고려대학교 그래픽스 연구실 Chapter 6 Collision Detection 6.1~6.4 고려대학교 그래픽스연구실 민성환

19 September 2001 Sunghwan Min The Type of Intersection  Three categories  Linear component versus object (picking)  Chapter 5 already described  Object versus plane (culling)  Chapter 4 described  Object versus object (general collision)

19 September 2001 Sunghwan Min Design Issues  Hierarchical representation of objects for collision purposes  Should the hierarchy be built top-down or bottom-up?  Top-down : decomposition of complex object  Bottom-up : construction the world from small models  Should the bounding volumes be built manually or automatically?  Automatic : not always generate a good set of volumes  Manual : can be time consuming  The best approach : mixture of the two

19 September 2001 Sunghwan Min Design Issues (cont.)  How should the intersection information be reported?  To use callbacks  How should the propagation of the test collision calls be controlled?  How much information should be retained about the current collision state to support future test collision calls?

19 September 2001 Sunghwan Min Dynamic Objects and Lines  The line  The Object  constant linear velocity  time interval  If  Moving parallel to the line (Static test)  Presented here  Determine only if the line and object will intersect on the time interval

19 September 2001 Sunghwan Min Spheres  The moving sphere has center  The distance C to the line is, where  If, then the line intersects the sphere

19 September 2001 Sunghwan Min Spheres  The problem is now one of determining the minimum of Q on the interval  Solve  T=-b/a  If : the minimum is Q(T)  If T<0 : the minimum is Q(0)  If T>t max : the minimum is Q(t max )  Then compared to

19 September 2001 Sunghwan Min Oriented Boxes  Static oriented box  R d >R b +R s : non intersection RbRb RsRs L R

19 September 2001 Sunghwan Min Oriented Boxes (cont.)  line  the only potential separating axes for i=0,1,2  For the motion case, is replaced by  If any of these tests are true  do not intersect

19 September 2001 Sunghwan Min Capsules  The moving capsule is E

19 September 2001 Sunghwan Min Lozenges  The moving lozenges is E0 E1

19 September 2001 Sunghwan Min Cylinders  An extremely complicated and some what expensive  Not recommended for use as bounding volumes

19 September 2001 Sunghwan Min Ellipsoids  Static ellipsoid  The line  The quadratic equation has a real- valued root 

19 September 2001 Sunghwan Min Ellipsoids (cont.)  For a moving ellipsoid  The center is

19 September 2001 Sunghwan Min Triangles  The plane of the triangles at time t  The line be

19 September 2001 Sunghwan Min Dynamic Objects and Planes  The Plane  The Object  constant linear velocity  time interval  Presented here  Determine only report an intersection time of t=0 when the object and plane are initially intersecting

19 September 2001 Sunghwan Min Spheres  The moving center  The distance between center and plane  If initially intersecting  Else  The first time of contact T of the sphere

19 September 2001 Sunghwan Min Oriented Boxes  The radius of the interval of the projected box  Computation of the first time of contact T is identical to that of a sphere versus a plane  If initially intersecting  Else  The first time of contact T of the sphere

19 September 2001 Sunghwan Min Capsules  Line segment  And where  Define the signed distances  If initially intersecting P0 P1 D

19 September 2001 Sunghwan Min Capsules (cont.)  The sign of  decide which of and is closer  Apply the intersection testing algorithm between a sphere and a plane

19 September 2001 Sunghwan Min Lozenges  Lozenges is  The four corners  The signed distance  Not all positive or not all negative  initially intersecting  Applied to the sphere corresponding to that corner P 00 P 10 E0 E1 P 01 P 11

19 September 2001 Sunghwan Min Triangles  Let the three vertices be  Three signed distances for 0<= i <=2  Initially intersecting  Not all positive or not all negative  The closest vertex  use signed distance

19 September 2001 Sunghwan Min Static Object-Object  In this section determine if two of the same type or stationary objects

19 September 2001 Sunghwan Min Spheres, Capsules, And Lozenges  Intersection  dist < rsum*rsum SphereCapsuleLozenge SphereDist(pnt,pnt)Dist(pnt,seg)Dist(pnt,rct) CapsuleDist(seg,pnt)Dist(seg,seg)Dist(seg,rct) LozengeDist(rct,pnt)Dist(rct,seg)Dist(rct,rct)

19 September 2001 Sunghwan Min Oriented Boxes  Let  first box have axes and extents  second box have axes and extents  The potential separating axe

19 September 2001 Sunghwan Min Oriented Boxes (cont.)  15 separating axis D R0R0 R1R1 L R a1A1a1A1 a2A2a2A2 b1B1b1B1 b2B2b2B2

19 September 2001 Sunghwan Min Oriented Boxes and Triangles  Let  Box have axes and extents  Triangles have vertices and the edges of the triangles are

19 September 2001 Sunghwan Min Oriented Boxes and Triangles (cont.)  Non-intersection test  Min(p0,p1,p2) > R, max(p0,p1,p2)<-R D L -R a1A1a1A1 a2A2a2A2 R E1E1 E0E0 p0p0 p1p1 p2p2 Min(u i ) Max(u i )

19 September 2001 Sunghwan Min Triangles  Non-intersection test  or L Min(v i ) D E0E0 E1E1 F1F1 F0F0 Max(v i ) Min(u i ) Max(u i ) p0p0 p1p1 p2p2 q0q0 q1q1 q2q2