extend) the curve by moving the pointer to add input points to the curve, based on the image fed back. The apparatus and method map non-linear coefficients of dependent control variables onto 'building variables' selected to combine in linear combinations to replace the non-linear coefficients. When new inputs are added, building variables are linearly transformed to new values, rather than being recalculated from original non-linear summation terms. The curve is rendered on an output device and fed back immediately to a user in real time as the user adapts the curve displayed by moving the pointer to add inputs.