TY - JOUR
AU - Blinn, James F.
AB -  A HOMOGENEOUS FORMULATION FOR LINES IN 3 SPACE James F. Blinn University of Utah ABSTRACT Homogeneous coordinates have long been a standard tool of computer graphics. They afford a convenient representation for various geometric quantities in two and three dimensions. The representation of lines in three dimensions has, however, never been fully described. This paper presents a homogeneous formulation for lines in 3 dimensions as an anti-symmetric 4x4 matrix which transforms as a tensor. This tensor actually exists in both covariant and contravariant forms, both of which are useful in different situations. The derivation of these forms and their use in solving various geometrical problems is described. Key Words and Phrases: geometric calculations, homogeneous coordinate's, computer graphics CR Categories: 3.15, 5.14, 8.2 The dot product of a point (row) vector and plane (column) vector is proportional to the a distance from the point to the plane. A special case of this is the fact that, if the dot product is zero, the point lies in the plane. If the dot product is non-zero, we can find the actual distance by the following means. Construct a three dimensional vector of unit length per(A B C) = (a b c)/ 
TI - A homogeneous formulation for lines in 3 space
DO - 10.1145/563858.563900
DA - 1977-07-20
UR - https://www.deepdyve.com/lp/association-for-computing-machinery/a-homogeneous-formulation-for-lines-in-3-space-1gzRloDZZ7
DP - DeepDyve
ER -