Virtual Sculpting using Implicit Surfaces

With the increasing use of computers in the fields of modelling and animation, users want to be able to create objects in a more free form manner. Such free form manipulation of objects on a computer is what we refer to as "virtual sculpting". Noble's PhD and original work in this area was based on modelling using parametric splines, in particular NURBS. A different approach is given by using implicit surfaces and that was the starting point of this project.

Unlike splines, implicit surfaces are automatically closed. They also allow branches, which is not an easy thing to model with splines. However, they do not have a simple compact representation which can be maintained when using them for sculpting. The point of this investigation was to see whether a virtual sculpting system could be set up which used implicit surfaces but which maintained a constant representational complexity for the modelled surface.

Clearly there is a balance between representational complexity and the amount of detail on the surface. In normal sculpting however, the representational complexity simply increases unchecked as the user performs sculpting actions. Our aim was to find a representation of a given fixed complexity that could approximate the current surface at any time during the sculpting.

Our basic sculpting system worked as follows. Both tool and clay are represented as implicit surfaces. The two deform on contact to give a common surface. The stiffness of the tool determining this common contact can be adjusted by the user. Since the action of the tool on the clay is in effect given by subtracting the tool implicit function, each time an action is performed an extra function is subtracted from the clay function. As sculpting proceeds, the model function builds and builds.

Typical tool / clay interaction is as shown in the picture. The system is fully 3 dimensional and surfaces are visualised by mapping triangular dots onto them. The system can run with stereoscopic pictures for full 3D visualisation

The pictures to the left show a sculpted model, both in triangle form and in rendered form. Rendering takes several seconds and so is not used during sculpting.

The sculpted surface is represented for visulaisation by the triangles, or points on the surface. These points can also be used to represent the surface. For a given number of points, the representational complexity will be constant, as required. To achieve this, the method of Witkin and Heckbert was used to distribute the points evenly across the surface. We then modified the control algorithm to allow the number of particles to be chosen by the user. This meant that whatever sculpting had been done, we could always represent the result with, say, 120 points. The algorithm was further modified to put more points on parts of the surface with higher curvature. The idea here was that higher curvature means more detail and therefore is better represented by an increased number of points.

Having put the points on the surface, the model was represented using radial basis functions, as for example in Turk and O'Brien. The idea is that each point on the surface has one associated radial basis function. The sum of all the functions approximates the surface. Since the functions are of a fixed form, with a fixed number of coefficients, the size of the representation for a given number of points is fixed, as required.

Clearly the system achieves a fixed complexity of representation for the sculpted surface, given that (say) 120 points are spread over it and the function calculated. The two major questions are, first, how accurate is the representation and secondly, is the representation better if the points are biased towards the high curvature regions?

Initial tests showed that the approximating surface converged towards the original surface as the number of points increased, as expected. Somewhat surprisingly however biasing points towards high curvature regions did not seem to improve the approximation. Further tests are being carried out to allow further analysis to be done.

Publications

NOBLE, R. A., ZHANG, K. & McDERMOTT, R. (2005) Virtual Sculpting Using Implicit Surfaces with Scattered Data Interpolation. UK Eurographics conference, Theory and Practice of Computer Graphics, University of Kent, Canterbury, 15 - 17 June 2005, pp. 67-74. ISBN 3-905673-56-8. Refereed. Published by the Eurographics Association. Published in the EG digital library.

NOBLE, R. A., ZHANG, K. & McDERMOTT, R. (2004) An Investigation of Multiple Tools Actions for Virtual Sculpting Using Implicit Surfaces. UK Eurographics conference, Theory and Practice of Computer Graphics, Bournemouth University, 8 — 10 June 2004, pp. 24 - 31. ISBN 0-7695-2137-1. Refereed. Proceedings published by the IEEE Computer Society Press.

NOBLE, R. A. & McDERMOTT, R. (2001) Virtual Sculpting using Implicit Surfaces, IASTED Int. Conf. on Visualization, imaging and image processing, 2001, pp. 107 — 112. Sept 3-5, 2001, Marbella, Spain. ISBN 0-88986-309-1, refereed. ACTA press.

References

WITKIN A. P., HECKBERT P. S.: Using particles to sample and control implicit surfaces. Computer Graphics 28, Annual Conference Series (1994), 269—277.

TURK G., O'BRIEN J. F.: Modelling with im-plicit surfaces that interpolate. ACM transactions on Graphics 21, 4 (2002), 866-873.