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CS6360 Collision Detection/Response Loose End

CS6360 Collision Detection/Response Loose End. David Johnson. Work Through An Example. Two objects Rectangle and Triangle. (-1,2) (1,2) (0,1). (-1, -2) (1,-2) (-1,-1) (1,-1). Compute Center of Mass. Find the area using signed area of polyline face

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CS6360 Collision Detection/Response Loose End

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  1. CS6360 Collision Detection/Response Loose End David Johnson

  2. Work Through An Example • Two objects • Rectangle and Triangle (-1,2) (1,2) (0,1) (-1, -2) (1,-2) (-1,-1) (1,-1)

  3. Compute Center of Mass • Find the area using signed area of polyline face • Nth vertex same as 0th • Compute centroid coordinates

  4. Translate the Triangle (-1,2) (1,2) (3,1) (-1, -2) (1,-2) (2,-1) (4,-1)

  5. Check for Collision • Use GJK • Pick a random direction to start the simplex (1,1) • Find the support vertex of Minkowski difference Z support(Z, d) = support(Y, d) – support(X, -d)

  6. Support for the Box Support(Y,d) = (1,2) (-1,2) (1,2) (-1, -2) (1,-2)

  7. Support for the Triangle support(X, -d) = (2,-1) (3,1) (2,-1) (4,-1)

  8. Total Support • support(Z, d) = support(Y, d) – support(X, -d) = (1,2) – (2,-1) = (-1,3) • Increase the simplex by finding new dir

  9. Find new support Support(Z,d) = (1,-2) – (3,1) = (-2,-3) (-1,2) (1,2) (3,1) (2,-1) (4,-1) (-1, -2) (1,-2)

  10. Extend Simplex • Simplex is now a line • Find closest point • Make new dir (-1.45, 0.24)

  11. Find new support Support(Z,d) = (1,-2) – (2,-1) = (-1,3) (-1,2) (1,2) (3,1) (2,-1) (4,-1) (-1, -2) (1,-2)

  12. Simplex Doesn’t Extend • Closest Point has same distance as last time • No collision (-1.45, 0.24)

  13. Look at Collision Case Support(Z,d) = (-1,2) – (2.5,-1) = (-3.5,3) (-1,2) (1,2) (1.5,1) (0.5,-1) (2.5,-1) (-1, -2) (1,-2)

  14. Initialize Simplex • Simplex is a point • Find closest point • Make new dir

  15. Look at Collision Case Support(Z,d) = (1,-2) – (1.5, 1) = (-0.5,-3) (-1,2) (1,2) (1.5,1) (0.5,-1) (2.5,-1) (-1, -2) (1,-2)

  16. Extend Simplex • Simplex is a line • Find closest point • Make new dir

  17. Look at Collision Case Support(Z,d) = (1,2) – (0.5, -1) = (0.5,-3) (-1,2) (1,2) (1.5,1) (0.5,-1) (2.5,-1) (-1, -2) (1,-2)

  18. Extend Simplex • Simplex is a line • Find closest point • Make new dir

  19. What is the Collision Normal? (-1,2) (1,2) (1.5,1) (0.5,-1) (2.5,-1) (-1, -2) (1,-2)

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