Euler Angles

118 Pages·2013·2.67 MB·English

Computer Vision Group
Prof. Daniel Cremers
Visual Navigation
for Flying Robots
3D Geometry and Sensors
Dr. Jürgen Sturm
Organization: Lab Course
 Robot lab: room 02.05.14 (different room!)
 Lecture: room 02.09.23 (here)
 You have to sign up for a team before May 2nd
(team list in student lab)
 After May 2nd, remaining places will be given to
students on waiting list
 First exercise sheet is due next Tuesday 10am
Visual Navigation for Flying Robots 2 Dr. Jürgen Sturm, Computer Vision Group, TUM
Today’s Agenda
 Linear algebra
 2D and 3D geometry
 Sensors
 First exercise sheet

Visual Navigation for Flying Robots 3 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vectors
 Vector and its coordinates

 Vectors represent points
in an n-dimensional space

Visual Navigation for Flying Robots 4 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vector Operations
 Scalar multiplication
 Addition/subtraction
 Length
 Normalized vector
 Dot product
 Cross product
Visual Navigation for Flying Robots 5 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vector Operations
 Scalar multiplication
 Addition/subtraction
 Length
 Normalized vector
 Dot product
 Cross product
Visual Navigation for Flying Robots 6 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vector Operations
 Scalar multiplication
 Addition/subtraction
 Length
 Normalized vector
 Dot product
 Cross product
Visual Navigation for Flying Robots 7 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vector Operations
 Scalar multiplication
 Addition/subtraction
 Length
 Normalized vector
 Dot product
 Cross product
Visual Navigation for Flying Robots 8 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vector Operations
 Scalar multiplication
 Addition/subtraction
 Length
 Normalized vector
 Dot product
 Cross product

are orthogonal if
is lin. dependent from if
Visual Navigation for Flying Robots 9 Dr. Jürgen Sturm, Computer Vision Group, TUM
Vector Operations
 Scalar multiplication
 Addition/subtraction
 Length
 Normalized vector
 Dot product
 Cross product

Visual Navigation for Flying Robots 10 Dr. Jürgen Sturm, Computer Vision Group, TUM