PRENTICE DESIGN NOTES

Sean E. O'Connor

Introduction Software Design

Introduction

Artist's software assistant.

Software Design

Prentice Screen

Perspective Transform Mathematics

a = (0, 0, -d) - (0, H/2, 0) = (0, -H/2, -d)

b = (-W/2, H/2, 0) - (0, H/2, 0) = (-W/2, 0, 0)

n = a x b =
| i    j    k |
| 0   -H/2 -d | 
| -W/2 0    0 |

= (0, dW/2, -WH/4) p = (0, H/2, 0) q = (x, y, z) Clip if n . (q - p) > 0

(  0    )   ( x - 0   ) 
( dW/2  ) . ( y - H/2 ) > 0
( -WH/4 )   ( z - 0   )

    dW/2 (y -H/2) -zWH/4 > 0
    or
    ydW/2 -dWH/4 -zWH/4 > 0
    implies
    -Hd + 2dy - Hz > 0

rearranging we get y / (d + z) > (H/2) / d which is just the same criterion using similar triangles. The eye's half viewing angle is tan^-1( (H/2) / d ).

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