We study the arc and curve complex AC(S) of an oriented connected surface S of finite type with punctures. We show that except for some finitely many special surfaces, the simplicial automorphism group of AC(S) coincides with the natural image of the extended mapping class group of S in that group. We also show that for any vertex of AC(S), the combinatorial structure of the link of that vertex...

This contribution addresses a problem of surface reconstruction from the point clouds which is applied in many scientific and engineering applications. Our aim is to obtain a visualization of data from 3D scanning and document the real objects digitally. We describe the digital reconstruction problem and the methods of surface reconstruction. We mention several known algorithms for surface reco...

An inversion equation takes the Cartesian coordinates of a point on a parametric curve or surface and returns the parameter value(s) of that point. A 2-D curve inversion equation has the form t = f(x, y)/g(x, y). This paper shows that practical insight into inversion can be obtained by studying the geometry of the implicit curves f(x, y) = 0 and g(x, y) = 0. For example, the relationship betwee...

The engine inner wall surface temperature was measured by the plug blind-hole extrapolation, and multiple thermocouples were installed at different depths in the substrate. The engine wall extrapolation model of transient high temperature was established according to the basic principles of heat transfer. The transient temperatures were measured by thermocouples buried at different depths of th...

We prove the “End Curve Theorem” which states that a normal surface singularity (X, o) with rational homology sphere link Σ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An “end-curve function” is an analytic function (X, o) → (C, 0) whose zero set intersects Σ in the knot given by a meridian curve of the exceptional curve ...

This paper presents a kinematic model of the human arm in which the workspace of the elbow is modeled as a triangular B ezier spline surface. It is also explained how this model is used for solving forward and inverse kinematics in computer animation systems. In order to solve inverse kinematics problems, it is necessary to nd a curve on the surface modeling the elbow workspace. This curve is o...

Skeletons are widely used in pattern recognition and image analysis. A way to obtain skeletons is the thinning approach, consisting in iteratively removing points from the object without changing the topology. In order to preserve geometric information, it is usual to preserve curve end points (for curve skeletons) or surface end points (for surface skeletons). In this paper we propose a new fa...

An outlier elimination algorithm for curve/surface fitting is proposed. This two-stage hybrid algorithm employs a proximitybased outlier detection algorithm, followed by a model-based one. First, a proximity graph is generated. Depending on the use of a hard/soft threshold of the connectivity of observations, two algorithms are developed, one graph-component-based and the other eigenspace-based...

In this paper, we present a practical algorithm to extract a curve skeleton of a 3D shape. The core of our algorithm comprises coupled processes of graph contraction and surface clustering. Given a 3D shape represented by a triangular mesh, we first construct an initial skeleton graph by directly copying the connectivity and geometry information from the input mesh. Graph contraction and surfac...

1. Page 13-14: Feature Ball Lemma 1.1 and its proof : Replace bd (B ∩ Σ) with (bd B) ∩ Σ.