473 Quaternion PPTs View free & download

Quaternions - Quaternions. An easy approach to determine the rotation matrix around arbitrary axis ... Quaternion is Complex. Consist of a 3D vector and one scalar ...

Quaternions. An easy approach to determine the rotation matrix around arbitrary axis ... Quaternion is Complex. Consist of a 3D vector and one scalar ...

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Quaternions - Finding the most natural and compact way to present rotation and orientations ... Length Preserving (Isometric) Reflection Preserving. Orthonormal ...

Finding the most natural and compact way to present rotation and orientations ... Length Preserving (Isometric) Reflection Preserving. Orthonormal ...

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Quaternions - This implies that there is possibly extra or redundant information in the axis/angle format ... Those extra 6 DOFs manifest themselves as 3 scales (x, y, and z) ...

This implies that there is possibly extra or redundant information in the axis/angle format ... Those extra 6 DOFs manifest themselves as 3 scales (x, y, and z) ...

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Quaternions - Quaternions can be converted to / from Euler angles and. rotation matrices ... An alternative to the correction term is to re-normalize. the quaternion periodically ...

Quaternions can be converted to / from Euler angles and. rotation matrices ... An alternative to the correction term is to re-normalize. the quaternion periodically ...

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Quaternions - Quaternion Multiplication ... We need this when we want to apply a quaternion rotation to a vector ... vector, V with the quaternion, Q, we take the following ...

Quaternion Multiplication ... We need this when we want to apply a quaternion rotation to a vector ... vector, V with the quaternion, Q, we take the following ...

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Quaternions - Rotations are defined as rotations about the x, y and z axes. ... Useful in animation because it is easy to interpolate rotations ...

Rotations are defined as rotations about the x, y and z axes. ... Useful in animation because it is easy to interpolate rotations ...

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Quaternionen PowerPoint PPT Presentation

Quaternionen - Quaternionen Eugenia Schwamberger Inhalt : Komplexe Zahlen Quaternionen Einheitsquaternionen Rotation mit Quaternionen Beispiel Matrix Conversion Anhang A: K rper ...

Quaternionen Eugenia Schwamberger Inhalt : Komplexe Zahlen Quaternionen Einheitsquaternionen Rotation mit Quaternionen Beispiel Matrix Conversion Anhang A: K rper ...

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Dual Quaternion Synthesis PowerPoint PPT Presentation

Dual Quaternion Synthesis - Title: Dual Quaternion Synthesis Author: Alba Perez Last modified by: J. M. McCarthy Created Date: 9/26/2002 9:45:59 PM Document presentation format

Title: Dual Quaternion Synthesis Author: Alba Perez Last modified by: J. M. McCarthy Created Date: 9/26/2002 9:45:59 PM Document presentation format

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Quaternion - Certain special properties exist for quaternions numbers too. ... Quaternion Julia Fractals use the same type of generating function, f(Z) = Z ...

Certain special properties exist for quaternions numbers too. ... Quaternion Julia Fractals use the same type of generating function, f(Z) = Z ...

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Quaternionic%20Splines%20of%20Camera%20Paths PowerPoint PPT Presentation

Quaternionic%20Splines%20of%20Camera%20Paths - Quaternionic Splines of Paths Robert Shuttleworth Youngstown State University Professor George Francis, Director illiMath2001 Order of Events History of the ...

Quaternionic Splines of Paths Robert Shuttleworth Youngstown State University Professor George Francis, Director illiMath2001 Order of Events History of the ...

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Quaternions Chapter 11 PowerPoint PPT Presentation

Quaternions Chapter 11 - Quaternions (Chapter 11) A quaternion is an extension of the complex plane to a four ... The multiplicative inverse of a quaternion q is denoted q-1. ...

Quaternions (Chapter 11) A quaternion is an extension of the complex plane to a four ... The multiplicative inverse of a quaternion q is denoted q-1. ...

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Dual Quaternion Synthesis - ... and the dimensions of each link such the the chain ... of Spatial RR Robot Manipulators Using the Denavit-Hartenberg Parameters, J. Mechanical Design ...

... and the dimensions of each link such the the chain ... of Spatial RR Robot Manipulators Using the Denavit-Hartenberg Parameters, J. Mechanical Design ...

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Quaternions - Cartesian coordinates (x,y,z) are an easy and natural means of representing a ... of any fixed poles or longitude/latitude, because no matter which direction they ...

Cartesian coordinates (x,y,z) are an easy and natural means of representing a ... of any fixed poles or longitude/latitude, because no matter which direction they ...

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Quaternion and Virtual Trackball PowerPoint PPT Presentation

Quaternion and Virtual Trackball - A quaternion is a 4-tuple of real number, which can be seen as a vector and a scalar ... (x,y,z) - we first convert it to a quaternion p' = ix jy kz 0 = (pv, 0) ...

A quaternion is a 4-tuple of real number, which can be seen as a vector and a scalar ... (x,y,z) - we first convert it to a quaternion p' = ix jy kz 0 = (pv, 0) ...

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A New Family Symmetry: Discrete Quaternion Group PowerPoint PPT Presentation

A New Family Symmetry: Discrete Quaternion Group - Discrete Quaternion Group. Michele Frigerio. University of California, Riverside ... QUATERNION FAMILY SYMMETRY OF QUARKS AND LEPTONS. Phys. ...

Discrete Quaternion Group. Michele Frigerio. University of California, Riverside ... QUATERNION FAMILY SYMMETRY OF QUARKS AND LEPTONS. Phys. ...

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Quaternions and Interpolation of Rotations PowerPoint PPT Presentation

Quaternions and Interpolation of Rotations - ... the quaternion multiplication is ... is a quaternion with zero real part (like v) ... unit quaternion multiplication corresponds to composition of rotations ...

... the quaternion multiplication is ... is a quaternion with zero real part (like v) ... unit quaternion multiplication corresponds to composition of rotations ...

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Quaternions Multivariate Vectors PowerPoint PPT Presentation

Quaternions Multivariate Vectors - ... are easy to see from diagrams. Wave theory: What is the speed ... Bohr is said to have developed his quantum atomic theory in 1913 immediately upon seeing it. ...

... are easy to see from diagrams. Wave theory: What is the speed ... Bohr is said to have developed his quantum atomic theory in 1913 immediately upon seeing it. ...

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Animating Rotations and Using Quaternions PowerPoint PPT Presentation

Animating Rotations and Using Quaternions - Euler Angles ... Euler Angles. . ?1. ?2. Can you do it? Line 1: P1 = (0,1,0) P2 = (1,0,1) ... Alternative to Euler angles for specifying orientation ...

Euler Angles ... Euler Angles. . ?1. ?2. Can you do it? Line 1: P1 = (0,1,0) P2 = (1,0,1) ... Alternative to Euler angles for specifying orientation ...

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Quaternions Multivariate Vectors - And we derive a potential energy relation, not a kinetic one. Kinetic theory of gases ... The potential energy equation applies to an orbit already in existence. ...

And we derive a potential energy relation, not a kinetic one. Kinetic theory of gases ... The potential energy equation applies to an orbit already in existence. ...

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Quaternions Design and Creation of Virtual Environments CISE 6930/4930 Section 6589/3146 PowerPoint PPT Presentation

Quaternions Design and Creation of Virtual Environments CISE 6930/4930 Section 6589/3146 - To create a unit quaternion that represents a rotation of degrees about an ... Remember this is quaternion multiplication not matrix multiplication! ...

To create a unit quaternion that represents a rotation of degrees about an ... Remember this is quaternion multiplication not matrix multiplication! ...

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Quaternions Multivariate Vectors - Fundamental physics only concerned with fermions and their interactions via gauge bosons. ... The fundamental equation for the fermion is the Dirac equation, ...

Fundamental physics only concerned with fermions and their interactions via gauge bosons. ... The fundamental equation for the fermion is the Dirac equation, ...

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3-D Kinematics PowerPoint PPT Presentation

3-D Kinematics - 3-D Kinematics Angle and Axis Problems: solution is not unique r is arbitrary when theta = 0 Unit Quaternion Unit quaternion is defined as Unit Quaternion Inverse ...

3-D Kinematics Angle and Axis Problems: solution is not unique r is arbitrary when theta = 0 Unit Quaternion Unit quaternion is defined as Unit Quaternion Inverse ...

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Computer Animation Algorithms and Techniques PowerPoint PPT Presentation

Computer Animation Algorithms and Techniques - Computer Animation Algorithms and Techniques Interpolating Values Bezier construction using quaternion operators Need quaternion-friendly operations to interpolate ...

Computer Animation Algorithms and Techniques Interpolating Values Bezier construction using quaternion operators Need quaternion-friendly operations to interpolate ...

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Teaching Python with Graphics PowerPoint PPT Presentation

Teaching Python with Graphics - How might we generate interesting graphics while learning to ... quaternion * quaternion. OSCON 2004. 22. Python is Interactive! v0 = Vector3d(1,1,0) ...

How might we generate interesting graphics while learning to ... quaternion * quaternion. OSCON 2004. 22. Python is Interactive! v0 = Vector3d(1,1,0) ...

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GDC 2005 - Creating Quaternion Creating Quaternion Creating Quaternion Multiplication Identity and Inverse Computing Inverse Vector Rotation Vector Rotation (cont ...

Creating Quaternion Creating Quaternion Creating Quaternion Multiplication Identity and Inverse Computing Inverse Vector Rotation Vector Rotation (cont ...

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Attitude Determination PowerPoint PPT Presentation

Attitude Determination - Quaternions. A quaternion consists of four composants. Where i,j ... Quaternions. A quaternion can be thought of as a 4 dimensional. vector with unit length: ...

Quaternions. A quaternion consists of four composants. Where i,j ... Quaternions. A quaternion can be thought of as a 4 dimensional. vector with unit length: ...

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3D Mechanics II PowerPoint PPT Presentation

3D Mechanics II - quaternions), and in comparing the efficiency of the multi-bond graph solution ... The Cardan angles or the quaternion vector respectively are integrated from the ...

quaternions), and in comparing the efficiency of the multi-bond graph solution ... The Cardan angles or the quaternion vector respectively are integrated from the ...

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AUTODOCK An Automated Docking Software for Predicting Optimal ProteinLigand Interaction PowerPoint PPT Presentation

AUTODOCK An Automated Docking Software for Predicting Optimal ProteinLigand Interaction - Quaternion reduction factor = 1. Torsional reduction factor = 1 # rotatable bonds = 12 ... Initial quaternion = Random. Initial dihedrals = Random. Translation ...

Quaternion reduction factor = 1. Torsional reduction factor = 1 # rotatable bonds = 12 ... Initial quaternion = Random. Initial dihedrals = Random. Translation ...

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Rigid Body Dynamics I An Introduction PowerPoint PPT Presentation

Rigid Body Dynamics I An Introduction - Unit quaternions can do it with 4 ... A rotation of ? about a unit axis u can be represented by the unit quaternion: ... Unit Quaternion Usage ...

Unit quaternions can do it with 4 ... A rotation of ? about a unit axis u can be represented by the unit quaternion: ... Unit Quaternion Usage ...

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Dr. Scott Schaefer PowerPoint PPT Presentation

Dr. Scott Schaefer - Quaternions History. Hamilton attempted to extend complex numbers from 2D to 3D... impossible ... The quaternion representing rotation about the unit axis v by is ...

Quaternions History. Hamilton attempted to extend complex numbers from 2D to 3D... impossible ... The quaternion representing rotation about the unit axis v by is ...

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Rigid Body Motion PowerPoint PPT Presentation

Rigid Body Motion - Rigid Body Motion Quaternion Rotation To rotate a vector r by about axis v: take q = (cos( /2), v sin( /2) Let p = (0,r) obtain p' from the quaternion resulting ...

Rigid Body Motion Quaternion Rotation To rotate a vector r by about axis v: take q = (cos( /2), v sin( /2) Let p = (0,r) obtain p' from the quaternion resulting ...

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Autofilter: automatic code generation for mathematical state estimation PowerPoint PPT Presentation

Autofilter: automatic code generation for mathematical state estimation - Inability to respond to unforeseen events. High cost in cycle from ... quaternion. quaternion. quaternion. Estimator Software. Interface software. State machine ...

Inability to respond to unforeseen events. High cost in cycle from ... quaternion. quaternion. quaternion. Estimator Software. Interface software. State machine ...

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3D orientation PowerPoint PPT Presentation

3D orientation - Quaternion. Exponential map. Joints and rotations ... Rotation of P=(0,r) about the unit vector n by an angle ? using the unit quaternion q=(s,v) ...

Quaternion. Exponential map. Joints and rotations ... Rotation of P=(0,r) about the unit vector n by an angle ? using the unit quaternion q=(s,v) ...

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Computer Animation Algorithms and Techniques - Affects of scale are divided out by the inverse appearing in quaternion rotation ... Smooth quaternion interpolation ... Quaternion operators ...

Affects of scale are divided out by the inverse appearing in quaternion rotation ... Smooth quaternion interpolation ... Quaternion operators ...

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681 - Introduction to Computer Graphics PowerPoint PPT Presentation

681 - Introduction to Computer Graphics - ... Review of Quaternion Rotations Rotq(v) = v = q * [0,v] * q-1 Rotq(v ... Interpolation Background De Casteljau construction of Bezier curve ...

... Review of Quaternion Rotations Rotq(v) = v = q * [0,v] * q-1 Rotq(v ... Interpolation Background De Casteljau construction of Bezier curve ...

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Coarse grained to atomistic mapping algorithm A tool for multiscale simulations PowerPoint PPT Presentation

Coarse grained to atomistic mapping algorithm A tool for multiscale simulations - Updated rotation is obtained by quaternion multiplication q0qs. ... efficiency comes from using quaternion arithmetic and from optimizing at ...

Updated rotation is obtained by quaternion multiplication q0qs. ... efficiency comes from using quaternion arithmetic and from optimizing at ...

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The Topological Structure of the Unit Octonions and Games with Quantum Communication PowerPoint PPT Presentation

The Topological Structure of the Unit Octonions and Games with Quantum Communication - The quaternions are spanned by the identity element 1 and ... A unit quaternion has length 1. Set of unit quaternions is S3 C2. Quaternionic multiplication: ...

The quaternions are spanned by the identity element 1 and ... A unit quaternion has length 1. Set of unit quaternions is S3 C2. Quaternionic multiplication: ...

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RealTime Simultaneous Localization and Mapping with a Single Camera Mono SLAM PowerPoint PPT Presentation

RealTime Simultaneous Localization and Mapping with a Single Camera Mono SLAM - Quaternion trivially defined by the angle-axis rotation vector : Previous value : ... Quaternion form for orientation (or rotation) Eular angle ...

Quaternion trivially defined by the angle-axis rotation vector : Previous value : ... Quaternion form for orientation (or rotation) Eular angle ...

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Interactive Cinematography PowerPoint PPT Presentation

Interactive Cinematography - Use quaternion [how? Code] Third-person Camera. Not to occlude the enemy ... Interpolate orientation: quaternion. Problem: camera colliding with level geometry ...

Use quaternion [how? Code] Third-person Camera. Not to occlude the enemy ... Interpolate orientation: quaternion. Problem: camera colliding with level geometry ...

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Preprocessing Techniques for Image Analysis Applications PowerPoint PPT Presentation

Preprocessing Techniques for Image Analysis Applications - Harmonic analysis on locally compact Abelian group. S2 is ... SO(3) is not Abelian. Torus. Quaternion. Circulating Tumor Cells. Automatic CTC Detection ...

Harmonic analysis on locally compact Abelian group. S2 is ... SO(3) is not Abelian. Torus. Quaternion. Circulating Tumor Cells. Automatic CTC Detection ...

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3D Mechanics PowerPoint PPT Presentation

3D Mechanics - Quaternions ... Quaternions are a four-dimensional extension to complex numbers: ... The complement of a quaternion is being defined as: ...

Quaternions ... Quaternions are a four-dimensional extension to complex numbers: ... The complement of a quaternion is being defined as: ...

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EASTERN MEDITERRANEAN UNIVERSITY PowerPoint PPT Presentation

EASTERN MEDITERRANEAN UNIVERSITY - 1.E. Doukhnitch, 'Synthesis for the Discrete Quaternion Transform Algorithms Class', in Proc. ... of a 4-D quaternion processor. HOUSEHOLDER TRANSFORMATION ...

1.E. Doukhnitch, 'Synthesis for the Discrete Quaternion Transform Algorithms Class', in Proc. ... of a 4-D quaternion processor. HOUSEHOLDER TRANSFORMATION ...

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Bootstrapping a Heteroscedastic Regression Model with Application to 3D Rigid Motion Evaluation PowerPoint PPT Presentation

Bootstrapping a Heteroscedastic Regression Model with Application to 3D Rigid Motion Evaluation - In quaternion representation the rigid motion constraint is. True values are related ... Translation estimate quaternion/SVD. Translation estimate HEIV ...

In quaternion representation the rigid motion constraint is. True values are related ... Translation estimate quaternion/SVD. Translation estimate HEIV ...

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The synthesis of motion capture data PowerPoint PPT Presentation

The synthesis of motion capture data - ... simple and dual quaternions efficiency. 3. Agenda. Overview ... bone, skeleton, animation, quaternion classes involved. Delphi import packages, manual included ...

... simple and dual quaternions efficiency. 3. Agenda. Overview ... bone, skeleton, animation, quaternion classes involved. Delphi import packages, manual included ...

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An Improved Kademlia Protocol In a VoIP System PowerPoint PPT Presentation

An Improved Kademlia Protocol In a VoIP System - Quaternion Node ID, IP address, Port, State ... We assume that the quaternion would become untrusty once it stays longer that ...

Quaternion Node ID, IP address, Port, State ... We assume that the quaternion would become untrusty once it stays longer that ...

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Orientation - Matrix to quaternion is not too bad, I just don't have room for it here ... Another possibility is to also compute the world matrices as quaternion multiplications. ...

Matrix to quaternion is not too bad, I just don't have room for it here ... Another possibility is to also compute the world matrices as quaternion multiplications. ...

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Skeletal Animation and Skinning PowerPoint PPT Presentation

Skeletal Animation and Skinning - Quaternion based rotations. Nice interpolation. Animation State ... Quaternion Spline (for joint rotations) Questions? demo's at http://www.msu.edu/~furtwan1 ...

Quaternion based rotations. Nice interpolation. Animation State ... Quaternion Spline (for joint rotations) Questions? demo's at http://www.msu.edu/~furtwan1 ...

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INCIDENCE GEOMETRIES PowerPoint PPT Presentation

INCIDENCE GEOMETRIES - Geometry from Quaternions. Example: Q = { 1,-1, i,-i, j,-j, k,-k} ... Quaternions Examle of Rank 4 Geometry. Levi graph was an octahedron. Notation: ...

Geometry from Quaternions. Example: Q = { 1,-1, i,-i, j,-j, k,-k} ... Quaternions Examle of Rank 4 Geometry. Levi graph was an octahedron. Notation: ...

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Find the Best Trademark Registration Cost PowerPoint PPT Presentation

Find the Best Trademark Registration Cost - Quaternions were introduced by Irish mathematician Sir William Rowan Hamilton in ... then promptly carved this equation into the side of the nearby Brougham Bridge ...

Quaternions were introduced by Irish mathematician Sir William Rowan Hamilton in ... then promptly carved this equation into the side of the nearby Brougham Bridge ...

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6.837 Fall 2001 PowerPoint PPT Presentation

6.837 Fall 2001 - Quaternion Interpolation. Linear interpolation (lerp) of quaternion representation of orientations gives ... two general quaternions are multiplied by a special ...

Quaternion Interpolation. Linear interpolation (lerp) of quaternion representation of orientations gives ... two general quaternions are multiplied by a special ...

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Shading Languages PowerPoint PPT Presentation

Shading Languages - Quaternion. Sparse matrix solvers. Skin bone deformation. Normal map. Displacement map ... Position / vertex normals / vertex colors / texture coordinates ...

Quaternion. Sparse matrix solvers. Skin bone deformation. Normal map. Displacement map ... Position / vertex normals / vertex colors / texture coordinates ...

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Catchwater The Game Interactive Particle-Based Fluid Simulation Modeling Water Flow Through Pipes PowerPoint PPT Presentation

Catchwater The Game Interactive Particle-Based Fluid Simulation Modeling Water Flow Through Pipes - Keep a quaternion per pipe. Maintained as user rotates while placing. Multiply by that quaternion for true direction. Pipe connector data. Tee. 0, 1, 0 (up connector) ...

Keep a quaternion per pipe. Maintained as user rotates while placing. Multiply by that quaternion for true direction. Pipe connector data. Tee. 0, 1, 0 (up connector) ...

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Relativistic quantum chemical methods for large systems PowerPoint PPT Presentation

Relativistic quantum chemical methods for large systems - Quaternion Modified Dirac equation. L. Visscher & T. Saue, J. Chem. Phys. 113 (2000) 3996. ... MO-integrals in quaternion form. L. Visscher, J. Comp. Chem. 23 ...

Quaternion Modified Dirac equation. L. Visscher & T. Saue, J. Chem. Phys. 113 (2000) 3996. ... MO-integrals in quaternion form. L. Visscher, J. Comp. Chem. 23 ...

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COMP790072 Robotics: An Introduction PowerPoint PPT Presentation

COMP790072 Robotics: An Introduction - Rotation as quaternion. Rotation as Euler Angles. Homogeneous TXF: T=H(R,d) UNC Chapel Hill ... is composed of some matrices or quaternions. UNC Chapel Hill ...

Rotation as quaternion. Rotation as Euler Angles. Homogeneous TXF: T=H(R,d) UNC Chapel Hill ... is composed of some matrices or quaternions. UNC Chapel Hill ...

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3D Kinematics - The computed rotation quaternion rotates about a fixed axis at constant speed. References: ... diku.dk/research-groups/image/teaching/Studentprojects/Quaternion ...

The computed rotation quaternion rotates about a fixed axis at constant speed. References: ... diku.dk/research-groups/image/teaching/Studentprojects/Quaternion ...

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Quaternionization of Maximally Entangled Two Player Quantum Games via Quantum Prisoners Dilemma PowerPoint PPT Presentation

Quaternionization of Maximally Entangled Two Player Quantum Games via Quantum Prisoners Dilemma - Let be real numbers that are coefficients of 1, i,j,k in the unit quaternion pq. ... Quaternions are a non-commutative 4 dimensional real normed division algebra. ...

Let be real numbers that are coefficients of 1, i,j,k in the unit quaternion pq. ... Quaternions are a non-commutative 4 dimensional real normed division algebra. ...

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