A Beginners Guide to Dual-Quaternions: What They Are, How They Work, and How to Use Them for 3D Character Hierarchies


Abstract

In this paper, we give a beginners guide to the practicality of using dual-quaternions to represent the rotations and translations in character-based hierarchies. Quaternions have proven themselves in many fields of science and computing as providing an unambiguous, un-cumbersome, computationally efficient method of representing rotational information. We hope after reading this paper the reader will take a similar view on dual-quaternions. We explain how dual number theory can extend quaternions to dual-quaternions and how we can use them to represent rigid transforms (i.e., translations and rotations). Through a set of examples, we demonstrate exactly how dual-quaternions relate rotations and translations and compare them with traditional Euler's angles in combination with Matrix concatenation. We give a clear-cut, step-by-step introduction to dual-quaternions, which is followed by a no-nonsense how-to approach on employing them in code. The reader, I believe, after reading this paper should be able to see how dual-quaternions can offer a straightforward solution of representing rigid transforms (e.g., in complex character hierarchies). We show how dual-quaternions propose a novel alternative to pure Euler-Matrix methods and how a hybrid system in combination with matrices results in a faster more reliable solution. We focus on demonstrating the enormous rewards of using dual-quaternions for rigid transforms and in particular their application in complex 3D character hierarchies.

Citation

Ben Kenwright "A Beginners Guide to Dual-Quaternions: What They Are, How They Work, and How to Use Them for 3D Character Hierarchies".  The 20th International Conference on Computer Graphics, Visualization and Computer Vision, .

Supplemental Material

Preview

Note: This file is about ~5-30 MB in size.

This paper appears in:
Date of Release:
Author(s): Ben Kenwright.
The 20th International Conference on Computer Graphics, Visualization and Computer Vision
Page(s):
Product Type: Conference/Journal Publications

 


Translations Permutations Orientations Optimize Efficiency Manner Tolerate Objects Velocities Condition Control Network Provide Modules Generation 62 Perception Engine Propose System Visual Visuomotor Fullbody Contacts Rering Segments Stards Closely Related 81 University Fields Smooth Obtain Applications Underlying Possible Across Textures Reference Resolutions Illustration Network 50 Optimization Regret Gaussian Bounds Setting Reused Programs Substance Domain Indeed Mridul Setaluri Aanjaneya Sifakis 94 Hawkins Moving Binocular Tracking Brains Offset Regression Particles Traditional Solvers 8 Unlike Remain Solvers Such Inaccessible Currently Scenarios Input Face Projecting Individual Components Sketch Refine Manifolds 8 Summer Herring Has Not Always The Case The 10 Weekbyweekpropaganda Policy Multiparty System Proportional Representation Voting Compulsory From 12 Follows Dynamics Physics Simulation Methods Focusing Locomotion Angles Optimize Animating Scattering Variety Doubles Digital Detail 43 Mimicking Polygonal Provides That Simple Approach Structural Numerically Counterpart Speeds When Surface Accelerates Increase Upward 13 Descriptors Different Papers Propose Graphics Vision Suitable Feature Clouds Structures Effect Deficient Numerical General Faithfully 78 Then Differentiate Themes Scientific Modes Inference Exploratory Data 19 Equations Stepped Easily Lagrangian Function Expansion Positions Relative Selected Prosing Simulation Simulating Method 60 Couple Ability Required Should Complex Iterations Sequence Jacques Stroking Resort Stards Winding Outline Numbers Filling 25 Contact Associated Chosen Penetration Cfully Artifacts Emphasize Locally Implies Proposition Alignment Minimizes Always Numerical Investigate 84 Throughout Use Boundaries Region Point Region Follows Smoothness Locally Oblivious Locally The Oblivious Reconstructs Smoothprior 14 Surface Neighbors Geodesic Consuming Strategy Relying Network Features Images Crosses Perturbations Trajectory Intersection 76 Refinement Create Domain Conceptual Experts Implications Design Algorithm Scales Parallel Nature Points Sparse Bucket Reward 0 Series Network Operators Assigned Through Vectors Integrated Evaluated Numerical Framework Oriented Differential Encode Densities Reasonable 87 Type Storms Historical Event The Observation 29 The The Encouraging The Inferred The Warm Angles Pose The Also Term Inferred The Perframe 13 Achieve Physics Updating Linear Computational Covariance Control Sequen Triangles Normal Geometry Displaced 11 Moreover Displacement Generate Vector Vectors Inverse Kinematics Mulate Problem Reference Consider Conventional Resulting Velocities 5