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ArtistA perspective drawing, showing construction lines, depicting several beautiful purple-haired women wearing purple velvet dresses, and several beautiful pink-haired women wearing multicoloured flouncy-sleeved tie-dye kaftans. They continue on toward the vanishing point.
As is well-known, 3D graphics uses matrix multiplication to transform the array of object polygons into world coordinates and the perspective projected viewport image.
VDU <:: perspmatrix +.* worldview +.* objectposn +.* itemarray
Each "+.*" operator represents a 4*4 H-matrix multiplication, where the H-matrices (homogenous matrices) are 4 by 4 tables of coefficients, producing rotations, translations, and scaling.
The top left hand corner of an H-matrix takes the form :
cos ø, sin ø
-sin ø, cos ø
where ø is the angle of rotation. We can also use a quaternion (w + ix + jy + zk) to represent 4vectors, to encode the top left 3*3 partial matrix, and a further displacement quaternion to be added to the result to represent the translation (3position) of the object in the room. The remaining matrix element (M[4][4]) represents the perspective factor, by which the projection matrix divides the 3D coordinates in order to scale the objects into the distance (Z axis).
KDS5000 used a similar perspective pipeline of matrix/quaternion operations, held in the Language Card (Apple ][ 16K ram card) in order to produce perspective views of user-designed kitchens in 1981 on the Apple ][. The kitchen manufacturer's catalog was held on Disk Volume 2, consisting of a database of kitchen cabinet shapes (::SHAPEF::) and manufacturer dimensions (::MANUFS::), along with the representation of the user's kitchen units as an array of polygons (::MEMDMP::). A separate Seg held a price list of each kitchen cabinet and accessories by manufacturer. Meanwhile, Disk Volume 1 held the "apps", namely ::CHOICE:: (a form filled in by the user, selecting colours and profiles), ::DESIGN:: (the pointer-driven screen display editor), and ::COSTNG:: (the costing and invoicing program).
