bilinear-inverse-mapper

A powerful C library for finding the parametric co-ordinates of bilinear mapping for any given point with respect to a quadrilateral. These parametric co-ordinates are also utilised in calculating the interpolation functions or shape functions at the given point.

https://github.com/sahu-indrajeet/bilinear-inverse-mapper

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Repository

A powerful C library for finding the parametric co-ordinates of bilinear mapping for any given point with respect to a quadrilateral. These parametric co-ordinates are also utilised in calculating the interpolation functions or shape functions at the given point.

Basic Info

Host: GitHub
Owner: sahu-indrajeet
License: mit
Language: C
Default Branch: main
Homepage:
Size: 98.6 KB

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Stars: 2
Watchers: 1
Forks: 0
Open Issues: 0
Releases: 0

Created over 2 years ago · Last pushed about 1 year ago

Metadata Files

Readme License Citation

README.md

[Paper]

Inverse Mapping Algorithm for Bilinear Interpolation of Quadrilaterals

A powerful C library for finding the parametric co-ordinates of bilinear mapping for any given point with respect to a quadrilateral. These parametric co-ordinates are also utilised in calculating the interpolation functions or shape functions at the given point. The library also helps in evaluating the Barycentric co-ordinates of a point in case of a triangle.

Overview

Given a point and a quadrilateral in the physical space, the function $\phi^{-1}(x)$ defines the inverse mapping to a corresponding point in the parametric space. The algorithm calculates the parametric co-ordinates $(\xi1,\xi2)$ corresponding to the given point $(x,y)$ in the physical space through this inverse mapping.

Mapping between parametric co-ordinates and spatial coordinates

Features

Compute parametric coordinates for any given point with respect to a bilinear quadrilateral.
Calculate interpolation functions (shape functions) at a given point.
Evaluate Barycentric coordinates for points within triangles.
Analytical solution that avoids convergence issues commonly encountered in iterative schemes.
Approximately 2.4 times faster than Newton’s iterative method for quadrilaterals with non-parallel opposite sides.

Installation

To install the library, simply clone this repository and include the header files in your project. Make sure to link the library during compilation.

git clone https://github.com/sahu-indrajeet/Bilinear-Inverse-Mapper

Refer to examples in this repository for a quick guide on this library's utility.

Citation

If you find this library useful, please cite:

Sahu, I. (2025). Bilinear-inverse-mapper: Analytical solution and algorithm for inverse mapping of bilinear interpolation of quadrilaterals. Advances in Engineering Software, 208, 103975.

Or use this BibTeX entry:

```bibtex @article{sahu2025bilinear, title={Bilinear-inverse-mapper: Analytical solution and algorithm for inverse mapping of bilinear interpolation of quadrilaterals}, author={Sahu, Indrajeet}, journal={Advances in Engineering Software}, volume={208}, pages={103975}, year={2025} }

Owner

Name: Indrajeet Sahu
Login: sahu-indrajeet
Kind: user
Location: Oxford
Company: University of Oxford

Repositories: 1
Profile: https://github.com/sahu-indrajeet

DPhil(PhD) at University of Oxford

Citation (citation.cff)

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
- family-names: "Sahu"
  given-names: "Indrajeet"
  orcid: "https://orcid.org/0000-0002-8822-8397"
title: "InBilMap"
version: 1.0
doi: 
date-released: 2023-03
url: "https://github.com/sahu-indrajeet/InBilMap"

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