2D Simulation and Mapping using the Cauchy-Green Complex Barycentric Coordinates

نویسنده

  • Aviv Segall
چکیده

2D Simulation and Mapping using the Cauchy-Green Complex Barycentric Coordinates Conformal maps are especially useful in geometry processing for computing shape preserving deformations, image warping and manipulating harmonic functions. The Cauchy-Green coordinates are complex-valued barycentric coordinates, which can be used to parameterize a space of conformal maps from a planar domain bounded by a simple polygon. In this work, we use the Cauchy-Green coordinates to simulate 2D potential flow with interactive control, and to construct conformal maps between planar domains.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Complex Barycentric Coordinates with Applications to Planar Shape Deformation

j j j k z T z T z = = ∑ where T is a 2D similarity transformation. Proof: Similarity transformations can be represented using a linear polynomial over the complex plane in the following way. If the similarity transformation T consists of rotation by positive angle θ, uniform scale s and a translation t = tx + ity, then according to the rules of complex numbers: ( ) ( ) i T x iy T z se z t z θ +...

متن کامل

Iterative Closest Conformal Maps between Planar Domains

Conformal maps between planar domains are an important tool in geometry processing, used for shape deformation and image warping. The Riemann mapping theorem guarantees that there exists a conformal map between any two simply connected planar domains, yet computing this map efficiently remains challenging. In practice, one of the main algorithmic questions is the correspondence between the boun...

متن کامل

Simulation of Ideal External and Internal Flows with Arbitrary Boundaries Using Schwarz Christoffel Transformation

The flow field, velocity and pressure coefficient distribution of some 2-D ideal flows are presented. Conformal mapping is used to simulate two-dimensional ideal flow for a variety of complex internal and external configurations, based on the numerical integration of Schwarz-Christoffel transformation. The advantages of this method are simplicity and high accuracy. The method presented in this ...

متن کامل

Positive Gordon-Wixom coordinates

We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in 2D. Our method extends weighted Gordon-Wixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boun...

متن کامل

A Complex View of Barycentric Mappings

Barycentric coordinates are very popular for interpolating data values on polyhedral domains. It has been recently shown that expressing them as complex functions has various advantages when interpolating two-dimensional data in the plane, and in particular for holomorphic maps. We extend and generalize these results by investigating the complex representation of real-valued barycentric coordin...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016