You Are Here: Coordinate Systems and Transformations

  • Kurt Cagle


In 1649, the French philosopher and mathematician Rene Descartes took a position with the Swedish Queen Christina as Royal Mathematician (see Figure 3-1). A few months into his stay, however, the cold and gloom of that northern country soon forced him into an extended bed-rest while he struggled (ultimately unsuccessfully) against a cold that turned into pneumonia. One day, while in bed, he watched an ant as it made its way up a wall and onto the ceiling, and he began wondering what the shortest path that the ant could take across the walls was to get from one point to another. The ruminations proved to be the foundation for Cartesian coordinate systems, where every point in a plane is assigned a pair of numbers corresponding to specific locations. Other than providing the morale that laying in bed all day can actually accomplish something useful, this development also laid the ground for most of modern mathematics and computer graphics.


Coordinate System Local Coordinate System Affine Transformation Absolute Unit Child Element 
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© Kurt Cagle 2002

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  • Kurt Cagle

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