TY - JOUR

T1 - Signed Distance Computation using the Angle Weighted Pseudo-normal

AU - Bærentzen, Jakob Andreas

AU - Aanæs, Henrik

PY - 2005

Y1 - 2005

N2 - The normals of closed, smooth surfaces have long been used to
determine whether a point is inside or outside such a surface. It is
tempting also to use this method for polyhedra represented as triangle
meshes. Unfortunately, this is not possible since at the vertices and
edges of a triangle mesh, the surface is not \$C\^1\$ continuous, hence,
the normal is undefined at these loci.
In this paper, we undertake to show that the angle weighted
pseudo-normal (originally proposed by Thürmer and Wüthrich and
independently by Sequin) has the important property that it
allows us to discriminate between points that are inside and
points that are outside a mesh, regardless of whether a mesh vertex,
edge or face is the closest feature.
This inside-outside information is usually represented as the sign in
the signed distance to the mesh. In effect, our result shows that this
sign can be computed as an integral part of the distance
computation. Moreover, it provides an additional argument in favour of
the angle weighted pseudo-normals being the natural extension of the
face normals.
Apart from the theoretical results, we also propose a simple and
efficient algorithm for computing the signed distance to a
closed \$C\^0\$ mesh. Experiments indicate that the sign computation
overhead when running this algorithm is almost negligible.

AB - The normals of closed, smooth surfaces have long been used to
determine whether a point is inside or outside such a surface. It is
tempting also to use this method for polyhedra represented as triangle
meshes. Unfortunately, this is not possible since at the vertices and
edges of a triangle mesh, the surface is not \$C\^1\$ continuous, hence,
the normal is undefined at these loci.
In this paper, we undertake to show that the angle weighted
pseudo-normal (originally proposed by Thürmer and Wüthrich and
independently by Sequin) has the important property that it
allows us to discriminate between points that are inside and
points that are outside a mesh, regardless of whether a mesh vertex,
edge or face is the closest feature.
This inside-outside information is usually represented as the sign in
the signed distance to the mesh. In effect, our result shows that this
sign can be computed as an integral part of the distance
computation. Moreover, it provides an additional argument in favour of
the angle weighted pseudo-normals being the natural extension of the
face normals.
Apart from the theoretical results, we also propose a simple and
efficient algorithm for computing the signed distance to a
closed \$C\^0\$ mesh. Experiments indicate that the sign computation
overhead when running this algorithm is almost negligible.

KW - pseudo-normal

KW - normal

KW - polyhedron

KW - signed distance field

KW - mesh

M3 - Journal article

VL - 11

SP - 243

EP - 253

JO - I E E E Transactions on Visualization and Computer Graphics

JF - I E E E Transactions on Visualization and Computer Graphics

SN - 1077-2626

IS - 3

ER -