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Normalized device coordinates

I am writing a library that deals with 2D graphic forms.

I'm just wondering why my coordinate system will range from [- 1, 1] for the x and y axis enter image description here

instead of [0, width] for x and [0, height] for y? enter image description here

I went to the last system because I felt it was straight ahead.

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From Jim Blinn The Journey Down The Graphic Pipeline, p. 138.

To begin with, at first it may seem like the easiest conversion: the normalized coordinates of the device into pixel space. Conversion

s_x * X_NDC + d_x = X_pixel s_y * Y_NDC + d_y = Y_pixel

The user / programmer performs the entire screen design at NDC. There are three unpleasant hardware realities that NDC hides from us:

  • The actual number of pixels in x and y.

  • Uneven distance between pixels in x and y.

  • Up and down for the Y coordinate. The NDC-to-pixel transformation will invert Y if you want the Y in NDC to point up.

...

 s_x = ( N_x - epsilon ) / 2 d_x = ( N_x - epsilon ) / 2 s_y = ( N_y - epsilon ) / (-2*a) d_y = ( N_y - epsilon ) / 2 epsilon = .001 a = N_y/N_x (physical screen aspect ratio)
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