Sphere Fix: Add branch for empty condition in expandByPoint function

[gkjohnson]

Related issue: --

Description

Currently when calling "Sphere.expandByPoint" on an "empty" sphere with a point that is < 1.0 distance from the sphere center nothing will happen because the radius is squared before checking if the point is already encapsulated:

sphere = new THREE.Sphere();
sphere.makeEmpty();

point = new THREE.Vector3( 0.5, 0, 0 );
sphere.expandByPoint( point );

console.log( sphere.radius ); // still - 1

cc @WestLangley

[WestLangley]

Nice find!

I expect union() has similar problems. In fact, for both methods, I would remove the references and just calculate the new center and radius analytically.

/ping @Mugen87

[gkjohnson]

In fact, for both methods, I would remove the references and just calculate the new center and radius analytically.

What do you mean by this? Do you mean the comment source references? It does look like union would have the same issue. It should be simple to handle the empty cases for both spheres in that function.

[WestLangley]

In union(), just set the new center and radius directly, without calling expandByPoint().

Also, the "nudge" comment makes it sound like it's a hack. It's not.

[gkjohnson]

It looks like the nudge comment is from the original source from which this was ported 🤷:

https://github.com/juj/MathGeoLib/blob/2940b99b99cfe575dd45103ef20f4019dee15b54/src/Geometry/Sphere.cpp#L649-L671

I can plan to at least fix the union function in another PR when I get a chance unless someone beats me to it. I'll let someone else rewrite the functions if necessary.

[Mugen87]

Why is the default radius -1 and not 0? It seems expandByPoint() would work if an empty sphere has a 0 radius.

[gkjohnson]

Why is the default radius -1 and not 0? It seems expandByPoint() would work if an empty sphere has a 0 radius.

-1 is used to indicate "empty" meaning both the sphere center and radius are invalid. If "empty" was denoted by a radius of 0 then it would be impossible to tell the difference between a sphere with a center that needed to be initialized by the first point and a valid bounding sphere that encapsulated a single point at the origin.

[Mugen87]

the difference between a sphere with a center that needed to be initialized by the first point and a valid bounding sphere that encapsulated a single point at the origin.

When do you need this kind of distinction? Does it actually matter?

[gkjohnson]

The code in this PR shows the very case where this distinction is important... here is what will happen when expanding by a point ( 1, 0, 0 ) in the cases where a radius of - 1 is used and 0 is used for "empty":

Radius == 0, Center == 0, 0, 0

• Point distance from center is measured as 1
• Radius is set to 0.5
• Center is moved to 0.5, 0, 0 because there's no way of knowing whether the sphere is already encapsulating the point (0, 0, 0).
• Final sphere is radius = 0.5, center = 0.5, 0, 0

Radius == - 1, Center == 0, 0, 0

• Sphere is seen as empty
• Center is set to the point position since it's the only point the sphere is supposed to encapsulate
• Radius is set to 0
• Final sphere is radius = 0, center = 1, 0, 0

[mrdoob]

Thanks!