(from Your Spectrum 16, July 1985)



3D DAZE



It's here - the ultimate in 3D graphics. Mr MegaBasic, Mike Leaman

shows another side to his talents with a program that'll transport you

into the third dimension.



How often have you wished you could create the smooth three

dimensional graphics like the ones Ultimate has made famous in

Knight Lore and Alien 8? Well, now you can - almost. Of course, the

Ultimate team doesn't actually program on the Spectrum but on a

much larger machine, then squirts it down. But you can get pretty

close with these machine code routines that'll enable you to move

objects in three dimensions.



The tricky bit about 3D graphics is making sure that the objects

meant to be at the front of the display look as though that's where

they are. So, how's it done? Well, briefly, you have to draw the

objects at the back first and then work your way forward.



I've tackled it by keeping a list of all the objects that appear on the

screen and this list contracts and expands according to how many

objects there are. The list starts at 64700 and each entry consists of

four bytes. Understanding these is the tricky bit. The first byte is the

'X' co-ordinate, the second the 'Y'-co-ordinate, the third the 'Z' co-

ordinate and the last byte is the objects' code number. The easiest

way to understand these co-ordinates is to think in terms of a

matchbox - hold it up in front of you. 'Y' runs along the bottom from

left to right, 'X' runs up the edge that goes from the top to bottom and

'Z' is the co-ordinate that travels along the edge that's going away

from you. If you're still in trouble or you want to go into further depth,

take a look at the articles on 3D plotting in YS issues 2 and 3.



Now back to that list. Those objects that are to be placed at the back

come at the start of the list. Then each time an object is displayed or

erased, the list is scanned and the appropriate action taken. The

shape of each object is stored in 64 bytes of RAM and I've included

three objects with the code. The shape list starts at 65047, so that's

where you'll find the first object, then the second object is at

65047+64 and so on. The 64 bytes of character info is split into two

halves - the first 32 bytes represent the actual shape of the object,

similar to the way you would define a UDG but with much more

information because of the third dimension. This is followed by the

second 32 byte block that describes the shape of the mask needed to

erase the object.



Now take a look at the code. It's in two parts - the first part that does

all the work starts at 64000 and the second part contains shape info

for the three example objects and starts at 65047. Here's how you

enter the code. First type in the Hex loader and save it - you may

need it later. Now RUN it and it'll automatically lower RAMtop so that

there's space for the code. You'll then be asked for a start address -

for the main block, enter 64000 and for the shape info enter 65047.

Once you've put those in, you can press on with entering the actual

code. For starters, you'l1 be prompted with an address - look at the

main listing - the first prompt'll be 64000 so you should enter F3. The

second prompt is 64001, so you'll enter CD93FB, remembering, of

course, not to enter any spaces.



When you've reached the end of a block, enter 'S' - the loader will

then ask you for a Checksum. For the main block enter 79933, then

for the shape data enter 17774. Now the loader checks the code for

errors. If it finds one you'll just have to go back and re-check. As

soon as you've entered the main block, carry on and enter the shape

data and then save the code using:



SAVE "code" CODE 64000,1368



Now enter NEW and type in the test program, again remembering to

save it just in case the code crashes. At last, you're there! If all's well,

you should be greeted by a number of bubbles moving across the

screen in full and glorious 3D.



OK, I can already hear you asking how you can use the routines

yourself. As I've said, it takes four parameters to describe an object -

the 'X', `Y' and 'Z' co-ordinates plus the shape code that defines what

shape the object is to take. These parameters are passed to the

machine code in four locations:



64637 'Y' co-ordinate

64638 'X' co-ordinate

64639 shape code

64640 'Z' co-ordinate



Well, there are three routines that you can usefully adapt. The first is

the one that covers the background. To understand this, you must

know that the middle third of the screen is printed first, so you can

use this part as a back drop. So, design your back drop and save it

into memory which you can do as follows: first, reserve an area of

memory using the CLEAR command, then POKE the address of this

area into locations 64635 and 64636. Once you've drawn your

backdrop, call the routine at 64423 and this'll save the middle third of

the screen into memory.



Now to print an object POKE its co-ordinates into the correct

memory locations and call the routine at 64489. Then to erase an

object POKE its co-ordinates into the correct locations and call the

routine at 64556.



You'll also have to remember to execute POKE 64703,0 before you

start printing - that way you'll clear the display list. And finally a word

of warning - so that the routine's as fast as possible I've left out all the

error checking. You'll have to make sure that none of your 3D objects

goes wandering off the edge of the screen or you may find yourself

with a system crash.



And now onto next month. Watch out for a 3D graphic designer that'll

let you create your own clockwork mice or mutant daleks. Plus, for all

the clever people who've mastered YS MegaBasic, I'll be showing you

how to convert this month's machine code into MegaBasic. All you'll

have to use then are a number of new Basic commands. Of course,

all you poor socially deprived Speccy owners still relying on Sinclair

Basic will have to resort to the infamous commands POKE and USR.

It's a tough life!