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• Indicate coordinate systems with every point or matrix – Point: p object – Matrix: M object world • Resulting transformation equation: p camera = (C camera world)‐1 M object world p object • In source code use similar names: – Point: p_object or p_obj or p_o – Matrix: object2world or obj2wld or o2w
Lecture L3 - Vectors, Matrices and Coordinate Transformations. By using vectors and defining appropriate operations between them, physical laws can often be written in a simple form. Since we will making extensive use of vectors in Dynamics, we will summarize some of their important properties.
We can represent general transformations of homogeneous coordinates by matrices. This idea has been used widely in geometric modeling to describe the relationships between objects.
Make it very explicit what coordinate system is used. Understand how to change coordinate systems. Understand how to transform objects. Understand difference between points, vectors, normals and their coordinates.
Many common spatial transformations, including translations, rotations, and scaling are represented by matrix / vector operations. Changes of coordinate frames are also matrix / vector operations. As a result, transformation matrices are stored and operated on ubiquitously in robotics.
Unit 5: Change of Coordinates Lecture 5.1. Given a basis Bin a linear space X, we can write an element v in X in a unique way as a sum of basis elements. For example, if v = 3 4 is a vector in X = R2 and B= fv 1 = 1 1 ;v 2 = 1 6 g, then v = 2v 1 + v 2. We say that 2 B are the B coordinates of v. The standard coordinates are v = 3 4 are assumed ...
Example. Given the previous figure, what is the angle φ between the vector to point Q = {1, 2} and the X coordinate axis? Answer. Project a line segment parallel to the Y axis that extends from the X axis to point Q at the head of the vector. The length of that line segment is 2.
