3.4.CONTACT GENERATION
Generating contacts between rigid bodies
Generating contacts between rigid bodies
Introduction to contact generation
A collision detection system may simply return the single point of
maximum interpenetration if two objects are found to be in contact.
Unfortunately, this does not provide adequate information to implement a
realistic physics simulation, i.e. a collision between two objects may
involve multiple points of contact (e.g. a car object resting on a surface).
As such, the process of contact generation should produce a set of points
of contact for each interpenetrating object pairing.
Introduction to contact generation
One box resting on top of another box will have a region (or patch) in direct
contact. The contact patch can be of any shape (depending on the
geometry of the touching objects). In order to simplify the process, a
contact patch is typically simplified to a representative contact point or set
of contact points.
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Single contact
Collision detection
Contact pair
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Contact generation
As such, a means of modelling a contact patch using a set of contact points
is needed. The next slide shows one means of accomplishing this mapping
(producing reasonable physical behaviour in most situations).
Common types of contact
Point-face
contact
Face-face
contacts
Edge-edge
contact
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In most cases, the following collision detection
algorithms will try to model a contact using
either point-face or edge-edge contacts
(primitives with curved surfaces will use some of
the other cases).
Face-face collisions are
needed when one or both
contact faces are curved,
otherwise, flat face-face
contacts can be modelling
using edge–edge and
edge–face contacts.
Common types of contact
Edge-face
contact
Point-edge
contact
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Edge–face contacts can often
be replaced by a pair of edge–
point contacts (except when
the face is curved).
Point-point
contact
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Point–point
contacts and
point–edge
contacts can be
effectively
ignored as they
are unlikely to
occur and can be
handled as a
point-face
contact.
Contact data
Assuming the types of contact identified above, the following
properties can be defined permitting the contact to be described:
• Colllision point – the representative point of contact
(given interpenetrate any number of points might be
selected – some arbitrary means of selecting a point
is adopted, e.g. mid penetration point)
• Collision normal - direction in which an impact
impulse will be applied between the two objects. By
convention, the contact normal points from the first
object involved toward the second.
• Penetration depth - amount that the two objects are
interpenetrating measured along the direction of the
collision normal passing through the collision point
Contact
normal
Contact ●
point
Penetration
depth
Contact data: Point-Face Contacts
Point–face contacts are the most
common and important type of contact.
1. The contact normal is given by the
normal of the surface at the point of
contact.
2.The contact point is given as the point
involved in the contact (if
interpenetrating, the midway point
between the object’s point and
projected face point could be used)
3. The penetration depth is calculated as
the distance between the object point
and the projected point.
Contact normal
●
Contact
point
Penetration
depth
Contact data: Edge-Edge Contacts
Edge–edge contacts are the second most
important type of contact and are used
to model resting contacts between
objects with flat or concave sides
1. The contact normal is at right angles to
the tangents of both edges (built using
a cross product)
2.The contact point is typically the
closest point on one edge to the other
(a point midway between both edges
could also be used)
3. The penetration depth is the distance
between the two edges.
Contact normal
Contact point
●
Contact data: Edge-Face Contacts
Edge–face contacts are only used with
curved surfaces (although the contact
data is generated in a very similar way
to point–face contacts)
1. The contact normal is given by the
normal of the face (the edge direction
is ignored)
2.The contact point is calculated as the
point of deepest penetration
geometrically.
3. The penetration depth is the distance
between the edge and the face along
the direction of the normal passing
through the contact point.
Contact normal
Contact point ●
Penetration
depth
Contact data: Face-Face Contacts
Face–face contacts occur when a curved surface comes in contact with
another face (either curved or flat). In this case, the contact data is more
arbitrarily selected.
1. The contact normal is given by the
normal of the first face.
2.The contact point is calculated as the
point of deepest penetration
geometrically. If a point of deepest
penetration cannot be readily obtained
(e.g. two interpenetrating flat
surfaces), an arbitrary point is selected.
3. The penetration depth is the maximum
distance between the two faces
involved within the contact.
Contact normal
Contact point ●
Coherence and Contact Generation
The most efficient algorithms for calculating collision information between
a pair of convex objects will typically terminate whenever the point of
deepest interpenetration is found, i.e. a single contact is provided.
Generating a complete set of contacts
is considerably more difficult as a
contact can be interpreted in different
ways (e.g. a point-face contact could
be interpreted as another point–face
contact for a different face, with a
different penetration depth). To
generate a complete set of contacts, a
means of interpretating and
integrating points of contact is
needed.
Coherence and Contact Generation
The problem of contact set generation can be (somewhat) avoided by
introducing a degree of frame coherence and then simply generating a
single contact (of maximum penetration), e.g.: consider two stacked boxes
Frame 1: A single contact is generated and resolved in the normal manner.
Frame 2: As only one point of contact was resolved, the boxes will likely reinterpenetrate but probably in a different way. This is detected as a new
contact, providing two contacts which are resolved.
Frame 3: A third point
of contact is generated.
We have three contacts
which is sufficient to
keep the boxes stacked
in a stable manner.
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Frame 1:
First contact
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Frame 2:
Second contact
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Coherence and Contact Generation
To take advantage of the coherence, we store the type of contact (e.g.
point–edge or edge–edge) and which feature was involved for each object.
If in the next frame, the same type of contact is generated (but with
updated contact properties) that the stored contact can be updated.
If a new type of contact has
been detected, then it is
added to the set of cached
contacts.
Contacts are removed from
the set of cached contacts if
the interpenetration depth is
less than some fixed value
(i.e. the contact has moved
sufficient apart).
Generating contacts between rigid bodies
Primitive Contact Generation Algorithms
A contact generation algorithm generates contact
information between pairs of potentially colliding
primitives, returning zero, one or more contacts.
Iterated over a set primitive pairings (e.g. as returned
from some form of collision broad pass algorithm) a
pool of contacts will be generated which can then be
passed to the physics engine to be resolved.
See the recommended course text book for details of
contact generation given
•
sphere-sphere, and
•
sphere-plane primitives.
Box-Plane Contact Generation
This algorithm can return more than one contact.
Only point-face contacts will be returned, i.e. rather than return a faceface contact, up to four point-face contacts will be returned (one for each
corner point in contact with the plane/half-space). Likewise, an edge-face
contact will be returned using two point-face contacts.
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Box-Plane Contact Generation
Contacts are generated by checking for interpenetration of
each box vertex against the plane, i.e. the vertex is in contact
if
(where p is the vertex location, n the plane
normal and d the plane distance)
foreach( Point p : box.Vertices ) {
float d = dot( p, plane.n ); Determine the vertex-plane distance
if( d < plane.d + ε ) {
An epsilon value might be introduced
to cover resting contacts
contact.Point =
Generate contact
p + plane.n * (d - plane.d);
information, assuming
the contact point is
contact.Normal = plane.n;
contact.Penetration = plane.d – d; midway between the
}
}
vertex and plane.
Sphere-Box Contact Generation
A sphere-box collision will result in a single contact, although the
contact type can differ (face-face, edge-face, or point-face).
All three types of contact can be tested/constructed using the same
approach (assuming that the collision normal is from the perspective of the
sphere), as follows:
1. Find the closest point on the box (OBB)
to the centre of the sphere (as outlined
within an earlier lecture). The closest
point may be in a box corner, edge or
face.
2. If the closest box point to sphere centre
distance is less than the sphere radius
then generate contact information.
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Box-Box Contact Generation
Generating box-to-box contacts is notably more complex than the
previous generation algorithms; however, the technique employed behind
box-to-box contact generation is similar to that for any pair of concave
shapes.
Type of Box-Box Contacts
There are six possible types of contact between two boxes
Pointedge
contact
Edgeedge
contact
Point-face
contact
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Face-face
contact
Edgeface
contact
Pointpoint
contact
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Type of Box-Box Contacts: Simplification
Face-face and edge-face contacts can be represented using a number of
point-face or edge-edge contacts.
The point–point and
point–edge contacts do
not have any obvious
means of determining a
contact normal,
additionally these forms
of contact are very
unlikely to occur. As such,
they can be safely
ignored (and will result in
a point-face or edge-face
contact).
Edgeface
contact
Face-face
contact
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Box-Box Contact Generation
In order to generate contacts between two boxes the following steps are
used:
1. Use a separating axis test along each possible separating axis as a
means of providing an early out for non-collision or to determine the
axis of greatest interpenetration.
2. Generate a contact for the point of greatest interpenetration.
3. Use the notion of contact coherence, to combine
the contact with previously detected contacts to
update/extend the set of box-box contacts.
Box-Box Contacts: Separating axes
The separating axis test can be
performed for two boxes by projecting
the half-size of the box onto the
separating axis, i.e.:
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bool FindPenetrationOnAxis ( Box one, Box two, Vector3 axis ) {
float oneProj = TransformToAxis(one, axis); Project the half-size of
float twoProj = TransformToAxis(two, axis); each box onto the axis
Determine the
Vector3 centre = two.Centre - one.Centre;
float distance = Math.Abs( Dot( center, axis) ); midpoint between
Return true if the projected half-widths overlap
return (distance < oneProj + twoProj);
}
the boxes and
project this onto
the axis
Return the accumulated projection of each box axis onto the separating axis
float TransformToAxis(Box
return box.HalfSizeX *
+ box.HalfSizeY *
+ box.HalfSizeZ *
}
box, Vector3 axis) {
Math.Abs( Dot( axis, box.AxisX ) )
Math.Abs( Dot( axis, box.AxisY ) )
Math.Abs( Dot( axis, box.AxisZ ) );
Box-Box Contacts: Separating axes test
A total of 15 different axes must be tested (to confirm interpenetration),
these include:
• The three principal axes of each box
• The nine axes which are perpendicular to each pair of principal axes from
each box
Box-Box Contacts: Building a contact
Once the point of deepest interpenetration has been found it is
necessary to interpret this point in terms of a particular type of
contact.
This is a complex problem to solve for general polyhedral. A workable
approach for box-to-box contacts is to simply (and exhaustively) check for
each possible type of point-face and edge-edge contact.
If the point of deepest interpenetration is:
•
Along one of the principles axis of a box, then it is a point-face contact,
•
Along a perpendicular axis, then it is an edge-edge contact
As only a single contact is returned, if more than one contact
is found within the search, then the contact that has the
greatest interpenetration is returned.
Box-Box Contacts: Point-Face
A point-face contact uses the same approach as for a sphere-box collision
(but assuming a zero-radius sphere).
Each vertex from one box is
projected onto the principal
axes of the other. If the vertex
is inside the box, then a point–
face collision is required. If the
vertex is inside the box on more
than one axis, then the axis
with the shallowest
penetration is used.
Box-Box Contacts: Point-Face
Ensure the point is
Vector3 relPoint = box.TransformToLocal(point);
expressed in the
Vector3 normal;
box’s local space
Determine the axis of least (positive) penetration
float minDepth = box.HalfSizeX – Math.Abs(relPoint.X);
if (min_depth < 0) return;
The collision normal will
normal = box.AxisX * ((relPoint.x < 0)?-1:1); be constructed to be
stored within the contact
float depth = box.HalfSizeY – Math.Abs(relPoint.Y);
if (depth < 0) return;
else if (depth < min_depth) {
min_depth = depth;
normal = box.AxisY * ((relPoint.Y < 0)?-1:1);
}
depth = box.HalfSizeZ – Math.Abs(relPoint.Z);
if (depth < 0) return 0;
else if (depth < min_depth) {
min_depth = depth;
normal = box. AxisZ * ((relPoint.Z < 0)?-1:1);
}
Build the contact using the determined point, normal and interpenetration depth
Box-Box Contacts: Edge-Edge
Each edge from one object is checked against the edges of the other
object. This is accomplished by:
1. Consider each edge of object A.
2. Work out its interpenetration with each edge of object B.
3. The shallowest interpenetration of an edge from A is the
interpenetration of the edge.
4. The edge from object A with the
deepest interpenetration is retained.
Directed physics reading
Directed reading
• Read Chapter 13 of Game Physics
Engine Development (pp263-297)
on rotations.
• Read Chapter 9 of Real Time
Collision Detection (pp383-412) on
convexity based methods of
intersection.
Summary
Today we
explored:
 How to
model
different
forms of
contact
 Means of
generating
contacts
between rigid
body
primitives