wozniak@utkux1.utk.edu (Bryon Lape) (09/30/89)
Does anyone know of an algorithm for translating 3-d to 2-d so that I can plot on my IBM-PC? I wish to display all axises at a rotation suitable to view everything. -bryon-
bill@hpcvlx.cv.hp.com (Bill Frolik) (10/03/89)
| Does anyone know of an algorithm for translating 3-d to 2-d so | that I can plot on my IBM-PC? I wish to display all axises at a The easiest way to map [x,y,z] into [x',y'] without perspective: x' = x y' = y The easiest way to map [x,y,z] into [x',y'] with perspective: x' = (x*d)/(z+d) y' = (y*d)/(z+d) where d, a constant, the distance from the viewer's eye to the screen, determines the amount of perspective. For derivation of these equations you examine a couple of triangles. The screen glass is at z=0, with increasing z going deeper into the screen; the center of the screen is at x=y=0; the viewer is distance d from the screen. In the diagram, the ratio of the lengths of side VA to VB will be the same as side Ap1 to Bp2. len(VA) len(Ap1) d x' ------- = -------- == --- = --- (and similar for y') len(VB) len(Bp2) d+z x B---------*p2 | /(x,y,z) | / ------------A------*p1--- <--screen (z=0) | | /(x',y') | | / d | / | | / | | / | |/ V <-- viewer A good value for d might be to set it equal to the width of the screen. (If your screen is 1024 units wide, i.e. screen X runs from something like -512..+511, set d=1024.) ________________________________________ Bill Frolik Hewlett-Packard Co. hp-pcd!bill Corvallis, Oregon
kennedy@sunshine4.DAB.GE.COM (Woody Kennedy) (10/10/89)
In article <1133@utkcs2.cs.utk.edu> wozniak@utkux1.utk.edu (Bryon Lape) writes: > > Does anyone know of an algorithm for translating 3-d to 2-d so >that I can plot on my IBM-PC? I wish to display all axises at a >rotation >suitable to view everything. > >-bryon- According to the authoritative volume "Principles of Hyperactive Computer Graphics", available from Acme publishing: The proper attainment of 3-d to 2-d transformation can be achieved by the party in question (Eatamus Roadrunnerus) obtaining one Anvilus Blackamus. A priori to the arrival of the object to be transformed (Runnimus Fastimus), the AB is elevated to a signicant altitude by means of a mechanical hoist or local mountinous prominitory. When the RF reaches the loci of descendance of the AB, the AB shall be released by the ER. Barring any unforseen collapse of the hoist or prominitory (which is almost guaranteed due to the nature of the problem) the RF shall be reduced from 3-d to 2-d, though it may sprout legs and walk away. -- Woody Kennedy, Software Engineer, Special Effects | Pay no attention to the General Electric Simulation & Control Systems Dept. | man behind the keyboard! kennedy@sunny.ge.com or +-----------------+-------------------------- (backbone)!ge-dab.ge.com!kennedy | Wanna' see something neat? Watch this...
wozniak@utkux1.utk.edu (Bryon Lape) (10/17/89)
Although my original post was very serious, I loved the reply!! Good ol' Buggs Bunny, Road Runner stuf!!!!!!!! -bryon-
mcooper@s.cs.uiuc.edu (10/20/89)
/* ---------- "Re: 3-d -----> 2-d" ---------- */ In article <1133@utkcs2.cs.utk.edu> wozniak@utkux1.utk.edu (Bryon Lape) writes: > > Does anyone know of an algorithm for translating 3-d to 2-d so >that I can plot on my IBM-PC? I wish to display all axises at a >rotation >suitable to view everything. > >-bryon- I hope I'm not being simplistic here, but it seems the easiest way to convert any 3D object into 2D is (assuming the object is made of polygons) sort the polygons by depth (z value) using a simple depth sort (or the painters' algorithm. Effective, but S-L-O-W) and then plot each polygon according to its x,y coords. Or are you asking something else? -Marc Cooper "When the going gets weird, mcooper@cs.uiuc.edu the weird turn pro." -Hunter S. Thompson University of Illinios, C-U
wozniak@utkux1.utk.edu (Bryon Lape) (10/21/89)
Since I posted the request for 3d--->2d conversion, I have received many different answers. Some good, so stupid, and so bad. What I want to do is the follows: Type in a function in 3 variables and plot them just like they are in my Calculus 3 book. -bryon-