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충돌 알고리즘(collision detection algorithms)
- 1. cos
- 2. 𝐴𝐵 𝐴 𝐵 𝐶 𝐴𝐶 𝐴𝐵 𝐴 𝐵 𝐶 𝐴𝐶 𝐴𝐵 ∙ 𝐴𝐶 > 0 𝐴𝐵 ∙ 𝐴𝐶 < 0
- 3. 𝑂𝐵 𝑂𝐴 𝑂𝐴′ 𝐴 𝐵 𝑂 𝐴′
- 4. 𝑂𝐴 ∙ 𝑂𝐵 𝑂𝐴 𝑂𝐵 cos𝜃 𝐴 𝐵 𝑂 𝐴′ 𝑂𝐴′ 𝑂𝐴 cos𝜃
- 5. 𝑂𝐵 𝑂𝐵 𝐴 𝐵 𝑂 𝐴′ 𝑂𝐴′ 𝑂𝐴 cos𝜃 𝑂𝐵 𝑂𝐵 ||𝑂𝐵||
- 6. 𝑎 = (𝑎𝑥, 𝑎𝑦, 𝑎𝑧) b = 𝑏𝑥, 𝑏𝑦, 𝑏𝑧 𝑎 × 𝑏 = (𝑎𝑦 ∙ 𝑏𝑧 − 𝑏𝑦 ∙ 𝑎𝑧, 𝑎𝑧 ∙ 𝑏𝑥 − 𝑏𝑧 ∙ 𝑎𝑥, 𝑎𝑥 ∙ 𝑏𝑦 − 𝑏𝑥 ∙ 𝑎𝑦)
- 7. 𝑎 × 𝑏 × 𝑐 𝑎 × 𝑏 × 𝑐
- 8. 𝑂𝐴 × 𝑂𝐴 × 𝑂𝐵 𝑂 𝐴 𝐵 𝑂𝐴 × 𝑂𝐵 𝑂𝐴 × 𝑂𝐴 × 𝑂𝐵
- 9. 𝑆1이 𝑆2일 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 고 𝑆2𝑚𝑎𝑥 𝑆1𝑚𝑖𝑛 𝑆1 𝑆2 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛
- 10. 3D AABB Algorithm - YouTube
- 11. AABB 정밀 충돌 감지 - YouTube
- 12. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 Ԧ 𝑣
- 13. (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 𝑆1 𝑆2 Ԧ 𝑑 Ԧ 𝑣 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 Ԧ 𝑣
- 14. (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 Ԧ 𝑣
- 15. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1𝑚𝑎𝑥 𝑆2m𝑖𝑛 Ԧ 𝑣 Ԧ 𝑣
- 16. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 17. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 18. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 19. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1 𝑆2 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 20. OBB Algorithm - YouTube
- 21. ⊕ ∈ ∈
- 22. ⊖ ∈ ∈
- 23. – → → 𝑆𝐶 Ԧ 𝑑 = 𝑆𝐴 ( Ԧ 𝑑) 𝑆𝐵 (− Ԧ 𝑑)
- 24. GJK Algorithm - Minkowski Different - YouTube
- 25. Ԧ 𝑑 𝑆𝑠3 Ԧ 𝑑 = 𝑆𝑠1 ( Ԧ 𝑑) 𝑆𝑠2 (− Ԧ 𝑑)
- 26. 𝐴𝑂 𝑆𝑠3 𝐴𝑂 = 𝑆𝑠1 (𝐴𝑂) 𝑆𝑠2 (−𝐴𝑂) 𝐴𝑂
- 27. 𝐴𝑂
- 28. 𝑂𝐵 𝐴𝑂 𝑂𝐵 ∙ 𝐴𝑂 𝐴𝑂 ∙ 𝑂𝐵
- 29. 𝑂𝐵 𝐴𝑂 𝐴𝑂 𝑂𝐵 𝑂𝐵 ∙ 𝐴𝑂
- 30. 𝐴𝑂 𝑂𝐵 𝑂𝐵 ∙ 𝐴𝑂
- 31. 𝐴𝐵
- 32. Ԧ 𝑑 𝐴𝐵 × 𝐴𝑂 × 𝐴𝐵 𝐴𝐵 𝐴𝑂 × Ԧ 𝑑 Ԧ 𝑑
- 33. 𝐴𝐵 × 𝐴𝑂 𝐴𝐵 𝐴𝑂 𝐴𝐵 𝐴𝑂 𝐴𝐵 𝐴𝑂
- 34. 𝐴𝐵 × 𝐴𝑂 × 𝐴𝐵 𝐴𝐵 Ԧ 𝑑 𝐴𝐵 𝐴𝑂 Ԧ 𝑑
- 35. Ԧ 𝑑 𝑂𝐶 ∙ Ԧ 𝑑 𝑂𝐶
- 36. 𝑅𝐴𝐵𝐶 𝑅𝐴𝐶 𝑅𝐵𝐶 𝑅𝐴𝐵 𝑅𝐴 𝑅𝐵 𝑅𝐶
- 37. 𝑅𝐴𝐵𝐶 𝑅𝐴𝐶 𝑅𝐵𝐶 𝑅𝐴𝐵 𝑅𝐴 𝑅𝐵 𝑅𝐶
- 38. 𝑅𝐴𝐵𝐶 𝐴𝑂 𝑅𝐴 𝑅𝐴𝐶 𝑅𝐵𝐶 𝑅𝐴𝐵 𝑅𝐴 𝑅𝐵 𝑅𝐶 𝐴𝑂
- 39. 𝑅𝐴𝐵𝐶 𝑅𝐵 𝑅𝐴𝐶 𝑅𝐵𝐶 𝑅𝐴𝐵 𝑅𝐵 𝑅𝐶
- 40. 𝑅𝐴𝐵𝐶 𝐴𝐵 𝑅𝐴𝐵 𝑅𝐴𝐶 𝑅𝐵𝐶 𝑅𝐴𝐵 𝑅𝐶
- 41. 𝑅𝐴𝐵𝐶 𝑅𝐶 𝑅𝐴𝐶 𝑅𝐵𝐶 𝑅𝐶
- 42. 𝑅𝐴𝐵𝐶 𝑅𝐵𝐶 𝑅𝐴𝐶 𝑅𝐴𝐵𝐶 𝑅𝐵𝐶 ((𝐶𝐴 × 𝐶𝐵 × 𝐶𝐵 ∙ 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 43. 𝐶𝐴 × 𝐶𝐵 (𝐶𝐴 × 𝐶𝐵 × 𝐶𝐵 𝐶𝐵 𝑅𝐴𝐶 𝑅𝐵𝐶 (𝐶𝐴 × 𝐶𝐵 × 𝐶𝐵
- 44. 𝑅𝐴𝐵𝐶 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 45. 𝑅𝐴𝐵𝐶 Ԧ 𝑑 𝐶𝑂 𝑅𝐵𝐶 𝑅𝐵𝐶 𝑅𝐴𝐶 𝑅𝐵𝐶
- 46. 𝑅𝐴𝐵𝐶 𝑅𝐴𝐶 (𝐶𝐵 × 𝐶𝐴 × 𝐶𝐴 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 47. 𝑅𝐴𝐵𝐶 ((𝐶𝐴 × 𝐶𝐵 × 𝐶𝐵 ∙ 𝐶𝑂 ((𝐶𝐵 × 𝐶𝐴 × 𝐶𝐴 ∙ 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 48. GJK Algorithm - YouTube
- 49. the GJK Collision detection algorithm — Harold Serrano - Game Engine Developer Separating Axis Theorem (SAT) Explanation. – YouTube https://developer.mozilla.org/en-US/docs/Games/Techniques/3D_collision_detection https://justicehui.github.io/other-algorithm/2018/06/23/OBB/ 여러 가지 물체 충돌 감지 알고리즘 속 수학적 원리 : 네이버 블로그 (naver.com)
