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--></style></head><body lang=EN-US link=blue vlink="#954F72" style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal>Two ways to code this:</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal> <BooleanSequencer DEF='Background3Sequencer' </p><p class=MsoNormal>key='0 0.09 0.11 0.22 0.43 0.55 0.63 0.73 0.85 0.86 1' </p><p class=MsoNormal>keyValue='true true true false false false false false false false true'/></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal> <BooleanSequencer DEF='Background1Sequencer' </p><p class=MsoNormal>key='0 0.22 1' </p><p class=MsoNormal>keyValue='true false true'/></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Both would produce the same number of value_changed events. </p><p class=MsoNormal><o:p> </o:p></p><ul style='margin-top:0in' type=disc><li class=MsoListParagraph style='margin-left:0in;mso-list:l0 level1 lfo1'>There is only an event out with a new timestamp if the<o:p></o:p></li><li class=MsoListParagraph style='margin-left:0in;mso-list:l0 level1 lfo1'>new value has changed compared to the last value.</li></ul><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I don’t think I need a new out event at each keytime. Only if the value_changed is actually changed. I might code the first version thinking that I would get an event at each keytime, regardless. I try to think of some situation where I definitely want an event at each keytime, regardless if out has changed or not. If I need that, I shouldn’t need to depend on this or any interpolator node </p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thanks and Best, </p><p class=MsoNormal>Joe</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='mso-element:para-border-div;border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal style='border:none;padding:0in'><b>From: </b><a href="mailto:andreasplesch@gmail.com">Andreas Plesch</a><br><b>Sent: </b>Monday, July 17, 2023 7:32 PM<br><b>To: </b><a href="mailto:joedwil@earthlink.net">Joseph D Williams</a><br><b>Cc: </b><a href="mailto:michalis.kambi@gmail.com">Michalis Kamburelis</a>; <a href="mailto:x3d-public@web3d.org">X3D Graphics public mailing list</a><br><b>Subject: </b>Re: STEP interpolation, was Blender > Exporting rig transforms to HAnim?</p></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The way STEP works currently is the same as regular LINEAR</p><p class=MsoNormal>interpolation. There is only an event out with a new timestamp if the</p><p class=MsoNormal>new value has changed compared to the last value. So with STEP there</p><p class=MsoNormal>are only a few events per cycle. Would that work for you?</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>In the case of two subsequent, identical keyValues, there is no event</p><p class=MsoNormal>when the second interval is entered. So an alternative may be to emit</p><p class=MsoNormal>an event in this case even if the value did not change. It may be</p><p class=MsoNormal>helpful in some cases and should not affect too much existing</p><p class=MsoNormal>behaviours.</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Andreas</p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>On Mon, Jul 17, 2023 at 9:59 PM Joseph D Williams <joedwil@earthlink.net> wrote:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> I like this and interesting how this works relative to another type of step node, the BooleanSequencer. For any initial state, I expect that the keyvalue will be set at the keytime, remain in that readable state until the next keytime, when the next keyvalue will out.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> As expected, the keyvalue has the same time stamp as the keytime event in.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <X3D profile='Immersive' version='3.3' xmlns:xsd='http://www.w3.org/2001/XMLSchema-instance' xsd:noNamespaceSchemaLocation='http://www.web3d.org/specifications/x3d-3.3.xsd'></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <head></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <meta content='background4.x3d' name='title'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> </head></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <Scene></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <WorldInfo title='background5.x3d'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <Viewpoint DEF='EntryView1' description='Hello character' position='0 2 10'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <Background DEF='Background1' skyColor='0 0 0'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <Background DEF='Background2'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> groundAngle='1.57' groundColor='0.3 0.6 0 0.7 1 0.5'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> skyColor='0 0.71 0.88'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <Background DEF='Background3'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> groundAngle='1.57' groundColor='0.9 0.39 0.6 0.2 1 0.5'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> skyColor='0.82 0.82 0.82'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <Background DEF='Background4' skyColor='0.6 0.6 0.6'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <!-- Animation controls --></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <TimeSensor DEF='Clock10Seconds' cycleInterval='10' loop='true'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <BooleanSequencer DEF='Background1Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key='0 0.11 1'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> keyValue='true false true'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <BooleanSequencer DEF='Background2Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key='0 0.11 0.55 1'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> keyValue='false true false false'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <BooleanSequencer DEF='Background3Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key='0 0.55 0.85 1'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> keyValue='false true false false'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <BooleanSequencer DEF='Background4Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key='0 0.85 1'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> keyValue='false true false'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='value_changed' fromNode='Background1Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_bind' toNode='Background1'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='value_changed' fromNode='Background2Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_bind' toNode='Background2'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='value_changed' fromNode='Background3Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_bind' toNode='Background3'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='value_changed' fromNode='Background4Sequencer'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_bind' toNode='Background4'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='fraction_changed' fromNode='Clock10Seconds'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_fraction' toNode='Background1Sequencer'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='fraction_changed' fromNode='Clock10Seconds'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_fraction' toNode='Background2Sequencer'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='fraction_changed' fromNode='Clock10Seconds'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_fraction' toNode='Background3Sequencer'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <ROUTE fromField='fraction_changed' fromNode='Clock10Seconds'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> toField='set_fraction' toNode='Background4Sequencer'/></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> </Scene></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> </X3D></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Thanks and Preserve the Cascade.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Joe</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> From: Andreas Plesch</p><p class=MsoNormal>> Sent: Monday, July 17, 2023 8:59 AM</p><p class=MsoNormal>> To: Michalis Kamburelis</p><p class=MsoNormal>> Cc: X3D Graphics public mailing list; Joseph D Williams</p><p class=MsoNormal>> Subject: Re: STEP interpolation, was Blender > Exporting rig transforms to HAnim?</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Hi Michalis,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> On Mon, Jul 17, 2023 at 9:23 AM Michalis Kamburelis</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> <michalis.kambi@gmail.com> wrote:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > For STEP, I am using the lower value of the interval:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ...</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > This corresponds to typical x3d interval use, and you may have done the same ?.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > Yes, that is indeed what Castle Game Engine / view3dscene is doing too.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > If input is between key[n] and key[n+1], then the output of STEP is keyValue[n].</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Super. There are also the edge cases:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key[exactly at n] => keyValue[n]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key[< nMin] => keyValue[nMin]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> key[> nMax] => keyValue[nMax]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Just to confirm.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > I started converting your testcase (</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > https://github.com/andreasplesch/x3dom/blob/step_interpolator/test/regression-suite/test/cases/interpolators/interpolators.html</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ) into standalone X3D file. I noticed a few things special to X3DOM I</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > think (aside from lowercase node / field names, which I understand is</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > just necessary for HTML5 integration):</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > - "alphaMode" and "alphaCutoff" specified at "PhysicalMaterial", while</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > in X3D 4 they are on "Appearance"</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Yes, for historical reasons, because they only apply to PhysicalMaterial.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Appearance has alphaClipThreshold for regular Material in x3dom. There</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> was some reason why it was not not reused for PhysicalMaterial perhaps</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> due to shader uniforms or subtle usage differences.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > - "PhysicalMaterial.unlit" boolean, while in X3D 4 we have separate</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > node "UnlitMaterial" instead</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > - baseColorFactor -> it is baseColor in X3D 4</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > - metallicfactor, roughnessfactor -> just metallic, roughness in X3D 4</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Will be easy to rename.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > - diffusefactor, specularfactor, glossinessfactor on PhysicalMaterial</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > -> in X3D 4 we follow te glTF standard "metallic-roughness" workflow,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > so there's no no specular / glossinness.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> There used to be specular/glossiness for glTF1. We would probably just</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> keep it as there is also an extension.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > In the end, it was a bit easier to take glTF from</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > https://github.com/KhronosGroup/glTF-Sample-Models/tree/master/2.0/InterpolationTest/glTF</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > and open it in view3dscene, or convert to X3D from view3dscene. But I</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > know this is not objective test, sure it was easier this way for me to</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > just open in CGE/view3dscene :)</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Of course.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> x3dom has a different DEF naming convention prefixing with 'glTF_' and</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> using the node.name when available but I do not think it is necessary</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> to align.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> I noticed the $ character in the DEF names but see</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> https://www.web3d.org/x3d/content/examples/X3dSceneAuthoringHints.html#NamingConventions:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> 'Most restrictive and most interoperable guidance regarding choice of</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> characters in names: can start with letter or underscore character,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> but not a number or a colon. Can then include letters, numbers,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> hyphen, underscore, or period characters. This interoperability is</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> important so that files can be converted equivalently between</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> encodings without validation problems.'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Shapes do not get named</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > Quickly scanning view3dscene output, the one CGE/view3dscene-specific</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > thing there is "ImageTexture.flipVertically" (we plan to add</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > alternative to it, using texture transform for max conformance), the</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > rest looks standard X3D 4.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> x3dom has boolean flipY which I believe corresponds to an OpenGl flag.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> I also noticed the boolean OrientationInterpolator.keyValueQuaternions</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> . x3dom converts all rotations from axis-angle to Quaternions during</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> parsing, so this would save a little bit time there but not during the</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> animation. I would assume Euler angles would be a more common format</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> to accept from modeling software but that might be one step too far.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Thank you for the nice list which will make it more manageable to work through.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> I found another animation example here:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> https://github.com/mrdoob/three.js/pull/12907</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> and uploaded it here:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> https://github.com/andreasplesch/Library/blob/gh-pages/Examples/gltf2/interpolation/InterpolationComparison.gltf</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Regards, Andreas</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > Regards,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > Michalis</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > pon., 17 lip 2023 o 07:16 Andreas Plesch <andreasplesch@gmail.com> napisał(a):</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > Hi Michalis,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > I am putting finishing touches on STEP and CUBICSPLINE interpolation modes.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > For STEP, I am using the lower value of the interval:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > key='0 1 2'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > keyValue='10 11 12'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > value at key= 0.6 : 10</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > value at key= -0.1 : 10</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > value at key= 2 : 12</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > value at key= 2.1 : 12</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > This corresponds to typical x3d interval use, and you may have done the same ?.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > I also added CUBICSPLINE to all interpolators except for</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ColorInterpolator (could be added but seems strange). Doing that I</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > found that for CoordinateInterpolator and NormalInterpolator the</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > layout of keyValues with in and out tangents was most natural this</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > way:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > keyValue='FrameData1, FrameData2..FrameDataN'</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > where FrameData is the data for a key frame and looks like:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > [inTangent1, inTangent2 .. inTangentM],</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > [value1, value2 .. valueM],</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > [outTangent1, outTangent2 .. outTangentM]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > where all entries are Vec3f.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > The total number of scalar values in keyValue is thus N * 3 * M * 3.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > I could not test CUBICSPLINE for Coordinate or NormalInterpolator yet</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > since I do not have a test example. Does any scene come to mind ?</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > Perhaps I can augment the Dolphin example with some arbitrary tangents</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > for testing.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > I also converted the glTF Interpolation Test example to X3D:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > https://github.com/andreasplesch/x3dom/blob/step_interpolator/test/regression-suite/test/cases/interpolators/interpolators.html</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > It may be useful for testing Position and OrientationInterpolator without glTF.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > Andreas</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > On Tue, Jun 27, 2023 at 10:34 AM Andreas Plesch <andreasplesch@gmail.com> wrote:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Hi Michalis,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Ok, let me work on adding a STEP interpolation mode to interpolators.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Do you want to raise a spec. improvement suggestion ?</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > As a side note, STEP mode is also related to x3d sequencers. A</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ScalarInterpolator in STEP mode would be equivalent to a hypothetical</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ScalarSequencer, except for the next and previous fields. Hm, perhaps</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > it makes sense to add next and previous fields to interpolators which</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > would step through intervals.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > The CUBICSPLINE algorithm for glTF is fairly well documented as far as</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > I remember. Feel free of course to look up the implementation in</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > x3dom.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > It is worth noting that the existing SplineInterpolator nodes only</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > allow for one (central) tangent per key and key value, whereas the</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > common cubic spline algorithm allows for two tangents (in, and out)</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > per key and key value. Those mathematically inclined may be able to</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > show that the x3d algorithm for spline interpolations is equivalent to</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > the cubic spline algorithm with identical in and out tangents.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > x3dom just mirrors glTF in that inTangent, value, outTangent occur in</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > triplets in the MF keyValue field. An alternative interface would</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > introduce keyInTangent and keyOutTangent fields which then would</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > require sensible default values. Not sure.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Some thoughts, Andreas</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > PS:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > A StringSequencer would be useful as a mechanism to store and select</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > alternative string values for display in Text nodes. I think the</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > current strategy is to use an IntegerSequencer to select from Shapes</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > in a Switch. A MFStringSequencer would be more concise and convenient.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Hm, similarly there could be a StringTrigger event utility.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > On Tue, Jun 27, 2023 at 8:18 AM Michalis Kamburelis</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > <michalis.kambi@gmail.com> wrote:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Indeed glTF has additional interpolation options, and I think it would</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > make sense to add them to X3D.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Looks like X3DOM and view3dscene/Castle Game Engine go in this</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > direction already :)</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > 1. X3DOM has SFString "interpolation" field, default "LINEAR", see</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > https://doc.x3dom.org/author/Interpolation/X3DInterpolatorNode.html .</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Andreas above explained how it supports "CUBICSPLINE" option.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > 2. view3dscene / Castle Game Engine allow to use "STEP" interpolation</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > explicitly.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > For this, we add such field:</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > SFString [in,out] interpolation "LINEAR" # range: ["LINEAR"|"STEP"]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > .. to all X3DInterpolatorNode descendants (so, all interpolator</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > nodes). This seems exactly like X3DOM, we just added "STEP", where</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > X3DOM added "CUBICSPLINE". In the end we should probably have all</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ["LINEAR"|"STEP"|"CUBICSPLINE"].</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > 3. Note that even without this field, with default linear</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > interpolation, it was possible to have effectively step interpolation,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > as Andreas mentions. You can just duplicate keys in the middle, like</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > key [0 0.33 0.33 0.66 0.66]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > keyValue [10 10 20 20 30 30]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > # interpolation "LINEAR"</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > This is valid with X3D ("""keys shall be monotonically</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > non-decreasing""" according to spec).</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > It is equivalent to</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > key [0 0.33 0.66]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > keyValue [10 20 30]</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > interpolation "STEP"</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Using explicit "STEP" is slightly better, as you need 50% less</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > memory to store it, less computation (no need to do lerp or detect</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > this special case to optimize), and seems just simpler for authors --</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > it specifies intention explicitly, which makes sense, also if one</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > hopes a round-trip e.g. import to Blender and export to Blender.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Having such additional interpolation options seems common, glTF</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > and Blender too have them (</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > https://docs.blender.org/manual/en/latest/editors/graph_editor/fcurves/properties.html#editors-graph-fcurves-settings-interpolation</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ).</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > 4. Note that view3dscene / Castle Game Engine do not support</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > "CUBICSPLINE" interpolation yet, but we plan to.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > For now we support curve interpolation by adding extra</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > intermediate keys to the linear interpolation -- so, we have</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > needlessly more keys / key values. But this is only a temporary</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > solution, we want to support "CUBICSPLINE" properly, like X3DOM.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Regards,</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > Michalis</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > niedz., 25 cze 2023 o 05:33 Andreas Plesch <andreasplesch@gmail.com> napisał(a):</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > Date: Sat, 24 Jun 2023 10:11:03 -0700</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > From: Joseph D Williams <joedwil@earthlink.net></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > To: Michalis Kamburelis <michalis.kambi@gmail.com></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > Cc: GPU Group <gpugroup@gmail.com>, X3D Graphics public mailing list</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > <x3d-public@web3d.org></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > Subject: Re: [x3d-public] Blender > Exporting rig transforms to HAnim?</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > > Which shows that yes, you have a list of the key times that just have to be ascending. Default is linear interpolation between keyvalues. Now new to me, I like the STEP option where value not interpolated but stays the same until next keyvalue change. For that effect, gltf makes it easier. I want that STEP option in x3d! And then there is also the cubic spline with specified tangents. Me want that one too.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > In order to support glTF x3dom added a CUBICSPLINE with tangents</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > option to interpolators, in the same form as glTF, eg. three values</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > (in tangent, value, out tangent) per key. Parallel to glTF x3dom</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > interpolators have a "interpolation" SFString field which can have</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > "LINEAR" and "CUBICSPLINE" values. I suspect due to glTF support other</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > viewers also already do something like that and could expose such a</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > mode to regular X3D.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > A STEP option is already elegantly solved by X3D with duplicate keys</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > with different values in series. That allows mixing step wise and</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > linear interpolation in one animation. x3dom just translates glTF STEP</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > to that format which is very straightforward. A dedicated STEP option</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > would be 50% more efficient in storage but I am not sure if this is</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > enough of a benefit to justify duplication of existing functionality.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > It may not or it may as x3dom already does it internally for glTF. It</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > would be possible to add to x3d as well but perhaps not necessary.</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > Andreas</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > _______________________________________________</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > x3d-public mailing list</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > x3d-public@web3d.org</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > > > http://web3d.org/mailman/listinfo/x3d-public_web3d.org</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > --</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Andreas Plesch</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > > Waltham, MA 02453</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > ></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > --</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > Andreas Plesch</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> > > Waltham, MA 02453</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> --</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Andreas Plesch</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>> Waltham, MA 02453</p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal>><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>--</p><p class=MsoNormal>Andreas Plesch</p><p class=MsoNormal>Waltham, MA 02453</p><p class=MsoNormal><o:p> </o:p></p></div></body></html>