This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the…mehr
This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
How to Read this Guide to Geometric Algebra in Practice.- Part I: Rigid Body Motion.- Rigid Body Dynamics and Conformal Geometric Algebra.- Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra.- Inverse Kinematics Solutions Using Conformal Geometric Algebra.- Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences through Reflections.- Part II: Interpolation and Tracking.- Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra using Polar Decomposition.- Attitude and Position Tracking / Kinematics.- Calibration of Target Positions using Conformal Geometric Algebra.- Part III: Image Processing.- Quaternion Atomic Function for Image Processing.- Color Object Recognition Based on a Clifford Fourier Transform.- Part IV: Theorem Proving and Combinatorics.- On Geometric Theorem Proving with Null Geometric Algebra.- On the Use of Conformal Geometric Algebra in Geometric Constraint Solving.- On the Complexity of Cycle Enumeration for Simple Graphs.- Part V: Applications of Line Geometry.- Line Geometry in Terms of the Null Geometric Algebra over R3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms.- A Framework for n-dimensional Visibility Computations.- Part VI: Alternatives to Conformal Geometric Algebra.- On the Homogeneous Model of Euclidean Geometry.- A Homogeneous Model for 3-Dimensional Computer Graphics Based on the Clifford Algebra for R3.- Rigid-Body Transforms using Symbolic Infinitesimals.- Rigid Body Dynamics in a Constant Curvature Space and the '1D-up' Approach to Conformal Geometric Algebra.- Part VII: Towards Coordinate-Free Differential Geometry.- The Shape of Differential Geometry in Geometric Calculus.- On the Modern Notion of a Moving Frame.- Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra.
How to Read this Guide to Geometric Algebra in Practice.- Part I: Rigid Body Motion.- Rigid Body Dynamics and Conformal Geometric Algebra.- Estimating Motors from a Variety of Geometric Data in 3D Conformal Geometric Algebra.- Inverse Kinematics Solutions Using Conformal Geometric Algebra.- Reconstructing Rotations and Rigid Body Motions from Exact Point Correspondences through Reflections.- Part II: Interpolation and Tracking.- Square Root and Logarithm of Rotors in 3D Conformal Geometric Algebra using Polar Decomposition.- Attitude and Position Tracking / Kinematics.- Calibration of Target Positions using Conformal Geometric Algebra.- Part III: Image Processing.- Quaternion Atomic Function for Image Processing.- Color Object Recognition Based on a Clifford Fourier Transform.- Part IV: Theorem Proving and Combinatorics.- On Geometric Theorem Proving with Null Geometric Algebra.- On the Use of Conformal Geometric Algebra in Geometric Constraint Solving.- On the Complexity of Cycle Enumeration for Simple Graphs.- Part V: Applications of Line Geometry.- Line Geometry in Terms of the Null Geometric Algebra over R3,3, and Application to the Inverse Singularity Analysis of Generalized Stewart Platforms.- A Framework for n-dimensional Visibility Computations.- Part VI: Alternatives to Conformal Geometric Algebra.- On the Homogeneous Model of Euclidean Geometry.- A Homogeneous Model for 3-Dimensional Computer Graphics Based on the Clifford Algebra for R3.- Rigid-Body Transforms using Symbolic Infinitesimals.- Rigid Body Dynamics in a Constant Curvature Space and the '1D-up' Approach to Conformal Geometric Algebra.- Part VII: Towards Coordinate-Free Differential Geometry.- The Shape of Differential Geometry in Geometric Calculus.- On the Modern Notion of a Moving Frame.- Tutorial: Structure Preserving Representation of Euclidean Motions through Conformal Geometric Algebra.
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