1. Let RE SO(3), a unit vector u denote the axis-angle satisfying: - R = 1 + sin 0 [u] x + (1 − cos 0)[u] ² a) What is the determinant of [u]x? / b) In epipolar geometry, we have the fundamental matrix F. Show the determinant of F det (F) =0. (Hint: det (A) det (B) = det (AB))( c) Given an arbitrary vector a= [1,0,0]T, and a 3D rotation transformation ,0] and the angle =, what is the a' T TT represented by axis u = 培 transformed from vector a with the 3D rotation?
1. Let RE SO(3), a unit vector u denote the axis-angle satisfying: - R = 1 + sin 0 [u] x + (1 − cos 0)[u] ² a) What is the determinant of [u]x? / b) In epipolar geometry, we have the fundamental matrix F. Show the determinant of F det (F) =0. (Hint: det (A) det (B) = det (AB))( c) Given an arbitrary vector a= [1,0,0]T, and a 3D rotation transformation ,0] and the angle =, what is the a' T TT represented by axis u = 培 transformed from vector a with the 3D rotation?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Let RE SO(3), a unit vector u denote the axis-angle satisfying:
R = I + sin 0 [u]x + (1 - cos 0)[u]
a) What is the determinant of [u]x?/
b) In epipolar geometry, we have the fundamental matrix F. Show the
determinant of F det (F)=0. (Hint: det (A) det (B) = det (AB)) (
c) Given an arbitrary vector a = [1,0,0], and a 3D rotation transformation
T
represented by axis u = [₁0] and the angle 0 = , what is the a'
-
transformed from vector a with the 3D rotation?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9dd77f94-a5e7-47d3-a2ba-eff6d53f0d48%2F1b9e860a-1a4e-4458-a714-7d5aca60c15a%2Fb3icur_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let RE SO(3), a unit vector u denote the axis-angle satisfying:
R = I + sin 0 [u]x + (1 - cos 0)[u]
a) What is the determinant of [u]x?/
b) In epipolar geometry, we have the fundamental matrix F. Show the
determinant of F det (F)=0. (Hint: det (A) det (B) = det (AB)) (
c) Given an arbitrary vector a = [1,0,0], and a 3D rotation transformation
T
represented by axis u = [₁0] and the angle 0 = , what is the a'
-
transformed from vector a with the 3D rotation?
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