The transformation between two coordinate systems is represented by a 3-by-3transformation matrix written as Because a transformation matrix has only six elements that can be changed, it isusually specified in PDF as the six-element array [abcdef].
Transformation vector definition.
Translations are specified as[1001txty], where txand tyare the distances totranslate the origin of the coordinate system in the horizontal and verticaldimensions, respectively. •Scaling is obtained by [sx00sy00]. This scales the coordinates so that 1unit in the horizontal and vertical dimensions of the new coordinate system isthe same size as sx and sy units, respectively, in the previous coordinate system. •Rotations are produced by [cosθsinθ−sinθcosθ00], which has the effectof rotating the coordinate system axes by an angle θ counterclockwise. •Skew is specified by [1tanαtanβ100], which skews the xaxis by an angleα and the y axis by an angle β.
Transformation vector component definitions.
But what if all things aren’t equal? If you’re choosing between working with someone who’s a trusted friend and a 7 out of 10 on competence, versus a stranger who’s a 9 out of 10 on competence, who should you pick? Answer: if the trusted friend is a fast learner, pick the trusted friend. Trade up on trust, even if it means you have to trade down on competency a bit. In other words, choose to work with someone you know who’s a fast learner over someone who’s a bit more qualified who you do not know. Assuming the person you know and trust is in Permanent Beta, he or she can round out their gaps in skills or experience in short order. I benefitted from Reid’s philosophy on this personally. For some assignments, I was not the most qualified person in the world, or even the most qualified within his own network. But given that we a) completely trust each other, b) I have a good sense of his priorities and values and preferences and he has a good sense of my own priorities and values and preferences, and c) I’m a quick learner, we could move at lightning speed together on projects.
This is the reason why personal networks (and individual biases) are so important to recognize and account for. What are the opportunities that you are providing to others to earn your trust? How do you assemble your social network & team?
Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Arts
This is where the thesis was submitted.