Differential Topology of Complex Surfaces

1993 ◽  
Author(s):  
John W. Morgan ◽  
Kieran G. O’Grady
Keyword(s):  
Complex Surfaces ◽  
Differential Topology

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

scholarly journals Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

2021 ◽  
Vol 2 (5) ◽  
Author(s):  
Soroosh Tayebi Arasteh ◽  
Adam Kalisz
Keyword(s):  
Computer Graphics ◽  
Geometric Design ◽  
The Other ◽  
Control Points ◽  
Complex Surfaces ◽  
Linear Transformations ◽  
Computer Aided Geometric Design ◽  
Cubic Curves ◽  
Original Curve ◽  
Computer Aided

AbstractSplines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

Automatic generation of venting system on complex surfaces of injection mold

2018 ◽  
Vol 98 (5-8) ◽  
pp. 1379-1389
Author(s):  
Yingming Zhang ◽  
Binkui Hou ◽  
Qian Wang ◽  
Zhigao Huang ◽  
Huamin Zhou
Keyword(s):  
Automatic Generation ◽  
Injection Mold ◽  
Complex Surfaces

Dynamics and Trackability of Stylus Systems

1996 ◽  
Vol 210 (2) ◽  
pp. 159-165 ◽  
Author(s):  
D J Whitehouse ◽  
W L Wang
Keyword(s):  
Measuring Instruments ◽  
Complex Surfaces ◽  
Optimum Parameters ◽  
Periodic Surfaces

Surface measuring instruments have been used for fifty years and their applications have been widespread. However, new demands are being made such as increased speed of measurement and also the capability of measuring more complex surfaces. This paper examines ways in which the design of the pick-up element can be optimized. It also deals in detail with the optimum parameters needed to measure a wide variety of random as well as periodic surfaces.

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