INTERACTION TECHNIQUES

Collision Detection andCollision Detection and

Other InteractionsOther Interactions

Overview

Why is collision detection important?Why is collision detection important?

Types of Collision Detection.Types of Collision Detection.

Approaches to Collision Detection and Approaches to Collision Detection and Response.Response.

Static Object Collision Detection and Response.Static Object Collision Detection and Response.

Overview

Dynamic Object Collision Detection and Dynamic Object Collision Detection and Response. Response.

Collision Detection and Response in NPSNET.Collision Detection and Response in NPSNET.

UNC Collision Detection Algorithms (Ming Lin, UNC Collision Detection Algorithms (Ming Lin, etc.)etc.)

Overview

Time Critical algorithm - Philip Hubbard, Time Critical algorithm - Philip Hubbard, Cornell University.Cornell University.

Why is Collision Detection important?

Especially important in Interactive Virtual Environments.Especially important in Interactive Virtual Environments.

Realism suffers dramatically when a vehicle such as a Realism suffers dramatically when a vehicle such as a submarine either drives through the pier, or through a submarine either drives through the pier, or through a ship.ship.

Needed for our simulations to be viable training tools.Needed for our simulations to be viable training tools.

Why is Collision Detection important

No matter how good the graphics and textures No matter how good the graphics and textures look, the poor realism resulting from a lack of look, the poor realism resulting from a lack of collision detection breaks the suspension of collision detection breaks the suspension of disbelief.disbelief.

Types of Collision Detection

Fixed Object - moving objects checking for Fixed Object - moving objects checking for collisions with fixed objects such as terrain, collisions with fixed objects such as terrain, trees, buildings, etc.trees, buildings, etc.

Dynamic - moving objects checking for Dynamic - moving objects checking for collisions with other moving objects.collisions with other moving objects.

Approaches to Collision Detection and Response

Ignore altogether (NPSNET I).Ignore altogether (NPSNET I).

Implement fixed object collision detection and Implement fixed object collision detection and response only (NPSNET-IV).response only (NPSNET-IV).

Implement both fixed object and dynamic Implement both fixed object and dynamic object collision detection and response object collision detection and response (NPSNET-II).(NPSNET-II).

Fixed Objects

Easy to test for collisions with fixed objects. Easy to test for collisions with fixed objects. They do not move!!They do not move!!

Commonly implemented in VR applications Commonly implemented in VR applications since it is relatively easy.since it is relatively easy.

Good enough if you only have a single moving Good enough if you only have a single moving entity, or entities are restricted in their entity, or entities are restricted in their movement such that collisions between them is movement such that collisions between them is not possible.not possible.

Fixed Objects in NPSNET

Added as part of NPSNET-II.Added as part of NPSNET-II.

Still implemented in NPSNET-IV.Still implemented in NPSNET-IV.

Checks for fixed objects at elevations less than Checks for fixed objects at elevations less than 1,000 meters.1,000 meters.

Reorient a unit vector in the z direction, to the Reorient a unit vector in the z direction, to the object’s heading, pitch, and roll.object’s heading, pitch, and roll.

Fixed Objects in NPSNET

Add to starting and calculated ending positions Add to starting and calculated ending positions for the interval to get global coordinate for the interval to get global coordinate reference.reference.

Subtract start position from ending position to Subtract start position from ending position to get segment along path just followed.get segment along path just followed.

Check to see if we hit any fixed objects along Check to see if we hit any fixed objects along these segments.these segments.

Fixed Objects in NPSNET

Fixed Objects in NPSNET

If we did, and the object is a ground vehicle or If we did, and the object is a ground vehicle or human entity, reset object to travel in a human entity, reset object to travel in a direction opposite of the previous segment, at direction opposite of the previous segment, at a speed of -1.0a speed of -1.0

If we did, and the object is something else, the If we did, and the object is something else, the object is DEAD.object is DEAD.

Check to see if we hit the ground or water Check to see if we hit the ground or water along these segments.along these segments.

Fixed Objects in NPSNET

If we did, the vehicle is DEAD.If we did, the vehicle is DEAD.

There are some exceptions to this for other There are some exceptions to this for other objects on the ground such as bridges and objects on the ground such as bridges and tunnels which are considered to be part of the tunnels which are considered to be part of the ground for collision detection purposes.ground for collision detection purposes.

Some specific entities such as the ship and Some specific entities such as the ship and submarine are a little different to account for submarine are a little different to account for the fact that they operate in the water.the fact that they operate in the water.

Dynamic Objects in NPSNET

NPSNET-IV does not support dynamic object NPSNET-IV does not support dynamic object collision detection.collision detection.

NPSNET-II supported dynamic object collision NPSNET-II supported dynamic object collision detection.detection.

Lost in the development process, probably to Lost in the development process, probably to improve performance, and lack of interest in improve performance, and lack of interest in improving the algorithm.improving the algorithm.

UNC Collision Detection

I-COLLIDE: An Interactive and Exact Collision I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Detection System for Large-Scale Environments.Environments.

OOBTree: A Hierarchical Structure for Rapid OOBTree: A Hierarchical Structure for Rapid Interference Detection.Interference Detection.

I-COLLIDE

Avoids “Brute Force” Method which compares Avoids “Brute Force” Method which compares the bounding volume of every object in the VE the bounding volume of every object in the VE with every other object in the VE. Very with every other object in the VE. Very expensive computationally, O(nexpensive computationally, O(n22). Acceptable ). Acceptable performance if only a small number of objects.performance if only a small number of objects.

Objective is to report all geometric contacts Objective is to report all geometric contacts between objects.between objects.

I-COLLIDE

In an interactive VE, we do not know the In an interactive VE, we do not know the positions and orientation in advance, as the positions and orientation in advance, as the user can change them at any time.user can change them at any time.

Therefore, assumes objects motions can not be Therefore, assumes objects motions can not be expressed as a closed form function of time.expressed as a closed form function of time.

Collision detection is currently on of the major Collision detection is currently on of the major bottlenecks in such environments.bottlenecks in such environments.

I-COLLIDE

This algorithm trims the O(nThis algorithm trims the O(n22) of n ) of n simultaneously moving objects using simultaneously moving objects using coherence to speed up pairwise interference coherence to speed up pairwise interference tests and reduce the number of these tests.tests and reduce the number of these tests.

Complexity is reduced to O(n + m), where m is Complexity is reduced to O(n + m), where m is the number of objects the number of objects very closevery close to each other. to each other.

I-Collide

First, a coarse check is done to see if objects First, a coarse check is done to see if objects have potentially collided. Checks to see if the have potentially collided. Checks to see if the overall bounding volumes of objects intersect overall bounding volumes of objects intersect (Sweep and Prune).(Sweep and Prune).

Second, if a collision has occurred, determine Second, if a collision has occurred, determine the exact collision position (Exact Collision the exact collision position (Exact Collision detection).detection).

Temporal and Geometric Coherence

Temporal coherence means that the Temporal coherence means that the application state does not change significantly application state does not change significantly between time steps, or frames.between time steps, or frames.

The objects move only slightly from frame to The objects move only slightly from frame to frame.frame.

Temporal and Geometric Coherence

The slight movement of the objects translates The slight movement of the objects translates into geometric coherence, because their into geometric coherence, because their geometries (vertex coordinates) change geometries (vertex coordinates) change minimally between frames.minimally between frames.

Underlying assumption is that time steps are Underlying assumption is that time steps are small enough that objects do not travel large small enough that objects do not travel large distances between frames.distances between frames.

Sweep and Prune

Objective is to reduce the number of pairs of Objective is to reduce the number of pairs of objects that are actually compared, to give O(n objects that are actually compared, to give O(n + m).+ m).

Assumes each object is surrounded by a 3-D Assumes each object is surrounded by a 3-D bounding volume.bounding volume.

Use Dimension Reduction to sort the objects in Use Dimension Reduction to sort the objects in 3-space.3-space.

3-D Bounding Volumes

Use Fixed-Size Bounding Cubes, or Use Fixed-Size Bounding Cubes, or Dynamically-Resized Rectangular bounding Dynamically-Resized Rectangular bounding bounding boxes.bounding boxes.

Fixed size bounding cubes add less overhead, Fixed size bounding cubes add less overhead, as their size remains constant. It is only as their size remains constant. It is only necessary to translate them with the object necessary to translate them with the object and recompute min and max x,y,z.and recompute min and max x,y,z.

3-D Bounding Volumes

Dynamically resized bounding boxes are the Dynamically resized bounding boxes are the “tightest” axis-aligned box containing the “tightest” axis-aligned box containing the object at a particular orientation.object at a particular orientation.

More overhead due to recomputation of min, More overhead due to recomputation of min, max x,y,z values since they are not a constant max x,y,z values since they are not a constant distance from the center of the bounding distance from the center of the bounding volume.volume.

3-D Bounding volumes

Dynamic resizing works well with oblong Dynamic resizing works well with oblong objects, which results in fewer overlaps.objects, which results in fewer overlaps.

In walkthrough environments, with few objects In walkthrough environments, with few objects moving, the savings gained by fewer pairwise moving, the savings gained by fewer pairwise comparisons outweighs the cost of comparisons outweighs the cost of recomputing dynamic bounding box volumes.recomputing dynamic bounding box volumes.

Dimension Reduction

If two bodies collide in 3-D space, their If two bodies collide in 3-D space, their orthogonal projections onto the xy, yz, and xy orthogonal projections onto the xy, yz, and xy planes, and x, y, and z axes must overlap.planes, and x, y, and z axes must overlap.

This is why the bounding boxes are axis This is why the bounding boxes are axis aligned.aligned.

Can effectively project the bounding boxes Can effectively project the bounding boxes onto lower dimension, and sort them.onto lower dimension, and sort them.

Dimension Reduction

Works better than space partitioning Works better than space partitioning approaches (NPSNET-II) where it is difficult to approaches (NPSNET-II) where it is difficult to choose good partition sizes. choose good partition sizes.

1-D Sweep and Prune

Bounding Volumes projected onto x, y, and z Bounding Volumes projected onto x, y, and z axis.axis.

Two objects intersect, if and only if their Two objects intersect, if and only if their projections onto all three axis intersect.projections onto all three axis intersect.

Have one list for each dimension, which is Have one list for each dimension, which is sorted with Bubble sort or insertion sort.sorted with Bubble sort or insertion sort.

Maintain Boolean flag which only changes if Maintain Boolean flag which only changes if swaps are made on sorted lists.swaps are made on sorted lists.

1-D Sweep and Prune

1-D Sweep and Prune

If flags are true for all 3 dimensions, then we If flags are true for all 3 dimensions, then we pass this pair on to exact collision detection.pass this pair on to exact collision detection.

Bubble sort works well if few objects move.Bubble sort works well if few objects move.

Insertion sort works well where large numbers Insertion sort works well where large numbers of objects move locally.of objects move locally.

Due to temporal coherence, individual lists are Due to temporal coherence, individual lists are likely almost sorted already.likely almost sorted already.

1-D Sweep and Prune

Both sorts swap only adjacent items, making it Both sorts swap only adjacent items, making it convenient to maintain an overlap status for convenient to maintain an overlap status for each polytope pair.each polytope pair.

Exact Collision Detection

Tracks Closest pairs between Convex Tracks Closest pairs between Convex polytopes.polytopes.

Each polytope has Voronoi regions associated Each polytope has Voronoi regions associated with each of its features (faces, edges, with each of its features (faces, edges, vertices)vertices)

Voronoi regions are those points that are Voronoi regions are those points that are closer to the given feature than to any other closer to the given feature than to any other feature, and are external to the object.feature, and are external to the object.

Exact Collision Detection

In order for two feature to be the closest, each In order for two feature to be the closest, each must lie in the Voronoi region of the other.must lie in the Voronoi region of the other.

If either feature fails the test, step to the next If either feature fails the test, step to the next feature which is on the other side of the feature which is on the other side of the bounding plane that caused the test to fail.bounding plane that caused the test to fail.

When a feature pair fails the test, the next pair When a feature pair fails the test, the next pair is guaranteed to be closer.is guaranteed to be closer.

Exact Collision Detection

Exact Collision Detection

Initial features to compare are chosen Initial features to compare are chosen arbitrarily.arbitrarily.

Successive tests narrow down to closest Successive tests narrow down to closest features.features.

Due to coherence, future tests will produce Due to coherence, future tests will produce closest features that are near previous closest closest features that are near previous closest features.features.

Exact Collision Detection

Even if objects are moving and changing Even if objects are moving and changing direction rapidly, reasonable performance is direction rapidly, reasonable performance is assured by the fact that each feature has a assured by the fact that each feature has a constant number of bounding planes for its constant number of bounding planes for its Voronoi region.Voronoi region.

If the objects have penetrated one another, a If the objects have penetrated one another, a closest pairs feature will not be found. Use an closest pairs feature will not be found. Use an interior pseudo-Voronoi region to solve.interior pseudo-Voronoi region to solve.

Penetration Detection

When polytopes interpenetrate, some features When polytopes interpenetrate, some features may not fall into any Voronoi regions.may not fall into any Voronoi regions.

Pseudo-Voronoi regions partition the interior Pseudo-Voronoi regions partition the interior space of the convex polytopes.space of the convex polytopes.

Penetration Detection

Penetration Detection

Extension to non-convex objects

Use hierarchical tree representation of the Use hierarchical tree representation of the object where interior nodes may or may not be object where interior nodes may or may not be convex, but all the leaf nodes are convex.convex, but all the leaf nodes are convex.

The bounding volume of each node, is the The bounding volume of each node, is the union of the bounding volume of all its union of the bounding volume of all its children.children.

Recursively traverse tree to determine exact Recursively traverse tree to determine exact collision.collision.

Extension to non-convex objects

If there is a collision between a pair of parent If there is a collision between a pair of parent nodes, algorithm expands their children.nodes, algorithm expands their children.

If children collide, recursively proceeds down If children collide, recursively proceeds down the tree to determine if collision has occurred.the tree to determine if collision has occurred.

Finds exact collision point.Finds exact collision point.

Extension to non-convex objects

Some other algorithms utilize similar Some other algorithms utilize similar techniques, but with different types of tree techniques, but with different types of tree structures.structures.

Various techniques are available for Various techniques are available for subdividing the bounding volume of the object subdividing the bounding volume of the object to build the tree structure.to build the tree structure.

OOBTree

Applicable to general polygonal models.Applicable to general polygonal models.

Pre-computes a hierarchical representation of Pre-computes a hierarchical representation of models using tight-fitting oriented bounding models using tight-fitting oriented bounding box trees (OOBTrees).box trees (OOBTrees).

At runtime, traverse the trees, checking for At runtime, traverse the trees, checking for overlaps between oriented bounding boxes overlaps between oriented bounding boxes based on separating axis theorem.based on separating axis theorem.

Separating axis theorem

Project bounding box onto axis (not necessarily Project bounding box onto axis (not necessarily a coordinate axis). a coordinate axis).

Each box forms an interval on the axis.Each box forms an interval on the axis.

If the intervals don’t overlap, the axis is called If the intervals don’t overlap, the axis is called the separating axis for the boxes.the separating axis for the boxes.

If they do overlap, further tests may be If they do overlap, further tests may be required.required.

Time Critical Algorithm

Collision detection algorithms for Interactive Collision detection algorithms for Interactive Virtual worlds must support real-time Virtual worlds must support real-time performance, and be able to deal with motion performance, and be able to deal with motion that is controlled by a user.that is controlled by a user.

Few collision detection algorithms support Few collision detection algorithms support both of these requirements.both of these requirements.

Detects collisions between simplified Detects collisions between simplified representations of objects.representations of objects.

Time Critical Algorithm

These representations support progressive These representations support progressive refinement. Having detected a collisions at a refinement. Having detected a collisions at a given level, proceed to a representation with given level, proceed to a representation with higher level of detail.higher level of detail.

All bounding volumes are spheres, with more All bounding volumes are spheres, with more spheres defined at each level.spheres defined at each level.

This process may be interrupted at any level This process may be interrupted at any level by the application to improve performance.by the application to improve performance.

Time Critical Algorithm

May sacrifice accuracy for time. May sacrifice accuracy for time.

Is this a good approach? A question of debate Is this a good approach? A question of debate amongst researchers. The UNC papers criticize amongst researchers. The UNC papers criticize it.it.

It all depends on the application. User’s may It all depends on the application. User’s may find it easier to deal with less accuracy, if it find it easier to deal with less accuracy, if it overcomes “time-lag” induced simulator overcomes “time-lag” induced simulator sickness.sickness.

Time Critical Algorithm

There are other algorithms to consider. Broad There are other algorithms to consider. Broad Phase - first step of algorithm which uses Phase - first step of algorithm which uses upper bounds on the objects’ accelerations to upper bounds on the objects’ accelerations to build a set of space-time bounds.build a set of space-time bounds.

Narrow Phase - second step progressively Narrow Phase - second step progressively refines the accuracy of the collision detection.refines the accuracy of the collision detection.

Broad Phase

Builds a set of space-time bounds, a 4-D Builds a set of space-time bounds, a 4-D structure.structure.

Space-time bounds serve as conservative Space-time bounds serve as conservative objects as to where the object will be in the objects as to where the object will be in the future.future.

Utilizing these bounds, calculate the time (tUtilizing these bounds, calculate the time (tii) )

at which a collision is possible between two at which a collision is possible between two objects.objects.

Broad Phase

Until tUntil ti i is reached, no collisions are possible, is reached, no collisions are possible,

and the broad phase need not do any work and the broad phase need not do any work during the intervening frames.during the intervening frames.

When tWhen tii is reached, again enter the broad is reached, again enter the broad

phase and determine is a collision has occurred phase and determine is a collision has occurred utilizing low level-of-detail space-time utilizing low level-of-detail space-time bounding box.bounding box.

Broad Phase

If no collision occurs at tIf no collision occurs at tii, build a new set of , build a new set of

space-time bounds, compute a new tspace-time bounds, compute a new tii, and , and

continue.continue.

If bounding boxes intersect at tIf bounding boxes intersect at tii, switch to the , switch to the

narrow phase of refinement.narrow phase of refinement.

Narrow Phase

Progressively refines the approximation of the Progressively refines the approximation of the object surfaces. Bounding spheres are split object surfaces. Bounding spheres are split into two or more spheres to provide a higher into two or more spheres to provide a higher level-of-detail bounding volume that looks level-of-detail bounding volume that looks more and more like the actual object.more and more like the actual object.

After each repetition, allows itself to be After each repetition, allows itself to be interpreted by the application.interpreted by the application.

Levels of Detail Refinement

Narrow Phase

Proceeds through progressive levels of Proceeds through progressive levels of refinement until objects no longer intersect, or refinement until objects no longer intersect, or the process is interrupted.the process is interrupted.

Thus, the accuracy of the collision detection Thus, the accuracy of the collision detection depends on the time that can be allocated for depends on the time that can be allocated for the narrow phase refinement.the narrow phase refinement.

Returns to broad phase for next loop.Returns to broad phase for next loop.