Barycentric Coordinates Calculator
Triangle Vertices
Point P Inside Triangle
Barycentric Coordinates Result
Weight α (at A)
0.00
Weight β (at B)
0.00
Weight γ (at C)
0.00
About the Barycentric Coordinates Calculator
The Barycentric Coordinates Calculator is a precise mathematical tool that computes the barycentric coordinates (α, β, γ) of any point P with respect to a triangle ABC. These coordinates represent the relative weights at each vertex such that P = αA + βB + γC and α + β + γ = 1. Based on the exact area-ratio method from classical geometry, this calculator is trusted in computer graphics, finite element analysis, and physics simulations. Proudly hosted on Agri Care Hub, it supports advanced scientific and engineering applications. Learn more at the official Barycentric Coordinates Wikipedia page.
What Are Barycentric Coordinates?
Barycentric coordinates express a point as a weighted average of triangle vertices. They are fundamental in computational geometry and used in 3D modeling, texture mapping, and interpolation.
Mathematical Formula
The coordinates are calculated as:
α = Area(PBC) / Area(ABC)
β = Area(PCA) / Area(ABC)
γ = Area(PAB) / Area(ABC)
Applications
- Computer Graphics: Smooth color/texture interpolation
- Finite Element Method: Shape functions in simulations
- Robotics: Path planning and collision detection
- Physics: Mass point geometry and center of mass