Consider the following two objects. (All matrices created in TRS form using uniform scaling.) Object 1:...

 

Transcribed Image Text:

Consider the following two objects. (All matrices created in TRS form using uniform scaling.) Object 1: OBB: Min = (-2.50, -2.00, -1.00) = Max (3.50, 2.00, 1.00) -0.474 -0.048 -0.151 0 Object 2: OBB: Min=(-4.75, -5.00, -3.50) Max (5.25, 5.00, 4.50) = W= 0 0.4767 -0.151 0.1581 -0.143 -0.452 0 4 0.3536 -0.289 -0.204 4 W-0 0.2887 -0.408 1 -2 00 1 0.3536 0.2887 0.2041 -6 0 1 00 We want to known if these object intersect. To determine this, we need to use the SAT test on 15 specific axes. For this question however, we'll only focus on a limited subset of axes, just to save time and avoid too much repetition. You need to work out the result of the projection tests only for the following three axes: 1) Object I's forward axis 2) Object 2's up axis 3) The cross-product of both of the above two axes a) Give these three axes b) For each of the three stated axes, perform the SAT overlap test. (Of course: show your work!) Seriously: use any tool available to compute inverses, etc... c) Based solely on the overlap answers for these three axes: Are the objects colliding? Consider the following two objects. (All matrices created in TRS form using uniform scaling.) Object 1: OBB: Min = (-2.50, -2.00, -1.00) = Max (3.50, 2.00, 1.00) -0.474 -0.048 -0.151 0 Object 2: OBB: Min=(-4.75, -5.00, -3.50) Max (5.25, 5.00, 4.50) = W= 0 0.4767 -0.151 0.1581 -0.143 -0.452 0 4 0.3536 -0.289 -0.204 4 W-0 0.2887 -0.408 1 -2 00 1 0.3536 0.2887 0.2041 -6 0 1 00 We want to known if these object intersect. To determine this, we need to use the SAT test on 15 specific axes. For this question however, we'll only focus on a limited subset of axes, just to save time and avoid too much repetition. You need to work out the result of the projection tests only for the following three axes: 1) Object I's forward axis 2) Object 2's up axis 3) The cross-product of both of the above two axes a) Give these three axes b) For each of the three stated axes, perform the SAT overlap test. (Of course: show your work!) Seriously: use any tool available to compute inverses, etc... c) Based solely on the overlap answers for these three axes: Are the objects colliding?