Talk:Slerp

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Computer graphics

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Please do not change "Slerp" to "slerp"; the initial capital is correct, regardless of what you may see elsewhere. Here's how Slerp appeared in print for the first time:

"A formula for spherical linear interpolation from q₁ to q₂, with parameter u moving from 0 to 1, can be obtained two different ways. From the group structure we find

Slerp(q₁,q₂;u) = q₁(q₁⁻¹q₂)^u ;

while from the 4-D geometry comes …"

Also do not change "animating rotation" to "animating rotations"; compare to the title of the original paper (also sometimes cited incorrectly).

If you think Wikipedia should have a Ken Shoemake page, feel free to restore that link. KSmrq 11:30, 2005 August 10 (UTC)

Regardless of the original capitalization, the word "slerp" is typically not capitalized in common usage in computer graphics.

And regardless of the fact that the title of the original paper uses the phrase "animating rotation" (singular), that is no reason not to use the phrase "animating rotations" (plural) when referring to slerp, when the plural is appropriate.50.205.142.50 (talk) 02:50, 13 June 2020 (UTC)[reply]

Who is Glen Davis[edit]

I'm in the NASA spaceflight community and very much agree that Slerp belongs in a mathematics section however the algorithm is not presented in the literature that I can find. It is credited in a footnote to Glen Davis in a Sigraph "paper" by Ken Shoemake, Vol 19, No 3, 1985. The method seems to be correct but it's not rigorous. I need a scholarly treatment. — Preceding unsigned comment added by 130.76.96.157 (talk) 18:54, 29 August 2018 (UTC)[reply]

Mathematics category[edit]

Editors tempted to delete the mathematics categorization should first study the content. There is more to mathematics than cohomology and modular forms, eh? This article draws on quaternions, differential geometry, Lie groups, and other advanced material. At most, it could be degraded to mere Applied Mathematics… ;-) KSmrq 10:50, 2005 August 15 (UTC)

Absurd. WP has more than ten thousand articles on mathematics. It is possible to categorize. linas 15:25, 3 October 2005 (UTC)[reply]

Linas, were you arguing for or against the math categorization? I'm with KSmrq in any case. I think this article is interpreted as "in computer graphics" as opposed to mathematics because it includes code, which should be pretty insulting to both camps. FWIW the sampled code comes from the cited page "Understanding Slerp, Then Not Using It" - cutting and pasting the code and omitting nlerp, etc. is pretty ironic considering the author's jab two paragraphs later:

"Currently, slerp is considered by most to be the authoritative method for rotation interpolation. This is because most programmers don't understand slerp, much less the alternatives; they just hear from other people that slerp is the right thing to do, then they paste the Shoemake routines into their source code." -- Jonathon Blow

Sobeita (talk) 02:51, 16 October 2017 (UTC)[reply]

Geometric Slerp Citation[edit]

Can we have a citation about the general geometric Slerp that explains this in detail? Maybe one from Glenn Davis?

I also think it should be stressed that this is valid for *spherical* curves in the Geometric Slerp section. Alanic 18:21, 30 October 2007 (UTC)[reply]

I've been using the following report for everything Slerp related: E.B. Dam, M. Koch, M. Lillholm, "Quaternions, Interpolation and Animation", University of Copenhagen, Copenhagen, 1998. It was prepared with Shoemake's extensive help, and explains pretty much literally everything you ever wanted to know about quaternions. --Mr. Neo Anderson (talk) 14:47, 29 April 2020 (UTC)[reply]

What exactly _is_ a Slerp?[edit]

Is is a formula? An algorithm? Shouldn't this be mentioned in the _first sentence_ of the article? —Preceding unsigned comment added by 136.163.44.101 (talk) 08:13, 25 March 2011 (UTC)[reply]

"It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1." Maybe this was added after your post, but that seems like a fine explanation to me. It's a closed form for distance along the geodesic between two points on a sphere after constant velocity for time t, roughly like taking a direct flight. Sobeita (talk) 02:32, 16 October 2017 (UTC)[reply]

Clamping to [-1,1] after guaranteeing that 0 <= dot <= threshold?[edit]

Sorry if a new topic is unnecessary, I'm not really sure what's standard in Wiki talk. Is there a reason for clamping dot? From earlier branches, like the title says, 0 <= "dot" <= "DOT_THRESHOLD". Similarly, is normalization necessary for "result" when it's a linear combination of two already-normalized vectors - is that to account for unbounded "t" or really just for rounding errors in the combination? Thanks for the help. Sobeita (talk) 02:24, 16 October 2017 (UTC)[reply]

The C++ algorithm interpolates angle quadratically, which can lead to "bounce" in angle[edit]

Is there a bug in the C++ slerp code that causes the angle to be interpolated quadratically rather than linearly? See charts here, comparing the Wikipedia C++ slerp algorithm to JOML's slerp algorithm (which uses a very different computation for slerp, derived from here).

Statement doesn't make a lot of sense[edit]

In the section Geometric Slerp this sentence appears:

"In the limit as Ω → 0, this formula reduces to the corresponding symmetric formula for linear interpolation,

\operatorname {Lerp} (p_{0},p_{1};t)=(1-t)p_{0}+tp_{1}.\,\!

"

This is not false. But at the point that Ω = 0, we also have that $p_{0}=p_{1}$ , which is strangely left unmentioned.

A second and more minor point is that "slerp" is not normally a capitalized word. So there is no reason to capitalize it here.50.205.142.50 (talk) 01:16, 13 June 2020 (UTC)[reply]

One more thing[edit]

The section Quaternion Slerp contains this sentence:

"Slerp also has expressions in terms of quaternion algebra, all using exponentiation."

This is more than a little ridiculous. Slerp is just a formula for a geodesic curve between two points on a sphere. The concept of a geodesic on any convex surface was already studied by Johann Bernoulli (1667-1748). So it makes no sense to pretend that the concept of such a curve originated with Ken Shoemake's formula for it.50.205.142.50 (talk) 02:42, 13 June 2020 (UTC)[reply]