{"id":6,"date":"2004-05-04T21:35:44","date_gmt":"2004-05-05T02:35:44","guid":{"rendered":"http:\/\/www.essentialmath.com\/blog\/?p=6"},"modified":"2004-12-28T15:30:27","modified_gmt":"2004-12-28T20:30:27","slug":"correction-quaternions","status":"publish","type":"post","link":"https:\/\/www.essentialmath.com\/blog\/?p=6","title":{"rendered":"Correction: Quaternions"},"content":{"rendered":"<p>Ah, our first errata.  How bittersweet. <\/p>\n<p>Eric Mumau sent me this one.  On page 499, equation 10.11 is wrong.  It should read:<\/p>\n<p><img decoding=\"async\" src=\"..\/..\/cgi-bin\/mimetex.cgi?(2w^2-1)\\mathbf{p}+2(\\mathbf{v} \\bullet \\mathbf{p})\\mathbf{v} + 2w(\\mathbf{v} \\times \\mathbf{p})\" alt=\"\"><\/p>\n<p>Correspondingly, the following equation should read:<\/p>\n<p><img decoding=\"async\" src=\"..\/..\/cgi-bin\/mimetex.cgi?R_\\mathbf{q}(\\mathbf{p}) = (2 \\cos^2 (\\theta\/2)-1)\\mathbf{p} + 2(\\hat{\\mathbf{r}}\\sin(\\theta\/2)\\bullet\\mathbf{p})\\hat{\\mathbf{r}}\\sin(\\theta\/2) + 2\\cos(\\theta\/2)(\\hat{\\mathbf{r}}\\sin(\\theta\/2)\\times\\mathbf{p})\" alt=\"\"><\/p>\n<p>The rest of the page follows as before.<\/p>\n<p>This affects the code which starts at the bottom of page 499.  At the top of 500, the first three lines should be rewritten as:<br \/>\n[cpp]<br \/>\nfloat vMult = 2.0f*(x*vector.x + y*vector.y + z*vector.z);<br \/>\nfloat crossMult = 2.0f*w;<br \/>\nfloat pMult = crossMult*w &#8211; 1.0f;<br \/>\n[\/cpp]<br \/>\nNote that the code on the CD is not the same as that given in the text, and in fact will actually work.  However, it is slightly less efficient than what is given here.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ah, our first errata. How bittersweet. Eric Mumau sent me this one. On page 499, equation 10.11 is wrong. It should read: Correspondingly, the following equation should read: The rest of the page follows as before. This affects the code which starts at the bottom of page 499. At the top of 500, the first [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,3],"tags":[],"class_list":["post-6","post","type-post","status-publish","format-standard","hentry","category-erratical","category-mathematical"],"_links":{"self":[{"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/6","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6"}],"version-history":[{"count":0,"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/6\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.essentialmath.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}