Agreed. I have update the article and removed the squared terms of i, j, and k.

Thanks!

]]>Thanks for pointing this out. After reading stephen’s comment on March 9, 2016 (here) I realized my mistake. I was treating [math]\mathbf{i}[/math], [math]\mathbf{j}[/math], and [math]\mathbf{k}[/math] as imaginary numbers but they are actually unit vectors.

I have fixed the article with this change.

]]>Doh, you are right! I was treating [math]\mathbf{i}[/math], [math]\mathbf{j}[/math], and [math]\mathbf{k}[/math] as imaginary numbers but in the equation they are unit vectors! I was so blind to this for so long and I couldn’t understand where the confusion was.

Thanks for pointing this out. I have updated the article.

]]>[math]s_{a}s_{b}-x_{a}x_{b}-y_{a}y_{b}-z_{a}z_{b}[/math]

If you factor out a [math]-1[/math] from the vector part you get:

[math]s_{a}s_{b}+-1\(x_{a}x_{b}+y_{a}y_{b}+z_{a}z_{b}\)[/math]

Which can be rewritten as:

[math]s_{a}s_{b}-\mathbf{a}\cdot\mathbf{b}[/math]

Is this clear?

]]>Can you provide a reference to your SLERP equation that shows a proof of the equation you are providing?

The SLERP method that uses [math]sin(\theta)[/math] provides a method of spherical interpolation that maintains a constant angular velocity while rotating between [math]q_1[/math] and [math]q_2[/math]. Note that it does not provide a method to maintain linear velocity over the curve. If the quaternions are not normalized, you may notice some “ease-in” and “ease-out” effects. But this is not a problem if the quaternions are normalized.

Perhaps your formula can better achieve constant linear velocity while allowing for non-normalized quaternions?

]]>FreeGLUT 3.0.0 no longer provides the Visual Studio project files. Instead they are using cmake (https://cmake.org/) and you have to generate the project files for your build toolchain yourself using the cmake tool.

If you download the zip file at the end of the article, you will see the project files in the “extern\freeglut-2.8.1\VisualStudio\2012\” folder.

]]>You’re right about the consistency of the formatting. I started updating the article for consistency but I don’t have a lot of time right now to go through the whole thing. In the future, I will be more careful about formatting of variables in the equations and in the text.

]]>Thanks for your feedback. I have made the change.

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