ch 15: collision and simple physics
TRANSCRIPT
Ch 15: Collision and Simple Physics
Quiz # 5 Discussion
Collision Detection Resources:
http://sharky.bluecog.co.nz/?p=108
Collision: Bounding Box
ò Circle or sphere around the object
ò Collision detection is:
If (d2 <= (r2 +r1)2)
collision = true; else collision = false;
x,y r
d r1 r2
Collision: Bounding Box (AABB) [XNA]
ò Axis-Aligned Bounding Box (AABB)
ò Collision detection is: If ( (object1.max.x < object2.min.x) || (object1.min.x > object2.max.x) )
return false; if ( (object1.max.y < object2.min.y) ||
(object1.min.y > object2.max.y) ) return false;
if ( (object1.max.z < object2.min.z) || (object1.min.z > object2.max.z) ) return false;
return true;
min (x, y, z)
max(x, y, z)
min (x, y, z)
max(x, y, z)
Collision: Bounding Box (OBB)
ò Oriented Bounding Box (OBB)
Collision: Others
ò Convex Hull
ò Divide model meshes – sphere around each mesh separately
Processing and Efficiency
1. Sphere
2. AABB
3. OBB
4. Convex Hull
Decrease in efficiency
Using XNA AABB Make sure to rotate and scale and translate the bounding box
BoundingBox boxbox = new BoundingBox(new Vector3(0, 0, 0), new Vector3(125, 100, 75));
BoundingBox playerbox = new BoundingBox( new Vector3(modelpos.X -‐ 50, -‐50, modelpos.Z -‐ 50), new Vector3(modelpos.X + 50, 50, modelpos.Z + 50));
if (playerbox.Intersects(boxbox))
{
System.Console.WriteLine("there is a collision");
}
Try it
ò Get your assignment # 2
ò Add another object
ò Move the object closer to the character
ò Just print out a message when a collision happens
More resources on Collision
ò Gottschalk, Stephan, Ming Lin and Dinesh Manocha, “OBB-Tree: A Hierarchical Structure for Rapid Interference Detection,” SIGGRAPH ‘96.
ò Ericson, Christer, Real-Time Collision Detection, Morgan Kaufmann, San Francisco, 2004.
ò Van den Bergen, Gino, Collision Detection in Interactive 3D Environments, Morgan Kaufmann, San Francisco, 2003.
ò Van Verth, James M. Essential Mathematics for Games and Interactive Applications A Programmer’s Guide, Morgan Kaufmann, San Francisco, 2004
For Physics
ò Physics and Collision:
ò Raycast: can be good for AI vision
ò Shapecast
ò Procedural Animation and Rag Doll physics: turned on at death or other events
ò Use a Physics engine. You can integrate:
ò Bullet: http://bulletphysics.org/wordpress/
ò ODE: http://www.ode.org/
Ray Casting
ò Shoot a ray from object to another:
ò Given Position, direction (use parametric line equation)
ò Check for collision along the way (object intersections)
Parametric line Equation
xy
!
"##
$
%&&=
xp0 + t(xp1 − xp0 )
yp0 + t(yp1 − yp0 )
(
)
**
+
,
-- p0
p1
For Physics
ò Physics and Collision:
ò Raycast: can be good for AI vision
ò Shapecast
ò Procedural Animation and Rag Doll physics: turned on at death or other events
ò Use a Physics engine. You can integrate:
ò Bullet: http://bulletphysics.org/wordpress/
ò ODE: http://www.ode.org/
Inverse Kinematics
1. Set goal configuration of end effector 2. calculate interior joint angles
Analytic approach – when linkage is simple enough, directly calculate joint angles in configuration that satisfies goal
Numeric approach – complex linkages At each time slice, determine joint movements that take you in direction of goal position (and orientation)
From Rick Parent’s slides
Forward Kinematics - review
Pose – linkage is a specific configuration
Pose Vector – vector of joint angles for linkage
Degrees of Freedom (DoF) – of joint or of whole figure
Articulated linkage – hierarchy of joint-link pairs
Types of joints: revolute, prismatic
Tree structure – arcs & nodes Recursive traversal – concatenate arc matrices Push current matrix leaving node downward Pop current matrix traversing back up to node
Goal
End Effector
θ1
θ2 θ3 L1
L2 L3
Inverse Kinematics
Animation
ò Procedural animation disadvantages:
ò Too expensive
ò Doesn’t look good – not controlled by the artist
ò Most games now use a mix of both
ò Alternative Smartbody by USC (blend of both with constraint system)
Animation & Control (the need for Physics)
GDC Vault