Modelling with Implicit Surfaces that Interpolate

"Modelling with Implicit Surfaces that Interpolate
Greg Turk and James F. O'Brien
ACM Transactions on Graphics
Vol. 21, No. 4, October 2002
Full Paper (PDF, 1.4 Mbytes).


We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction and shape transformation, but the emphasis of our work is on model creation. These implicit surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is created from these constraints using a variational scattered data interpolation approach, and the iso-surface of this function describes a surface. Like other implicit surface descriptions, these surfaces can be used for CSG and interference detection, may be interactively manipulated, are readily approximated by polygonal tilings, and are easy to ray trace. A key strength for model creation is that interpolating implicit surfaces allow the direct specification of both the location of points on the surface and the surface normals. These are two important manipulation techniques that are difficult to achieve using other implicit surface representations such as sums of spherical or ellipsoidal Gaussian functions ("blobbies"). We show that these properties make this form of implicit surface particularly attractive for interactive sculpting using the particle sampling technique introduced by Witkin and Heckbert. Our formulation also yields a simple method for converting a polygonal model to a smooth implicit model, as well as a new way to form blends between objects.

Click on images below for larger pictures.

Surfaces from constraints based on tetrahedron (left) and branching structure (right).

Polygonal mesh (left) and resulting implicit bunny (right).

Polygonal fist (left) and resulting implicit surface (right).

Particle-based surface (left) and similar surface after normal constraint changed (right).

Blended tori.

Ray traced implicits using sphere tracing.

Boolean implicits, also rendered with ray tracing.

Go to Greg Turk's Home Page.