https://rigidgeometricalgebra.org/wiki/index.php?action=history&feed=atom&title=Contents 2026-04-08T07:12:09Z Revision history for this page on the wiki MediaWiki 1.40.0 https://rigidgeometricalgebra.org/wiki/index.php?title=Contents&diff=477&oldid=prev 2025-06-28T07:46:45Z

<p><span dir="auto"><span class="autocomment">See Also</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:46, 28 June 2025</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l127">Line 127:</td> <td colspan="2" class="diff-lineno">Line 127:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.amazon.com/dp/B0CXY8C72T/?tag=terathon-20 ''PGA Illuminated'' on Amazon.com]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* [https://www.amazon.com/dp/B0CXY8C72T/?tag=terathon-20 ''PGA Illuminated'' on Amazon.com]</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* [[Exercises]]</ins></div></td></tr> </table>

Eric Lengyel https://rigidgeometricalgebra.org/wiki/index.php?title=Contents&diff=471&oldid=prev 2025-06-28T07:21:28Z

<p>Created page with &quot;This is the table of contents for &#039;&#039;Projective Geometric Algebra Illuminated&#039;&#039;. * Preface * 1 Conventional Mathematics ** 1.1 The Cross Product ** 1.2 Homogeneous Coordinates ** 1.3 Lines and Planes *** 1.3.1 Parametric Forms *** 1.3.2 Implicit Forms *** 1.3.3 Distance Between a Point and a Line *** 1.3.4 Intersection of a Line and a Plane *** 1.3.5 Intersection of Multiple Planes *** 1.3.6 Reflection Across a Plane *** 1.3.7 Homogeneous Formulas *** 1.3.8 P...&quot;</p> <p><b>New page</b></p><div>This is the table of contents for ''Projective Geometric Algebra Illuminated''.<br /> <br /> * Preface<br /> * 1 Conventional Mathematics<br /> ** 1.1 The Cross Product<br /> ** 1.2 Homogeneous Coordinates<br /> ** 1.3 Lines and Planes<br /> *** 1.3.1 Parametric Forms<br /> *** 1.3.2 Implicit Forms<br /> *** 1.3.3 Distance Between a Point and a Line<br /> *** 1.3.4 Intersection of a Line and a Plane<br /> *** 1.3.5 Intersection of Multiple Planes<br /> *** 1.3.6 Reflection Across a Plane<br /> *** 1.3.7 Homogeneous Formulas<br /> *** 1.3.8 Plane Transformation<br /> *** 1.3.9 Line Transformation<br /> ** 1.4 Quaternions<br /> *** 1.4.1 Quaternion Fundamentals<br /> *** 1.4.2 Rotations With Quaternions<br /> *** 1.4.3 Interpolating Quaternions<br /> *** 1.4.4 Dual Quaternions<br /> **Historical Remarks<br /> * 2 Flat Projective Geometry<br /> ** 2.1 Algebraic Structure<br /> *** 2.1.1 The Wedge Product<br /> *** 2.1.2 Bivectors<br /> *** 2.1.3 Trivectors<br /> *** 2.1.4 Basis Elements<br /> ** 2.2 Complements<br /> ** 2.3 Antiproducts<br /> ** 2.4 3D Flat Geometry<br /> *** 2.4.1 Points<br /> *** 2.4.2 Lines<br /> *** 2.4.3 Planes<br /> ** 2.5 Join and Meet<br /> ** 2.6 Duality<br /> ** 2.7 Exomorphisms<br /> ** 2.8 Metric Transformations<br /> *** 2.8.1 The Metric<br /> *** 2.8.2 The Antimetric<br /> *** 2.8.3 Bulk and Weight<br /> *** 2.8.4 Attitude<br /> ** 2.9 Inner Products<br /> ** 2.10 Norms<br /> *** 2.10.1 Bulk and Weight Norms<br /> *** 2.10.2 Unitization<br /> *** 2.10.3 The Geometric Norm<br /> ** 2.11 Euclidean Distances<br /> ** 2.12 Duals<br /> ** 2.13 Interior Products<br /> *** 2.13.1 Contractions<br /> *** 2.13.2 Projection and Rejection<br /> *** 2.13.3 Euclidean Angles<br /> *** 2.13.4 Parametric Forms<br /> *** 2.13.5 Expansions<br /> *** 2.13.6 Geometric Projection<br /> ** 2.14 2D Flat Geometry<br /> ** 2.15 Dependencies<br /> ** Historical Remarks<br /> * 3 Rigid Transformations<br /> ** 3.1 The Geometric Product<br /> ** 3.2 Dual Numbers<br /> ** 3.3 Reflection and Rotation<br /> ** 3.4 Reversion<br /> *** 3.4.1 Reverse and Antireverse<br /> *** 3.4.2 Dual Identities<br /> *** 3.4.3 Geometric Constraint<br /> ** 3.5 Euclidean Isometries<br /> *** 3.5.1 Reflection<br /> *** 3.5.2 Rotation<br /> *** 3.5.3 Translation<br /> *** 3.5.4 Inversion<br /> *** 3.5.5 Transflection<br /> ** 3.6 Motors<br /> *** 3.6.1 Motion Operator<br /> *** 3.6.2 Parameterization<br /> *** 3.6.3 Line to Line Motion<br /> *** 3.6.4 Matrix Conversion<br /> *** 3.6.5 Implementation<br /> ** 3.7 Flectors<br /> *** 3.7.1 Reflection Operator<br /> *** 3.7.2 Matrix Conversion<br /> *** 3.7.3 Implementation<br /> ** 3.8 2D Rigid Transformations<br /> ** 3.9 Operator Duality<br /> *** 3.9.1 Complement Isometries<br /> *** 3.9.2 Transformation Groups<br /> *** 3.9.3 Quaternions Revisited<br /> ** Historical Remarks<br /> * 4 Round Projective Geometry<br /> ** 4.1 Construction<br /> ** 4.2 3D Round Geometry<br /> *** 4.2.1 Representations<br /> *** 4.2.2 Duals<br /> *** 4.2.3 Carriers<br /> *** 4.2.4 Centers<br /> *** 4.2.5 Containers<br /> *** 4.2.6 Partners<br /> *** 4.2.7 Attitude<br /> ** 4.3 Norms<br /> ** 4.4 Alignment<br /> ** 4.5 Dot Products<br /> *** 4.5.1 Round Points<br /> *** 4.5.2 Spheres<br /> *** 4.5.3 Partners<br /> *** 4.5.4 Conjugates<br /> ** 4.6 Containment<br /> ** 4.7 Join and Meet<br /> ** 4.8 Expansions<br /> ** 4.9 2D Round Geometry<br /> ** 4.10 Degrees of Freedom<br /> * 5 Conformal Transformations<br /> ** 5.1 Generalized Operators<br /> *** 5.1.1 Rigid Transformations<br /> *** 5.1.2 Sphere Inversion<br /> *** 5.1.3 Circle Rotation<br /> ** 5.2 Dilation<br /> ** 5.3 Duals and Complements<br /> ** 5.4 2D Conformal Transformations<br /> * A Multiplication Tables<br /> * B Geometric Properties<br /> * C Notation Reference<br /> * Bibliography<br /> * Index<br /> <br /> == See Also ==<br /> <br /> * [https://www.amazon.com/dp/B0CXY8C72T/?tag=terathon-20 ''PGA Illuminated'' on Amazon.com]</div>

Eric Lengyel