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충돌 알고리즘(collision detection algorithms)
- 4.
- 5. 𝐴𝐵 𝐴 𝐵 𝐶 𝐴𝐶 𝐴𝐵 𝐴 𝐵 𝐶 𝐴𝐶 𝐴𝐵 ∙𝐴𝐶 > 0 𝐴𝐵 ∙ 𝐴𝐶 < 0
- 6.
- 7. 𝑂𝐴 ∙ 𝑂𝐵𝑂𝐴 𝑂𝐵 cos𝜃 𝐴 𝐵 𝑂 𝐴′ 𝑂𝐴′ 𝑂𝐴 cos𝜃
- 8. 𝑂𝐵 𝑂𝐵 𝐴 𝐵 𝑂 𝐴′ 𝑂𝐴′𝑂𝐴 cos𝜃 𝑂𝐵 𝑂𝐵 ||𝑂𝐵||
- 9. 𝑎 = (𝑎𝑥,𝑎𝑦, 𝑎𝑧) b = 𝑏𝑥, 𝑏𝑦, 𝑏𝑧 𝑎 × 𝑏 = (𝑎𝑦 ∙ 𝑏𝑧 − 𝑏𝑦 ∙ 𝑎𝑧, 𝑎𝑧 ∙ 𝑏𝑥 − 𝑏𝑧 ∙ 𝑎𝑥, 𝑎𝑥 ∙ 𝑏𝑦 − 𝑏𝑥 ∙ 𝑎𝑦)
- 12. 𝑎 × 𝑏× 𝑐 𝑎 × 𝑏 × 𝑐
- 13. 𝑂𝐴 × 𝑂𝐴× 𝑂𝐵 𝑂 𝐴 𝐵 𝑂𝐴 × 𝑂𝐵 𝑂𝐴 × 𝑂𝐴 × 𝑂𝐵
- 15. 𝑆1이 𝑆2일 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛고 𝑆2𝑚𝑎𝑥 𝑆1𝑚𝑖𝑛 𝑆1 𝑆2 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛
- 16. 3D AABB Algorithm- YouTube
- 20. AABB 정밀 충돌감지 - YouTube
- 30. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 −𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 Ԧ 𝑣
- 31. (𝑆2𝑚𝑎𝑥 − 𝑆1min)∙ Ԧ 𝑣 𝑆1 𝑆2 Ԧ 𝑑 Ԧ 𝑣 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 Ԧ 𝑣
- 32. (𝑆2𝑚𝑎𝑥 − 𝑆1min)∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 − 𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 Ԧ 𝑣
- 33. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 −𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1𝑚𝑎𝑥 𝑆2m𝑖𝑛 Ԧ 𝑣 Ԧ 𝑣
- 34. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 −𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 35. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 −𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 36. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 −𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 37. 𝑆1𝑚𝑖𝑛 𝑆1𝑚𝑎𝑥 𝑆2𝑚𝑎𝑥 𝑆2𝑚𝑖𝑛 (𝑆2𝑚𝑎𝑥 −𝑆1min) ∙ Ԧ 𝑣 (𝑆1𝑚𝑎𝑥 − 𝑆2m𝑖𝑛) ∙ Ԧ 𝑣 𝑆1 𝑆2 𝑆1min 𝑆2𝑚𝑎𝑥 Ԧ 𝑣 𝑆2m𝑖𝑛 𝑆1𝑚𝑎𝑥 Ԧ 𝑣 Ԧ 𝑣
- 38. OBB Algorithm -YouTube
- 44.
- 45.
- 49. – → → 𝑆𝐶 Ԧ 𝑑 = 𝑆𝐴( Ԧ 𝑑) 𝑆𝐵 (− Ԧ 𝑑)
- 52. GJK Algorithm -Minkowski Different - YouTube
- 55. Ԧ 𝑑 𝑆𝑠3 Ԧ 𝑑 = 𝑆𝑠1( Ԧ 𝑑) 𝑆𝑠2 (− Ԧ 𝑑)
- 56. 𝐴𝑂 𝑆𝑠3 𝐴𝑂 =𝑆𝑠1 (𝐴𝑂) 𝑆𝑠2 (−𝐴𝑂) 𝐴𝑂
- 57.
- 58. 𝑂𝐵 𝐴𝑂 𝑂𝐵 ∙𝐴𝑂 𝐴𝑂 ∙ 𝑂𝐵
- 59.
- 60.
- 61.
- 62. Ԧ 𝑑 𝐴𝐵 ×𝐴𝑂 × 𝐴𝐵 𝐴𝐵 𝐴𝑂 × Ԧ 𝑑 Ԧ 𝑑
- 63. 𝐴𝐵 × 𝐴𝑂 𝐴𝐵𝐴𝑂 𝐴𝐵 𝐴𝑂 𝐴𝐵 𝐴𝑂
- 64. 𝐴𝐵 × 𝐴𝑂× 𝐴𝐵 𝐴𝐵 Ԧ 𝑑 𝐴𝐵 𝐴𝑂 Ԧ 𝑑
- 65.
- 67.
- 68.
- 69.
- 70.
- 71.
- 72.
- 73. 𝑅𝐴𝐵𝐶 𝑅𝐵𝐶 𝑅𝐴𝐶 𝑅𝐴𝐵𝐶 𝑅𝐵𝐶 ((𝐶𝐴× 𝐶𝐵 × 𝐶𝐵 ∙ 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 74. 𝐶𝐴 × 𝐶𝐵 (𝐶𝐴× 𝐶𝐵 × 𝐶𝐵 𝐶𝐵 𝑅𝐴𝐶 𝑅𝐵𝐶 (𝐶𝐴 × 𝐶𝐵 × 𝐶𝐵
- 75.
- 76.
- 77. 𝑅𝐴𝐵𝐶 𝑅𝐴𝐶 (𝐶𝐵 × 𝐶𝐴× 𝐶𝐴 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 78. 𝑅𝐴𝐵𝐶 ((𝐶𝐴 × 𝐶𝐵× 𝐶𝐵 ∙ 𝐶𝑂 ((𝐶𝐵 × 𝐶𝐴 × 𝐶𝐴 ∙ 𝐶𝑂 𝑅𝐴𝐶 𝑅𝐵𝐶
- 79. GJK Algorithm -YouTube
- 80. the GJK Collisiondetection 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)