Output details

Signed Lp-distance fields

In computer art and computer-aided design applications, distance from a given point in space to a geometric object is quite useful, for example, for implementing collision detection between two models or metamorphosis operation, which transforms one shape into another. For many applications, the exact distance field is not needed and even is damaging due to derivative discontinuities (directional jumps), which cause unexpected artefacts. For example, if one uses the exact distance to describe a gradual material distribution within the shape, material will have stress concentrations around the derivative discontinuities. For metamorphosis, unexpected creases appear in the intermediate shapes. Smooth approximations of the distance field have to be employed in these cases.

Originality

In this paper, we have introduced a family of smooth approximations of the distance field based on a generalization of double-layer potentials. The proposed Lp-distance fields deliver accurate approximations of the distance function not only near the boundary of the object but also deep inside the object.

Significance

The proposed Lp-distance fields are useful in applications involving gradually changing material modelling, controlled offsets, shape metamorphosis and others. We illustrate the field properties with artistic shapes and a mechanical part design.

Rigour

An analytical solution was derived for the proposed field in the case of the shape presented as a polygonal mesh. This means that the Lp-distance can be calculated by summing up the contribution of each polygon in the mesh. Our theoretical results are supported by numerical experiments which reveal the high practical potential of our approach.