Adaptive Slicing of Parametrizable Algebraic Surfaces for Layered Manufacturing

1995 ◽  
Author(s):  
Prashant Kulkarni ◽  
Debasish Dutta
Keyword(s):  
Variable Thickness ◽  
Algebraic Surface ◽  
Layered Manufacturing ◽  
Algebraic Surfaces ◽  
Geometric Accuracy ◽  
Adaptive Slicing ◽  
Staircase Effect

Abstract As the various applications of Layered Manufacturing (LM) expand from just prototyping, the geometric accuracy issues become more prominent. Variable thickness, or adaptive, slicing aides in reducing a major source of geometric inaccuracy, the staircase effect. This paper develops a procedure for the adaptive slicing of a parametrizable algebraic surface to be manufactured by an LM process. An implemented example of the procedure is presented.

A Volumetric Difference-based Adaptive Slicing and Deposition Method for Layered Manufacturing

2003 ◽  
Vol 125 (3) ◽  
pp. 586-594 ◽  
Author(s):  
Y. Yang ◽  
J. Y. H. Fuh ◽  
H. T. Loh ◽  
Y. S. Wong
Keyword(s):  
Local Features ◽  
Layered Manufacturing ◽  
Deposition Method ◽  
Adaptive Slicing ◽  
Surface Normal ◽  
Staircase Effect ◽  
Slicing Method ◽  
Cusp Height ◽  
The Difference ◽  
New Criterion

Adaptive slicing capable of producing variable thickness is a useful means to improve the fabrication efficiency in layered manufacturing (LM) or Rapid Prototyping (RP) processes. Many approaches have been reported in this field; however, most of them are based on the cusp height criteria, which is not an effective representation of the staircase effect when the surface normal is near vertical. Furthermore, most of the existing methods slice the model without considering the local features in the plane of the sliced layer. This paper introduces a novel difference-based adaptive slicing and deposition method. The advantage of this slicing method is that the slicing error is independent of the surface normal. A new criterion for adaptive slicing is evaluated and compared with that based on cusp-height. An adaptive slicing algorithm, which uses the volumetric difference between two adjacent layers as the criterion for slicing, has been developed in this work. Different deposition strategies for the common area and the difference area are applied to layer fabrication while considering the local features of the sliced layer. The algorithm has been tested with a sample part, and the results indicate that a better surface finish can be achieved for both surfaces whose normals are nearly in the slicing plane and surfaces whose normals are nearly perpendicular to the slicing plane. It is found that the building time can be reduced by 40% compared with the traditional adaptive slicing. The proposed method has minimized the volumetric error between the built LM part and the original CAD model while achieving a higher efficiency. It is suitable for most commercialized LM systems due to its simplicity in implementation.

scholarly journals Complete algebraic vector fields on affine surfaces

2020 ◽  
Vol 31 (03) ◽  
pp. 2050018
Author(s):  
Shulim Kaliman ◽  
Frank Kutzschebauch ◽  
Matthias Leuenberger
Keyword(s):  
Algebraic Surface ◽  
Vector Fields ◽  
Algebraic Surfaces ◽  
Algebraic Vector ◽  
Dual Graphs ◽  
Holomorphic Automorphisms

Let [Formula: see text] be the subgroup of the group [Formula: see text] of holomorphic automorphisms of a normal affine algebraic surface [Formula: see text] generated by elements of flows associated with complete algebraic vector fields. Our main result is a classification of all normal affine algebraic surfaces [Formula: see text] quasi-homogeneous under [Formula: see text] in terms of the dual graphs of the boundaries [Formula: see text] of their SNC-completions [Formula: see text].

scholarly journals ALGEBRAIC SURFACES WITH INFINITELY MANY TWISTOR LINES

2019 ◽  
Vol 101 (1) ◽  
pp. 61-70
Author(s):  
A. ALTAVILLA ◽  
E. BALLICO
Keyword(s):  
Algebraic Surface ◽  
Existence Results ◽  
Algebraic Surfaces ◽  
Odd Degree

We prove that a reduced and irreducible algebraic surface in $\mathbb{CP}^{3}$ containing infinitely many twistor lines cannot have odd degree. Then, exploiting the theory of quaternionic slice regularity and the normalisation map of a surface, we give constructive existence results for even degrees.

scholarly journals Towards the weighted Bounded Negativity Conjecture for blow-ups of algebraic surfaces

2019 ◽  
Vol 163 (3-4) ◽  
pp. 361-373
Author(s):  
Roberto Laface ◽  
Piotr Pokora
Keyword(s):  
Line Bundle ◽  
Characteristic Zero ◽  
Algebraic Surface ◽  
Intersection Number ◽  
Algebraic Surfaces ◽  
The Self ◽  
Projective Surface ◽  
Intersection Numbers ◽  
Weighted Version ◽  
Smooth Projective Surface

AbstractIn the present paper we focus on a weighted version of the Bounded Negativity Conjecture, which predicts that for every smooth projective surface in characteristic zero the self-intersection numbers of reduced and irreducible curves are bounded from below by a function depending on the intesection of curve with an arbitrary big and nef line bundle that is positive on the curve. We gather evidence for this conjecture by showing various bounds on the self-intersection number of curves in an algebraic surface. We focus our attention on blow-ups of algebraic surfaces, which have so far been neglected.

On the canonical systems of certain algebraic surfaces

1937 ◽  
Vol 33 (3) ◽  
pp. 311-314
Author(s):  
D. Pedoe
Keyword(s):  
Algebraic Surface ◽  
Base Point ◽  
Canonical System ◽  
Algebraic Surfaces ◽  
Simple Point ◽  
Canonical Systems ◽  
Base Points ◽  
Complete Linear System ◽  
Pass Through ◽  
Simple Points

A complete linear system of curves on an algebraic surface may have assigned base points. The canonical system, from its definition, has no assigned base points at simple points of the surface. But we may construct surfaces on which, all the same, the canonical system has “accidental base points” at simple points of the surface. The classical example, due to Castelnuovo, is a quintic surface with two tacnodes. On this surface the canonical system is cut out by the planes passing through the two tacnodes. These planes also pass through the simple point in which the join of the two tacnodes meets the surface again. This point is the accidental base point of the canonical system on the quintic surface.

A parametric and adaptive slicing (PAS) technique: general method and experimental validation

2019 ◽  
Vol 25 (1) ◽  
pp. 126-142 ◽  
Author(s):  
Francesco Rosa ◽  
Serena Graziosi
Keyword(s):  
Design Methodology ◽  
Three Dimensional ◽  
Smooth Transition ◽  
Constant Thickness ◽  
Parametric Surfaces ◽  
Adaptive Slicing ◽  
Content Type ◽  
Staircase Effect ◽  
Multiple Reference ◽  
General Method

Purpose The purpose of this paper is to describe an innovative Parametric and Adaptive Slicing (PAS) technique to be used for generating material addition paths along three-dimensional surfaces. Design/methodology/approach The method is grounded on the possibility to generate layers starting from multiple reference surfaces (already available in the model or created on purpose). These are used for mathematically deriving a family of parametric surfaces whose shape and spacing (the layer thickness) can be tuned to get the desired aesthetic, technical and functional characteristics. The adhesion among layers is obtained guaranteeing a smooth transition among these surfaces. Findings The examples described in the paper demonstrate that the PAS technique enables the addition of the material along non-planar paths and, hence, the elimination of the staircase effect. In addition, objects printed using this technique show improved mechanical properties with respect to those printed using standard planar layers. Research limitations/implications As the method allows a local control of the material addition/deposition, it can be used to design the mechanical behavior of the objects to be printed. Originality/value The technique proposed in this paper overcomes the limitations of currently available adaptive and curved layer slicing strategies, by introducing the possibility to generate layers with a non-constant thickness whose shape morphs smoothly from one layer to another.

Algebraic Surfaces and the Miyaoka-Yau Inequality

2017 ◽  
Author(s):  
Paula Tretkoff
Keyword(s):  
Differential Geometry ◽  
Algebraic Surface ◽  
Smooth Surface ◽  
General Type ◽  
Kodaira Dimension ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Smooth Complex ◽  
Dimension 2

This chapter discusses complex algebraic surfaces, with particular emphasis on the Miyaoka-Yau inequality and the rough classification of surfaces. Every complex algebraic surface is birationally equivalent to a smooth surface containing no exceptional curves. The latter is known as a minimal surface. Two related birational invariants, the plurigenus and the Kodaira dimension, play an important role in distinguishing between complex surfaces. The chapter first provides an overview of the rough classification of (smooth complex connected compact algebraic) surfaces before presenting two approaches that, in dimension 2, give the Miyaoka-Yau inequality. The first, due to Miyaoka, uses algebraic geometry, whereas the second, due to Aubin and Yau, uses analysis and differential geometry. The chapter also explains why equality in the Miyaoka-Yau inequality characterizes surfaces of general type that are free quotients of the complex 2-ball.

Adaptive Slicing of Heterogeneous Solid Models for Layered Manufacturing

1998 ◽  
Author(s):  
Vinod Kumar ◽  
Prashant Kulkarni ◽  
Debasish Dutta
Keyword(s):  
Process Planning ◽  
Layered Manufacturing ◽  
Functionally Graded ◽  
Adaptive Slicing ◽  
Heterogeneous Objects ◽  
Solid Models ◽  
Fundamental Process ◽  
Planning Task ◽  
Material Information ◽  
Heterogeneous Solid

Abstract A novel feature of Layered Manufacturing, an emerging manufacturing technology, is that it enables fabrication of heterogeneous objects (multi-material and functionally graded interiors). In our earlier work, we developed new modeling schemes (called heterogeneous solid models) for representing these heterogeneous objects by capturing both geometry and material information. One of the crucial steps for fabricating these heterogeneous objects in LM is adaptive slicing, a fundamental process planning task. In this paper, we describe how the heterogeneous solid models can be adaptively sliced to aid in the LM fabrication of heterogeneous objects.

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