text: Game Development Reference
  In-Depth Information
  F IGURE 2.3
  A vector as a movement in space.
  vector is the change along each axis. So
  x
  y
  z
  a
  =
  where x is the change in the position along the X axis from a 0 to a 1 ,givenby
  x
  =
  x 1
  x 0
  where x 0 is the X coordinate of a 0 and x 1 is the X coordinate of a 1 . Similarly for y
  and z .
  Position and change in position are really two sides of the same coin. We can
  think of any position as a change of position from the origin (written as 0 ,where
  each component of the vector is zero) to the target location.
  If we think in terms of the geometry of a vector being a movement from the ori-
  gin to a point in space, then many of the mathematical operations we'll meet in this
  chapter have obvious and intuitive geometric interpretations. Vector addition and
  subtraction, multiplication by a scalar, and different types of multiplication can all be
  understood in terms of how these movements relate. When drawn as in figure 2.3, the
  visual representation of an operation is often much more intuitive than the mathe-
  matical explanation. We'll consider this for each operation we meet.
explanation: The document is a reference text on game development, specifically discussing vectors and their mathematical representation. It explains how vectors can represent changes in position along the X, Y, and Z axes and how these changes can be understood geometrically. The text does not contain a specific question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: Game Development Reference
  In-Depth Information
  F IGURE 2.3
  A vector as a movement in space.
  vector is the change along each axis. So
  x
  y
  z
  a
  =
  where x is the change in the position along the X axis from a 0 to a 1 ,givenby
  x
  =
  x 1
  x 0
  where x 0 is the X coordinate of a 0 and x 1 is the X coordinate of a 1 . Similarly for y
  and z .
  Position and change in position are really two sides of the same coin. We can
  think of any position as a change of position from the origin (written as 0 ,where
  each component of the vector is zero) to the target location.
  If we think in terms of the geometry of a vector being a movement from the ori-
  gin to a point in space, then many of the mathematical operations we'll meet in this
  chapter have obvious and intuitive geometric interpretations. Vector addition and
  subtraction, multiplication by a scalar, and different types of multiplication can all be
  understood in terms of how these movements relate. When drawn as in figure 2.3, the
  visual representation of an operation is often much more intuitive than the mathe-
  matical explanation. We'll consider this for each operation we meet.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a reference text on game development, specifically discussing vectors and their mathematical representation. It explains how vectors can represent changes in position along the X, Y, and Z axes and how these changes can be understood geometrically. The text does not contain a specific question or a question and answer.
  
  Label: no-question