Application of Haptic Navigation to Modify Free-Form Surfaces Through Specified Points and Curves

Abstract

In this paper, we propose a method which modifies free-form surfaces to pass through not only specified points, but also specified curves with the assistance of haptic navigation. Using the method, designers of aesthetic shapes, such as a car body, can manipulate the model of the shape in real-time looking at its stereoscopic image and feeling its haptic sensation as if there were a clay model. The haptic navigation helps designers, letting them capture and recognize the object easily and constraining their operation to the appropriate direction or along the specified geometric element. In addition, the designers can get force feedback proportional to the modification quantity. To obtain a smoothly modified shape, we introduce correction functions to the given surface equations. A correction function distributes the effect of the change over the whole shape or the specified region according to the distance of the point in the normal direction of the given surface. The values of the correction function are 1 at the indicated point and 0 at the boundaries, and the shape is modified to keep the original smoothness. The correction values of the functions at the indicated points are determined to pass through all of them by solving a linear equation. To apply this to the specified curves including boundaries of a trimmed surface, we treat points composing the curve similarly to the point specification by representing them with a Cardinal spline. We have confirmed that the system is effective to manipulate a shape with its feeling and that smooth surfaces are obtained in real time as designers want.