Cse 381 advanced game programming collision detection
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CSE 381 – Advanced Game Programming Collision Detection. Remember This?. We spent a lot of time on this in the spring Remember what we learned What will we add? Sweep and Prune algorithm (today) GJK algorithm (Monday). What is collision detection?.

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Remember this
Remember This?

  • We spent a lot of time on this in the spring

  • Remember what we learned

  • What will we add?

    • Sweep and Prune algorithm (today)

    • GJK algorithm (Monday)


What is collision detection
What is collision detection?

  • Determining if, when, & where two objects intersect

  • What objects?

    • Linear components, planes, triangles, rectangles, oriented boxes, spheres, capsules, lozenges, cylinders, ellipsoids, etc.

  • Hugely important part of a 3D game engine. Why?

    • done continuously every frame

    • involves huge amounts of computations

  • Entire textbooks are written on this subject alone

    • Real-Time Collision Detection by Christer Ericson

    • Collision Detection in Interactive 3D Environments by Gino van den Bergen


For what is collision detection used
For what is collision detection used?

  • In 3D gaming:

    • prevent players/monsters from walking through walls

    • prevent players/monsters from walking/falling through terrain

    • react to players/monsters colliding with each other

    • react to players/monsters colliding with game objects

      • i.e., pick up ammo

    • react to projectiles colliding with players/monsters

      • i.e., take health away for being hit by a bullet

    • ragdoll physics


Why so important
Why so important?

  • Because if done improperly, it can ruin a game

    • collision detection problems can still be found in state of the art games

      • Ever get stuck in a wall?

      • Ever go behind a wall you’re not supposed to?

      • Ever have a collision that doesn’t look like a collision?

  • Because if done inefficiently, it will ruin gameplay


Collision detection graphics
Collision Detection & Graphics

  • Work together in a game engine

  • Should be developed together

  • Both share:

    • geometric data

    • timing elements

  • So, pool resources for their algorithms

    • e.g., scene graphs, spatial partitioning (octrees, bsps…)


Game engine collision detection
Game Engine Collision Detection

  • 2 phases

    • Broad phase: determine which pairs of shapes need to be tested for collision

    • Narrow phase: determine collision results for each pair identified in broad phase

  • All game objects maintain collision sets

    • data for collisions calculations

    • i.e., bounding volumes


Types of collisions
Types of Collisions

  • Object versus plane (navigation or culling)

  • Object versus object (general collision)

  • Linear component versus object (picking)


Imagine a complex world
Imagine a complex world

  • Hundreds of interior structures, each with rooms

  • Complex external terrain environment

  • Water with underwater structures (interiors)

  • Rather than testing these items serially, we can do so hierarchically

    • much faster

    • continuously reduce the problem


How should collision data be organized
How should collision data be organized?

  • One of the most important questions in designing a collision system

  • Game world might contain a large number of interacting objects

    • an exhaustive comparison is too exhaustive

  • Objects should be organized into collision groups

    • e.g., rooms, partitions, etc.


Rooms as collision groups
Rooms as collision groups

  • Scene graphs & collision sets are not static, they change with the game

    • as players, NPCs, or other game objects move/change

  • When a player enters a room, the scene graph is reconfigured

    • player is now part of room collision group

  • Only objects moving within a room are tested against one another for collisions


Collision detection game physics
Collision Detection Game Physics

  • This is a huge topic

  • Game physics is rapidly changing


Collision detection response
Collision Detection & Response

  • Collision Detection

    • detecting what game objects are colliding with each other

  • Collision Response

    • providing a programmed response to collisions that fits with the game’s design & custom laws of physics


Static vs dynamic objects
Static vs. Dynamic Objects

  • Static objects never move

  • Dynamic objects move

  • Collisions may be between:

    • Static objects & dynamic objects (fast & easy)

    • Dynamic objects & dynamic objects (harder)


What types of collisions might we care about
What types of collisions might we care about?

  • Main character and static objects:

    • terrain, floor, tiles, walls, furniture, buildings, game objects (i.e. power-ups, ammo), etc.

  • Main character & dynamic objects:

    • enemies, projectiles (i.e. bullets, arrows, etc.), particles (expensive), etc.

  • Other dynamic objects and:

    • other static objects

    • other dynamic objects


Collisions in pairs
Collisions in Pairs

  • In collision detection, we always compare pairs of objects. Easier to:

    • understand

    • design & implement solutions

  • A naïve approach:

    • one pair at a time, compare all game objects in a game world against all other game objects in a game world


Collision detection calculations
Collision Detection Calculations

  • What data are we looking for?

    • Do these two objects potentially collide?

    • Do these two objects collide?

    • When did these two objects collide?

    • Where did these two objects collide?

      • where on geometry of objects, points of impact

  • These 4 questions get progressively:

    • more computationally expensive to implement

    • more complex to implement (more math)


Phases of collision detection
Phases of Collision Detection

  • Spatial Partitioning Algorithms

    • problem reduction

    • only perform additional phases on pairs of object on same “islands”

  • Broad Phase – early rejection tests

    • Do the coarse Bounding Volumes of two objects collide?

  • Narrow Phase

    • What are the contact points on object geometries?

      • Done down to the last triangle in 3D games


Bounding volumes
Bounding Volumes

  • The base geometry used for all collision tests

    • instead of the shape’s geometry, which is too expensive

  • Properties of desirable BVs:

    • inexpensive intersection tests

    • tight fitting

    • inexpensive to compute

    • easy to rotate and transform

    • use little memory

  • Ref: [1]


Assumptions you might make
Assumptions you might make

  • All collideable game objects:

    • have rectangular Bounding Volumes

    • don’t rotate, or

    • if they do rotate, we don’t care about them colliding with stuff

  • Thus:

    • no polytope collision detection equations

    • no rotation equations

    • this makes life much easier (no narrow phase)


Common bounding volumes
Common Bounding Volumes

  • Note that the space craft has been rotated

  • Ref: [1], Figure 4.2

  • This semester, we like AABBs and/or Spheres

    • axis-aligned bounding boxes


How about a big complicated object
How about a big, complicated object?

  • We can have 2 AABBs

    • Don’t test them against each other


Spatial partitioning
Spatial Partitioning

  • First, reduce the problem

  • only perform additional phases on pairs of object on same “islands”

  • Common Solutions:

    • Octree Algorithms (quadtrees for 2D)

    • also: Portals (ala Quake), BSP trees (Binary Space Partitions), Spatial Hashing, etc.


  • Octrees
    Octrees

    • Used to divide a 3D world into “islands”

      • 2D divided via Quadtrees

    • Why?

      • to make rendering more efficient

      • to make collision detection more efficient

    • What would be the data for these nodes?

      • region coordinates for cell

        • though a smart implementation might eliminate this too

      • AABBs


    Octree
    Octree

    • Source: http://en.wikipedia.org/wiki/Image:Octree2.png


    Octree drawbacks
    Octree Drawbacks

    • Objects cross islands

      • octree has to be constantly updated

      • not so bad

    • Objects straddle islands

      • collision detection may involve objects from multiple islands

      • can be a headache


    Uniform grids
    Uniform Grids

    • Fast mechanism for reducing the problem

      • used for 2D & 3D games

    • Steps:

      • divide the world into a grid of equal sized cells

      • associate each object with the cells it overlaps

      • only objects sharing a cell are compared

    • Serves 2 purposes:

      • reduces the problem for object-object collision detection

      • provides solution for easy object-terrain collision detection


    Calculating grid position
    Calculating Grid Position

    • What cells does our object currently occupy?

    • How would you calculate that?

      • For min/max tile rows/columns:

        • object.X/terrainCellW

        • object.Z/terrainCellL

        • (object.X+aabb.Width)/terrainCellW

        • (object.Z+aabb.Height)/terrainCellL

      • For this guy, cells (0,y,0), (0,y,1), (1,y,0), & (1,y,1)

        • only test against:

          • other objects in those cells

          • collidable tiles in those cells (treat like objects)

            • don’t let sprites occupy “collidable cells”


    Grid cell collision walkable surfaces
    Grid Cell Collision & Walkable Surfaces

    • Side-scrollers simulate gravity

      • not necessarily accelerated (constant velocity)

      • move all affected sprites down by dY

    • This way, characters can fall

    • We must detect when sprites are colliding with a floor/platform

    • Easy solution: make a tile with a walkable surface at the very top of the image

    • Collision system will handle response


    Grid cell collision advantages disadvantages
    Grid Cell Collision Advantages/Disadvantages

    • Advantages

      • easy to implement

      • very fast (computationally inexpensive)

    • Only good for certain types of predicatable collisions

      • Physics simulations require more complex approaches


    Again
    Again

    • Spatial Partitioning

      • Octrees

      • Portals, BSPs, etc.

      • Uniform Grids

    • What purpose do they serve?

      • reduce the problem of collision detection

      • How?

        • reduce the number of object-object tests


    Object tests premise
    Object Tests Premise

    • Think of all collision tests as between pairs of collidable objects

    • In our games this means:

      • object – to – object

    • In a single game loop, for each object, we may have to check against

      • other moving objects (tricky)

      • other stationary objects (easier)


    Broad phase
    Broad Phase

    • Do the coarse AABBs of two objects collide?

    • Common solution:

      • separating axis algorithms

      • including temporal coherence

    • For efficiencies use:

      • Sweep & Prune

      • an extension of separating axis, more efficient for many elements


    Narrow phase
    Narrow Phase

    • What are the contact points on object geometries?

      • for 3D might be convex hulls

    • Two Steps

      • determine potentially colliding primitives (ex: triangles) of a pair of objects

        • AABB tree algorithms

      • determine contact between primitives

        • GJK algorithms

    • Ref[3]


    Position calculations
    Position Calculations

    • New Position with constant velocity:

      xt = x0 + (vx * t)

      yt = y0 + (vy * t)

      zt = z0 + (vz * t)

    • Velocity is a Vector, (vx, vy, vz), or (vx, vy) in 2D

    • Example, object at (1, 5), velocity of (4, -3)


    Velocity vectors
    Velocity Vectors

    • Velocities have direction, their vector

      Vtotal = √(Vx2 + Vy2 + Vz2) for 3D games

      Vtotal = √(Vx2 + Vy2) for 2D games


    Acceleration
    Acceleration

    • Rate of change of velocity

    • New Velocity (vt) with Acceleration:

      vt = dx/dt = v0 + (a * dt)

    • NOTE – each of these calculations are in one dimension

      • You would perform similar calculations on y & z axes

    • NOTE: we will avoid mid-frame acceleration

      • everybody does it, so will we


    Trajectory assumption
    Trajectory Assumption

    • In a single frame, if no force is exerted upon an object, it will have a constant velocity for that frame


    Forces and vectors
    Forces and vectors

    • F = ma

    • Collisions produce forces on both colliding objects

    • Forces have direction, their vector

      • Forces in x, y, & z axes

    • Ftotal = √(Fx2 + Fy2 + Fz2) for 3D games

    • Ftotal = √(Fx2 + Fy2) for 2D games


    Forces can be summed
    Forces can be summed

    • Done axis by axis

      Fx = F1x + F2x + F3x

      Fy = F1y + F2y + F3y

      Fz = F1z + F2z + F3z


    Momentum
    Momentum

    • (P) – A property that objects in motion have

      P = m * v, measured in kg * m/s

    • Force equation can be reduced to:

      F = dP/dt


    Momentum collisions
    Momentum & Collisions

    • Note: Ignore friction for now

    • Momentum transfer – if 2 objects collide:

      • A perfectly elastic collision: no loss of energy

        • Momentum is conserved

      • An imperfect elastic collision: some energy is converted into heat, work, & deformation of objects

        • Momentum is reduced after collision


    Rigid bodies
    Rigid Bodies

    • Note: we are only dealing with rigid bodies

    • No deformation due to collisions


    Calculating new velocities
    Calculating new velocities

    • Note:

      • ignore rotation/angular velocities for now

      • ignore centers of mass for now

    • 2 moving blocks collide:

      • Block A: mA & vAi

      • Block B: mB & vBi

    • Question, if they collide, what should their velocities be immediately after the collision?

      • vAf & vBf


    Why are we interested in final velocities
    Why are we interested in final velocities?

    • When a collision precisely happens, we want to:

      • move our objects to that precise location

      • change their velocities accordingly


    Calculating v af v bf
    Calculating vAf & vBf

    • If momentum is conserved after collision:

      PAi + PBi = PAf + PBf

      (mA * vAi) + (mB * vBi) = (mA * vAf) + (mB * vBf)

    • Problem has 2 unknowns (vaf & vbf)

      • we need a second equation (Kinetic energy equation)

      • ke = (m * v2)/2, where ke is never negative Joules (J)

      • insert the ke equation into our momentum equation

        vAf = ((2 * mB * vBi) + vAi * (mA – mB))/(mA + mB)

        vBf = ((2 * mA * vAi) – vBi * (mA – mB))/(mA + mB)


    Example
    Example

    • 2 blocks moving

    • Block A:

      • mass is 10, initial velocity is (4, 0)

    • Block b:

      • mass is 10, initial velocity is (-4, 1)

    • Results:

      • Block A final velocity is (-4, 1)

      • Block B final velocity is (4, 0)

    • See my ElasticCollisionsVelocityCalculator.xls


    Continuous collision detection
    Continuous Collision Detection

    • For each moving object, compute what grid cells it occupies and will cross & occupy if its current velocity is added

    • Find the first contact time between each object pair

    • Sort the collisions, earliest first

    • Move all affected objects to time of first collision, updating positions

    • Update velocities of collided objects

    • Go back to 1 for collided objects only

    • If no more collisions, update all objects to end of frame

    • Ref[3]


    Time in between frames
    Time in between frames

    • We will make calculations and update velocities and positions at various times

    • When?

    • In response to:

      • input at start of frame

      • AI at start of frame

      • collisions/physics when they happen

        • likely to be mid-frame


    Axis separation tests
    Axis Separation Tests

    • How do we know if two AABBs are colliding?

      • if we can squeeze a plane in between them

      • i.e. if their projections overlap on all axes

    NO COLLISION

    COLLISION

    A

    C

    B

    D


    Be careful of tunneling
    Be careful of Tunneling

    • What’s that?

    • An object moves through another object because collision is never detected


    A note about timing
    A note about timing

    • If we are running at 30 fps, we are only rendering 1/30th of the physical states of objects

      • Squirrel Eiserloh calls this Flipbook syndrome [2]

    • More things happen that we don’t see than we do

    • We likely won’t see the ball in contact with the ground


    One way to avoid tunneling
    One way to avoid tunneling

    • Swept shapes

    • Potential problem: false positives

      • Good really only for early rejection tests


    Better way to avoid tunneling
    Better way to avoid tunneling

    • Calculate first contact times

    • Resolve contacts in order of occurrence


    Times as
    Times as %

    • You might want to think of your times as % of the frame

    • Then correct positions according to this %

    • For example, if I know my object is supposed to move 10 units this frame (we’ve locked the frame rate), if a collision happens ½ way through, move all affected objects ½ distance of their velocity and recompute collisions data for collided data

    • Re-sort collisions and find next contact time


    Example1
    % Example

    • A at (1, 5,0), velocity of (4, -3,0)

    • B stationary at (4, 4,0)

    • When will they collide?

      • When A goes one unit to the right

      • How long will that take?

      • If it takes 1 frame to go 4 units, it will take .25 frames to go 1

    (0, 0, 0)

    + x

    + y


    What about 2 moving objects
    What about 2 moving objects?

    • Solution, give the velocity of one to the other for your calculations

      • make one of them stationary

      • then do the calculation as with grid tiles

      • make sure you move both objects

      • make sure you update the velocities of both objects


    So how do we calculate the when
    So how do we calculate the when?

    • We can do it axis by axis

      • What’s the first time where there is overlap on all 3 axes?

    • For each axis during a frame, what is the time of first and last contact?

    • Time of first contact is


    Again for 2 moving bodies freeze one
    Again, for 2 moving bodies, freeze one

    • Object A

      • (xA, yA, zA, vxA, vyA, vzA)

    • Object B

      • (xB, yB, zB, vxB, vyB, vzB)

    • Give velocity of B to A, now A is:

      • (xA, yA, zA, vxA-vxB, vyA-vyB, vzA-vzB)


    First time of contact
    First time of contact

    • For object A, in x-axis

      • (xA, yA, zA, vxA-vxB, vyA-vyB, vzA-vzB)

      • Time = distance/velocity

      • Since velocity = distance/time

        if ((xB-(Bwidth/2)) > (xA+(Awidth/2)))

        {

        tx_first_contact = (xB-(Bwidth/2) – (xA + (Awidth/2)))/(vxA-vxB);

        tx_last_contact = ((xB + (Bwidth/2)) – (xA-(Awidth/2)))/vxA-vxB);

        if (tx_first_contact > 1) no collision

        }

    What if ((xB-(Bwidth/2)) < (xA+(Awidth/2)))?


    Time calculation example
    Time Calculation Example

    • Awidth = 2, Bwidth = 2

    • A at (1, 1, 0), velocity of (4, 3, 0)

    • B at (4, 2, 0), velocity of (-1, 0, 0)

    • When will they start colliding on x-axis?

      • if ((xB-(Bwidth/2)) > (xA+(Awidth/2)))

      • {

      • tx_first_contact = (xB-(Bwidth/2) – (xA + (Awidth/2)))/(vxA-vxB);

      • tx_last_contact = ((xB + (Bwidth/2)) – (xA-(Awidth/2)))/vxA-vxB);

      • if (first_contact > 1) no collision

      • }

    (0, 0, 0)

    tx_first_contact = 1/5 t

    tx_last_contact = 1t


    Physics timing
    Physics & Timing

    • Christer Ericson & Erin Catto’s recommendations:

      • physics frame rate should be higher resolution than rendering

      • minimum of 60 frames/second for physics calculations

      • makes for more precise, and so realistic interactions

    • How do we manage this?

      • tie frame rate to 60 fps, but don’t render every frame

      • don’t worry about this for now

    • Note: these operations might commonly be done in different threads anyway (have their own frame rates)


    Sweep prune
    Sweep & Prune

    • Also called Sort & Sweep

    • A broad phase algorithm

    • This is an efficient way of managing data for method of separating axis (MSA) tests

    • Baraff, D. (1992), Dynamic Simulation of Non-Penetrating Rigid Bodies, (Ph. D thesis), Computer Science Department, Cornell University


    Improvements on msa
    Improvements on MSA

    • It greatly reduces the number of object-object comparisons.

    • How?

      • it only compares objects near each other on one of the 3 axes

    • How?

      • sorting


    Sweep prune approach
    Sweep & Prune approach

    • Think of each axis separately, for each object considered:

    • Calculate position range on x-axis

      • extract (minX, maxX)

    • Place all (minX, maxX) pairs into array

    • Sort array by minX

      • now, it’s easy to see what overlaps in X axis

      • an O(N) problem, not O(N2). Why?

        • don’t compare all objects to one another, only ones “near” each other

      • note, we’ll have sorting costs, of course

    • For x-axis collided pairs, repeat for Y & Z axes

    • Pairs that overlapped on all 3 tests collided


    Combining our algorithms
    Combining our Algorithms

    • Sweep and Prune will tell us if a collision might happen

    • Continuous collision detection will tell us when it happens

      • it might also tell us S & P gave us a false positive


    Picking
    Picking

    • Selecting a 3D object from its 2D projection on the screen by pointing and clicking with a mouse

    • Why is this useful?

      • players selecting game objects/targets

        • i.e., which enemy to attack

      • bullets traveling through game world

        • determining which player/NPC it hits


    How is picking done
    How is picking done?

    • Build a ray (like a vector)

      • Where’s the origin?

        • the camera

        • a gun

      • What direction is the ray?

        • from camera to a world point that projects onto the screen at the screen location

    • Find those objects that are intersected by the ray


    Testing for picking intersections
    Testing for picking intersections

    • Traverse through scene graphs to find those with triangles that intersect the ray

    • Gather data about these intersections as needed

      • Point of intersection

      • Normal vector at intersection

      • Surface attributes (color, texture coordinate)

      • Etc.

    • Find the closest triangle to the ray’s origin


    How do we test intersections with linear components
    How do we test intersections with linear components?

    • Depends on what it’s intersecting

      • sphere

      • box

      • triangle

    • Each use different types of calculations

      • e.g., sphere collision equations based on use of quadratic equation


    Recursively finding triangles pseudocode
    Recursively finding triangles pseudocode

    void FindPickTriangles(Node node, Ray ray, PickResults results)

    {

    if (ray intersects node.boundingVolume)

    {

    if (node is a leaf)

    {

    for each triangle of node do

    {

    if (ray intersects triangle)

    add intersection information to results;

    }

    }

    else

    {

    for each child of node do

    DoPick(child, ray, results);

    }

    }

    }


    Scene graphs picking
    Scene Graphs & Picking

    • What’s a node?

      • represents a visual object in the game

      • has a bounding volume

      • may have child nodes

    • If a ray intersects a node, it may intersect a child of that node

    • If a ray does not intersect a node, it will not intersect any of its child nodes

    • So what?

      • this will greatly reduce the problem at hand


    References
    References

    • [1] Real Time Collision Detection by Christer Ericson

    • [2] Physics for Game Programmers by Squirrel Eiserloh

    • [3] Collision Detection in Interactive 3D Environments by Gino van den Bergen


    References1
    References

    • [1] Real Time Collision Detection by Christer Ericson

    • [2] Physics for Game Programmers by Squirrel Eiserloh

    • [3] Collision Detection in Interactive 3D Environments by Gino van den Bergen


    References2
    References

    • Advanced Collision Detection Techniques

      • http://www.gamasutra.com/features/20000330/bobic_01.htm

    • N-Tutorials: Collision Detection & Response

      • http://www.harveycartel.org/metanet/tutorials/tutorialA.html

    • Physics in BSP Trees: Collision Detection

      • http://www.devmaster.net/articles/bsp-trees-physics/

    • 3D Game Engine Design by David H Eberly


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