Given is a 2D vector field with the vectors Voo ( V10- The velocities are given at the corners of a quad and we can assume a bilinear interpolation. We intend to find the critical points of this vector field by using a recursive subdivision algorithm. In other words, we look for zero-crossings in the u component and the v component. Since we bilinearly interpolate the velocity components, we know that a zero-crossing can only exist if at least one corner has a different sign. The subdivision algorithm is simple: If either all u components of a quad have the same sign or if all v components of a quad have the same sign, we can definitely be sure that no critical point exists. If this is not the case, the quad is subdivided into four subquads and the processes is repeated for each of them. Compute the subdivision for one step and decide in which subquad you might find critical points! V01 = (+2) B V0o= =(+3) a) Compute interpolation. A (1) (2) (3) 0 (4) V11 V₁₁ = (+50) E V10 = D A: (3.5,9) B: (-2.5 5.5) C: (-0.75, 3.75) D:(1.2) E: (-5.-1.5) b) Classfiy subquads (1) to (4) (1) no critical point (2) no critical point (3) no critical point (4) continue subdivision
Given is a 2D vector field with the vectors Voo ( V10- The velocities are given at the corners of a quad and we can assume a bilinear interpolation. We intend to find the critical points of this vector field by using a recursive subdivision algorithm. In other words, we look for zero-crossings in the u component and the v component. Since we bilinearly interpolate the velocity components, we know that a zero-crossing can only exist if at least one corner has a different sign. The subdivision algorithm is simple: If either all u components of a quad have the same sign or if all v components of a quad have the same sign, we can definitely be sure that no critical point exists. If this is not the case, the quad is subdivided into four subquads and the processes is repeated for each of them. Compute the subdivision for one step and decide in which subquad you might find critical points! V01 = (+2) B V0o= =(+3) a) Compute interpolation. A (1) (2) (3) 0 (4) V11 V₁₁ = (+50) E V10 = D A: (3.5,9) B: (-2.5 5.5) C: (-0.75, 3.75) D:(1.2) E: (-5.-1.5) b) Classfiy subquads (1) to (4) (1) no critical point (2) no critical point (3) no critical point (4) continue subdivision
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For the 1.square there is a sign change,but it is stated as "no critical point"I couldn't understand it ,please explain me
Transcribed Image Text:Given is a 2D vector field with the vectors Voo (
V10-
The velocities are given at the corners of a quad and we can assume a bilinear interpolation. We intend to find the critical points of this vector field by using a recursive subdivision algorithm. In other words, we look for zero-crossings in the u
component and the v component. Since we bilinearly interpolate the velocity components, we know that a zero-crossing can only exist if at least one corner has a different sign. The subdivision algorithm is simple: If either all u components of
a quad have the same sign or if all v components of a quad have the same sign, we can definitely be sure that no critical point exists. If this is not the case, the quad is subdivided into four subquads and the processes is repeated for each of
them. Compute the subdivision for one step and decide in which subquad you might find critical points!
V01 = (+2)
B
V0o=
=(+3)
a) Compute interpolation.
A
(1)
(2)
(3)
0
(4)
V11
V₁₁ = (+50)
E
V10 =
D
A: (3.5,9)
B: (-2.5
5.5)
C: (-0.75, 3.75) D:(1.2)
E: (-5.-1.5)
b) Classfiy subquads (1) to (4)
(1) no critical point
(2) no critical point
(3) no critical point
(4) continue subdivision
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