Object models for computer aided design

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118 All of these transfor􁪽􋵡atio􁪽􋵳s ITL:st be :0 allOW flexibility 􁪽􋵮n chcosing coer6ina􁪽􋵥e spaces, o􁪽􋵥e can 6efi􁪽􋵥e 􁪽􋵲ransforrrations 􁪽􋵨hich ITap the coor􁪽􋵩inates fer the ffioroe􁪽􋵴t, t􁪽􋵡a: all ccordi􁪽􋵡ates are definec l􁪽􋵡 a single de£initio􁪽􋵳 s c ec e , t r.e n ene' can look at the task of o e ne r a t i ne a picture largely as a rr2p􁪽􋵩ing from this definition space into the coordinate systerr. of the output device. The tr􁪽􋴚􁪽􋵳sfcrrraticns necessary for a perspective mapping of 3D ccorcir.ates c􁪽􋵴to a 2D 􁪽􋵩isplay Gevice are illustrated in The retation, translation, anc tra􁪽􋵳sfcr􁪽􋴲2tions 􁪽􋵡ay be dec0􁪽􋴚􁪽􋵯os5d into rotation rratrices a trar.slation r.atrix, and 2 5 C a 1. i :-l C; ;:- a t r i x • The" 'n' inc 0 'n' " t ran s for IT a t ion i 5 a s cal :.. 􁪽􋴹 9 cocrc5inates into a f r u s t r urr. (trc􁪽􋵣ca:􁪽􋵤d ?yr􁪽􋵲rrid) of vision. Those carts of the 􁪽􋵩icture cc t s i c s t:.e frustrurr r.us t be "clipped" to avoid "v r e c+e r c o nc " pr oc l ens and then mappe d onto the d i p l a y e r e a 􁪽􋴚􁪽􋵲r£cr􁪽􋵥e6 in order to generate c picture. cevices pe::-fc::-rr - 1 , c._ ..... er -_ .. :--c. _ c: t r.e s e :':3r.sfcr􁪽􋴲2tio􁪽􋵳s as harcware functions. For those d􁪽􋵶vices