Interpretation of contact "position" needs to be unified.

[SeanCurtis-TRI]

In the documetation of fcl::Contact, the pos field is simply described as:
"Contact position, in world space".

However, understanding the interpretation of this contact point w.r.t. the normal, the penetration depth, and the colliding geometries is a bit incoherent.

Sometimes, the contact position is the mid-point between the points on the colliding bodies that most deeply penetrate each other (e.g., halfspace-* collisions), other times, it lies completely on one surface (e.g., box-box, plane-, triangle-), and other times it is a point that lies somewhere on the line segment connecting the two most deeply-penetrating points (e.g., sphere-sphere). This inconsistency makes it nearly impossible to ascribe any physical interpretation on the contact position. We have several options:

1. Continue the pattern in halfspace-* collision where it always lies at the mid-point,
2. Follow the pattern of plane-* where it always lies on one particular geometry. In this case, it should always like, by convention, either on object 1 or object 2, and its corresponding point should be pos + normal * penetration_depth so that the pair of points can be consistently constructed, regardless of object ordering.
3. Rather than producing a single point, we produce a pair of points (the two most deeply penetrating points). For contact points p1 and p2, normal n and penetration depth d, we would assert that (|p2 - p1|.dot(n) = d).

All three of these representations are interchangeable; from one you can reach either of the other two. No matter what, we should consider the sphere-sphere behavior incorrect.

Of the three, I have a slight bias for the first option. But, no matter what, the contact data needs to be unified so that code making collision queries can reason about the data without having to have special case code which depends on the types of geometries colliding.

[sherm1]

For better physical interpretation, where I think we want to get to eventually with these "one point" contact queries is:

4. Calculate the centroid C of the overlap volume, and normal 𝗻. Project C along 𝗻 in both directions to get points p₁ and p₂ on the surfaces of objects 1 and 2, resp. Then define penetration depth d≜|p₂−p₁|.

I don't think we know how to do that yet for most primitives, but in the meanwhile option 3 above seems closest to me, using the result of option 1 (midpoint) as a stand-in for the centroid. Is that feasible?

[SeanCurtis-TRI]

I would argue that 1-3 are equal approximations of 4. They are all interchangeable. Given one, you can get either of the other two. As such, it is impossible to favor one over another for mathematical reasons. Option 4 is definitely a superior mathematical model (in how it defines C). But once C and n are defined, you can then apply 1-3 as the encoding of C and n arbitrarily.

That said, in the absence of infrastructure for 4 and given that options 1-3 are all mathematically equivalent, I would suggest a different metric for preferring one -- minimize churn to interface. Option 1 & 2 don't change the structure of the Contact class -- option 3, would. So, generally, I favor option 1 or 2 (with a slight bias for two based on the litany of examples based on halfspace-* collisions).

[sherm1]

@SeanCurtis-TRI and I discussed f2f. We agreed that this would be the best approach for this query:

• This query returns a point p, unit normal 𝗻, and depth d.
• For a good physical response, the caller may need to know the line segment between "contact points" p₁ and p₂, one on each body. That allows, for example, adjusting the actual contact point based on the relative stiffness of the two materials in contact, by sliding along the line segment.
• We propose to always define point p as the midpoint of that line segment, with p₁=p−(d/2)𝗻 and p₂=p+(d/2)𝗻.
• The chosen location of p and direction of 𝗻 will vary for different geometries and algorithms and can be improved over time but would always retain the same interpretation for the caller.

The idea would be to standardize on this representation as the meaning of the result for this particular query, regardless of the types of geometry in contact. Does anyone object to that standardization?