Geometric algebra is a universal mathematical language which provides very comprehensive techniques for analyzing the complex geometric situations occurring in robotics and computer vision. The application of the 4D motor algebra for the linearization of the the hand-eye calibration problem is presented. Geometric algebra and its associated linear algebra framework is a very elegant language to...

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanic...

This work presents a novel method for haptic rendering contact force and surface properties for virtual objects using the Conformal Geometric Algebra orthogonal decomposition approach. The mathematical representation of geometric primitives along with collision algorithms based on its mathematical properties is presented. The orthogonal decomposition of contact and interaction forces is achieve...

in this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. the stages for prey have been considered. the proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. the model is analyzed by using linear stability analysis to ob...

When geometric similarity, or isometry, prevails among animals of different sizes their form and proportions are similar. Weight increases as the cube of the length dimension, while cross-sectional areas increase as its square, so in load-bearing structural elements the stress, caused by the body weight, increases in direct proportion to the length dimension, both for pure axial loads and for t...

The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technolog...

This paper addresses the problem of path planning for a thin elastic metal plate under fairly general manipulation constraints. The underlying geometric model for the plate is provided by a B ezier representation. The geometric model is augmented by a realistic mechanical model. We assume that the plate is manipulated in accordance with a set of user-deened grasping constraints that specify the...

We present some notes on the definition of mathematical design as well as on the methods of mathematical modeling which are used in the process of the artistic design of the environment and its components. For the first time in the field of geometric modeling, we perform an aesthetic analysis of planar Bernstein-Bézier curves from the standpoint of the laws of technical aesthetics. The shape fe...