coordinates - COORDINATES/DISTANCES O Knill Math21a...

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Unformatted text preview: COORDINATES/DISTANCES O. Knill, Math21a HOMEWORK: 11.2: 8,12,20,58,60 CARTESIAN COORDINATE SYSTEMS. A point on the line is labeled by a single coordinate x , a point in the plane is fixed by 2 coordinates ( x, y ) and a point in space is determined by three coordinates ( x, y, z ). Depending on which coordinates are positive, one can divide the line, the plane or the space into half lines , quadrants or octants . 1D space = line =2 half lines 2D space = plane=4 quadrants 3D space = space=8 octants x x y (x,y) x y z (x,y,z) CHOICE OF COORDINATE SYSTEM. Fixing the three coordinate axis determines a coordinate system in space. The choice of the convenient coordinate system depends on the situation. On earth for example the coordinate system is often chosen so that the z- axis points ”up” and perpendicular to the ground. These directions depend on the position on earth of course. EXAMPLE. Usually, we draw the coordinate system, such that the x,y coordinates are on the ground and the z-coordinate points ”up”. In two dimensions, on a sheet of paper, the x-coordinate usually is chosen to point ”east” and the y-coordinate to point ”north”. EXAMPLE. PHOTOGRAPHERS COORDINATE SYSTEM: In 3D graphics like computer games, virtual reality or ray tracing, it is custom to have the y-axis pointing up, the x-axis to the right and the z axis in front....
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