<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">You can get it also here <a href="https://web.mit.edu/2.998/www/QuaternionReport1.pdf">https://web.mit.edu/2.998/www/QuaternionReport1.pdf</a><div><br><div>
<div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div dir="auto" style="text-align: start; text-indent: 0px; overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">--</div><div style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">Holger Seelig</div><div style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">Leipzig, Germany</div><div style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;"><br></div><div style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0); letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">holger.seelig@yahoo.de</div><div>https://create3000.github.io/x_ite/</div></div></div></div></div></div></div>
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<div><br><blockquote type="cite"><div>Am 25.07.2023 um 17:21 schrieb Joseph D Williams <joedwil@earthlink.net>:</div><br class="Apple-interchange-newline"><div><meta charset="UTF-8"><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Thank You Michalis and Holger,<span class="Apple-converted-space"> </span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Joe</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10.5pt; font-family: "Segoe UI", sans-serif; color: rgb(31, 35, 40); background: rgb(255, 235, 233);">Unable to render code block<o:p></o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10.5pt; font-family: "Segoe UI", sans-serif; color: rgb(31, 35, 40); background: rgb(255, 235, 233);">Is a message I got when looking at the pdf titania article.<o:p></o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10.5pt; font-family: "Segoe UI", sans-serif; color: rgb(31, 35, 40); background: rgb(255, 235, 233);"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><span style="font-size: 10.5pt; font-family: "Segoe UI", sans-serif; color: rgb(31, 35, 40); background: rgb(255, 235, 233);"><o:p> </o:p></span></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="border-width: 1pt medium medium; border-style: solid none none; border-color: rgb(225, 225, 225) currentcolor currentcolor; border-image: none; padding: 3pt 0in 0in;"><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif; border: medium; padding: 0in;"><b>From:<span class="Apple-converted-space"> </span></b><a href="mailto:michalis.kambi@gmail.com" style="color: blue; text-decoration: underline;">Michalis Kamburelis</a><br><b>Sent:<span class="Apple-converted-space"> </span></b>Tuesday, July 25, 2023 3:04 AM<br><b>To:<span class="Apple-converted-space"> </span></b><a href="mailto:joedwil@earthlink.net" style="color: blue; text-decoration: underline;">Joseph D Williams</a><br><b>Cc:<span class="Apple-converted-space"> </span></b><a href="mailto:x3d-public@web3d.org" style="color: blue; text-decoration: underline;">X3D Graphics public mailing list</a><br><b>Subject:<span class="Apple-converted-space"> </span></b>Re: [x3d-public] SLERP or LERP</div></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">"HAnimJoint.rotation" is SFRotation, and the only interpolators in X3D standard</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">to animate SFRotation are</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">1. OrientationInterpolator . This indeed does SLerp.</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <span class="Apple-converted-space"> </span>Supported by pretty much all X3D browsers, used by a lot X3D</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">models to animate any rotations, also for "Transform.rotation".</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">2. SquadOrientationInterpolator. This does SQUAD interpolation.</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"> <span class="Apple-converted-space"> </span>Less often used and implemented, from what I see. I actually</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">never saw a real-life (not testcase) model using</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">SquadOrientationInterpolator, and I don't know who supports it</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">(CGE/view3dscene do not).</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Both of those interpolators can be used to animate any SFRotation,</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">including "HAnimJoint.rotation" or "Transform.rotation".</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Regards,</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">Michalis</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;"><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">wt., 25 lip 2023 o 07:43 Joseph D Williams <joedwil@earthlink.net> napisał(a):</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> 19.4.6 OrientationInterpolator</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> … An OrientationInterpolator interpolates between two orientations by computing the shortest path on the unit sphere between the two orientations. The interpolation is linear in arc length along this path. …</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> So to me that means we are SLERP’n.</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> Joe</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">><o:p> </o:p></div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> _______________________________________________</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> x3d-public mailing list</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> x3d-public@web3d.org</div><div style="margin: 0in; font-size: 11pt; font-family: Calibri, sans-serif;">> http://web3d.org/mailman/listinfo/x3d-public_web3d.org</div></div></div></blockquote></div><br></div></body></html>