### Table des matières

## PART 20 : Faces sorting

Hi all! It has been a _long_ time since my last trainer (as I am sure many of you have noticed) A lot has happened between now and the last trainer… but for once I won't bore you with the details ;) I do have a full time job though, coding C++ applications.

I have taken over the production of the PCGPE from Mark Feldman. He is mailing all the articles written so far, and as soon as I get them I will get to work on releasing the PCGPE II. Mark is working on the Windows GPE.

This trainer is on 3d hidden face removal and face sorting. I was going to add shading, but that can wait until a later trainer. For conveniance I will build on the 3d code from tut 16(?). The maths for face removal is a bit tricky, but just think back to your old High School trig classes.

I have noticed that in my absence, one or two people have started their own trainer series. Read Hornet DemoNews for a great column by Trixter covering some of the more tricky demo effects.

Well, on with the trainer!

If you would like to contact me, or the team, there are many ways you can do it :

1) Write a message to Grant Smith/Denthor/Asphyxia in private mail on the ASPHYXIA BBS. 2) Write to : Grant Smith P.O.Box 270 Kloof 3640 Natal South Africa 3) Call me (Grant Smith) at (031) 73 2129 (leave a message if you call during varsity). Call +27-31-73-2129 if you call from outside South Africa. (It's YOUR phone bill ;-)) 4) Write to denthor@beastie.cs.und.ac.za in E-Mail. 5) Write to asphyxia@beastie.cs.und.ac.za to get to all of us at once.

NB : If you are a representative of a company or BBS, and want ASPHYXIA to do you a demo, leave mail to me; we can discuss it. NNB : If you have done/attempted a demo, SEND IT TO ME! We are feeling quite lonely and want to meet/help out/exchange code with other demo groups. What do you have to lose? Leave a message here and we can work out how to transfer it. We really want to hear from you!

http://goth.vironix.co.za/~denthor (WWW) ftp.eng.ufl.edu pub/msdos/demos/code/graph/tutor (FTP)

### Face Sorting

There are many ways to sort faces in a 3d object. For now, I will show you just about the easiest one of the lot.

Say you have to polygons….

------P1 ------------------P2 Eye

As you can see, P1 has to be drawn before P2. The easiest way to do this is as follows:

On startup, find the mid point of each of the polys, through the easy equations,

x = (P2.1.x + P2.2.x + P2.3.x + p2.4.x)/4 y = (P2.1.y + P2.2.y + P2.3.y + p2.4.y)/4 z = (P2.1.z + P2.2.z + P2.3.z + p2.4.z)/4

NOTE : For a triangle you would obviously only use three points and divide by three.

Anyway, now you have the X,Y,Z of the midpoint of the polygon. You can then rotate this point with the others. When it comes time to draw, you can compare the resulting Z of the midpoint, sort all of the Z items, and then draw them from back to front.

In the sample program I use a simple bubble sort… basically, I check the first two values against each other, and swap them if the first is bigger then the second. I continue doing this to all the numbers until I run through the entire list without swapping once. Bubble sorts are standard seven computer science topics… perhaps borrow a text book to find out more about them and other (better) sorting methods.

The above isn't perfect, but it should work 90% of the time. But it still means that when you are drawing a cube, you have to draw all 6 sides every frame, even though only three or so are visible. That is where hidden face removal comes in…

### Hidden Face Removal

Pick up something square. A stiffy disk will do fine. Face it towards you, and number all the corners from one to four in a clockwise direction.

1 +-------------+ 2 | | | | | | | | 4 +-------------+ 3

Now rotate the stiffy disk on all three axese, making sure that you can still see the front of the disk. You will notice that whenever you can see the front of the disk, the four points are still in alphabetical order. Now rotate it so that you can see the back of the stiffy. Your points will now be :

2 +-------------+ 1 | | | | | | | | 3 +-------------+ 4

The points are now anti-clockwise! This means, in it's simplest form, that if you define all your poygon points in a clockwise order, when drawing you ignore the polys that are anticlockwise. (Obviously when you define the 3d object, you define the polygons facing away from you in an anticlockwise order)

To find out weather a poly's points are clockwise or not, we need to find it's normal. Here is where things start getting fun.

In school, you are told that a normal is perpendicular to the plane. In ascii :

| Normal | | --------------------------- Polygon

As you can see, the normal is at 90 degrees to the surface of the poly. We must extend this to three dimensions for our polygons. You'll have to trust me on that, I can't draw it in ascii :)

To find a normal, you only need three points from your poly (ABC) :

A(x0,y0,z0), B(X1,Y1,Z1), C(X2,Y2,Z2)

then the vector normal = AB^AC = (Xn,Yn,Zn) with

Xn=(y1-y0)(z0-z2)-(z1-z0)(y0-y2) Yn=(z1-z0)(x0-x2)-(x1-x0)(z0-z2) Zn=(x1-x0)(y0-y2)-(y1-y0)(x0-x2)

We are interested in the Z normal, so we will use the function :

normal:=(x1-x0)(y0-y2)-(y1-y0)(x0-x2);

The result is something of a sine wave when you rotate the poly in three dimensions. A negative value means that the poly is facing you, a posotive value means that it is pointing away.

The above means that with a mere two muls you can discount an entire poly and not draw it. This method is perfect for “closed” objects such as cubes etc.

I am anything but a maths teacher, so go borrow someones math book to find out more about surface normals. Trust me, there is a lot more written about them then you think.

An extension of calculating your normal is finding out about light-sourcing your polygons. Watch for more information in one of the next few tutors.

A combination of the above two routines should work quite nicely in creating 3d objects with little or no overlapping. The example file will show you the two methods and how well they work.

### In closing

As you can see, the above was quite easy. I have a few ideas for tut 21, so keep watch for it. Also keep an eye open for PCGPE ][ (but don't mail me asking when it's due! I already get too many of those!

My sister got married a few days ago. The worst part was that I was forced to cut my hair. My hair was quite long (slightly longer then when the pic on my web page was taken), and it is all quite depressing. Anyway, the wedding was great, so it wasn't all for nothing.

I hope to get tut 21 and possibly 22 out before christmas, but I will be on holiday from the 18th. I will be in Cape Town sometime after christmas day for a week or two, so if you're there I'll meet you on the cable car

I wrote a quote for this tut, but I have decided I didn't like it. I'll try do better for tut 21 ;)

Byeeeee…. Denthor 14-12-95

PS. I seem to have lost my list of distribution sites… could you all re-mail me your details? Thanks.

Denthor VGA Trainer