The uses of homogeneous barycentric coordinates in plane euclidean geometry
نویسندگان
چکیده
The notion of homogeneous barycentric coordinates provides a powerful tool of analysing problems in plane geometry. In this paper, we explain the advantages over the traditional use of trilinear coordinates, and illustrate its powerfulness in leading to discoveries of new and interesting collinearity relations of points associated with a triangle.
منابع مشابه
Geometry, Duality and Robust Computation in Engineering
Robustness of computations in engineering is one of key issues as it is necessary to solve technical problems leading to ill conditioned solutions. Therefore the robustness and numerical stability is becoming a key issue more important that the computational time. In this paper we will show selected computational issues in numerical precision, well known cases of failures in computations. The E...
متن کاملBarycentric coordinates computation in homogeneous coordinates
Homogeneous coordinates are often used in computer graphics and computer vision applications especially for the representation of geometric transformations. The homogeneous coordinates enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them properly. Today’s graphics hardware based on GPU offers a very high computational power using pixel ...
متن کاملRay-Triangle and Ray-Quadrilateral Intersections in Homogeneous Coordinates
Recent articles in Ray Tracing News have discussed solutions to the problem of intersecting a ray with a triangle using the triangle’s barycentric coordinates. This article shows yet another way to think about the ray-triangle intersection problem. The idea is to think of the barycentric coordinates of the intersection point, not as the ratio of areas, but rather as the as ratios of the volume ...
متن کاملDuality and Robust Computation
Robustness of computations in engineering is one of key issues as it is necessary to solve technical problems leading to ill conditioned solutions. Therefore the robustness and numerical stability is becoming a key issue more important that the computational time. In this paper we will show selected computational issues in numerical precision, well known cases of failures in computations. The E...
متن کاملFractions, Projective Representation, Duality, Linear Algebra and Geometry
This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations and this paper presents equivalence of the cross–product operation and solution of a system of linear equations Ax = 0 or Ax = b using projective space representation and homogeneous coordinates. It leads to conclusion th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004