An introduction to Geometric Algebra that will give a strong grasp of its relationship to linear algebra and its significance for 3D programming of geometry in graphics, vision, and robotics is found.Expand

IEEE Transactions on Pattern Analysis and Machine…

1 April 1984

TLDR

It is proved that every ``straight'' chaincode string can be represented by a set of four unique integer parameters, and a mathematical expression is derived for the set of all continuous line segments which could have generated a given chain code string.Expand

IEEE Transactions on Pattern Analysis and Machine…

1 February 2005

TLDR

This paper performs the first order error analysis of the Procrustes method for the 3D case, fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion.Expand

The estimation of the length of a continuous curve from discrete data is considered and optimal estimators are given for ideal straight chaincode strings and the applicability to nonstraight strings is discussed.Expand

The slope transform is presented, which provides tangential morphology with the analytical power which the Fourier tansform lends to linear signal processing, in particular: dilation becomes addition (just as under a Fourier transform, convolution becomes multiplication).Expand

The algorithm is developed and an application to robot path planning in configuration space, where the graph topology, transition costs, or start/goals may change simultaneously, is discussed.Expand

This chapter gives explicit formulas for the square root and the logarithm of rotors in 3D CGA and classifies the types of conformal transformations and their orbits.Expand

It is possible to set up a correspondence between 3D space and R , interpretable as the space of oriented lines (and screws), such that special projective collineations of the 3D space become… Expand