The TIA (as seen by the programmer)

7.0 Horizontal Positioning

The horizontal position of each object is set by writing to its associated reset register (RESP0, RESP1, RESM0, RESM1, RESBL) which are all strobe registers (they trigger their function as soon as they are addressed). That causes the object to be positioned wherever the electron bean was in its sweep across the screen when the register was reset. for example, if the electron beam was 60 color clocks into a scan line when RESP0 was written to, player 0 would be positioned 60 color clocks "in on the next scan line. Whether or not P0 is actually drawn on the screen is a function of the data in the GP0 register, but if it were drawn, it would show up at 60. Resets to these registers anywhere during horizontal blanking will position objects at the left edge of the screen (color clock 0). Since there are 3 color clocks per machine cycle, and it can take up to 5 machine cycles to write the register, the programmer is confined to positioning the objects at 15 color clock intervals across the screen. This course positioning is fine tuned by the Horizontal Motion, explained in section 8.0.

Missiles have an additional positioning command. Writing a 1 to D1 of the reset missile-to-player register (RESMP0, RESMP1) disables that missiles graphics (turns it off) and repositions it horizontally to the center of its associated player. Until a 0 is written to the register, the missiles horizontal position is locked to the center of its player in preparation to be fired again.

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See also: 'TIA 1A - TELEVISION INTERFACE ADAPTOR (MODEL 1A) - 4. Horizontal Position Counters'