- THE OUTLAW TRIAD DEMO-SERIES - 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴퀼 PART XIV �컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Written by : Vulture/OT Code in : Pascal Topic : Hidden face removal 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Introduction �컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Welcome to the Outlaw Triad demo-series! In these series we will be talking about programming demo-effects in either pascal or assembler. Theory behind the effects shall be discussed while a full sourcecode is also provided. Another one on 3d! This time we will implement code to perform hidden face removal. With this, you can skip drawing faces which would not be visible on the screen when the entire object has been draw. So if coded correctly, this method will speed up your engine quite a bit. And 3d engines are never fast enough, right? Enjoy! 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴퀼 Theory �컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� - HIDDEN FACE REMOVAL - Well, it's time to do some optimizing. Sofar, we've made a rather nice 3d engine which is able to perform some cool effects but of course, we want it to be faster. Hmm, we can do that by using more assembler code or by looking at the program and trying to code it more efficiently. We're going to use the latter, that is, we are going to implement code to perform socalled hidden face removal. Now, what's that? Well, that's an easy one (did I say that before? :-)). For example, a cube consist of six sides. Sofar, when drawing a cube, we actually painted all six sides. But only three of them are visible from whatever side you are looking at the object (if you rotate on all three axis, otherwise even less sides are visible!). So why draw polygons which are not visible? That's not necessary at all! Here's where hidden face removal comes in. It involves methods to determine if the side you are about to draw is visible or not. Ok, question is how hidden face removal works. Well, as usual, there are several ways to determine if a face should or should not be drawn on the screen. I will show you a basic one which is good enough for objects with little or no overlapping of polygons. Here we go... To put it simply, it's a matter of clockwise versus anti clockwise. We need to setup the objects polygons so that the 3d points of visible polygons are in a clockwise order. The 3d points of non-visible polygons have to be setup in an anti clockwise order (remember, you do this when DEFINING the object!). Now, when drawing, you only draw those polygons from which the 3d points are clockwise. And if they are anti clockwise, don't draw the poly. Examine this: 1旼컴컴컴컴컴컴컴컴컴�2 � � � � � � � � � � � � � � � � 4읕컴컴컴컴컴컴컴컴컴�3 This is the front (visible side) of a polygon, ok? The 3d points are ordered in a clockwise direction. Now if you rotate it so you can see the back of the polygon, the 3d points will be ordered like this: 2旼컴컴컴컴컴컴컴컴컴�1 � � � � � � � � � � � � � � � � 3읕컴컴컴컴컴컴컴컴컴�4 They are ordered in an anti clockwise direction! Obviously, when you rotate this polygon again so that the points are in a clockwise direction again, you will see the front of the polygon again. So remember: clockwise = front anti clockwise = back Where the front of the polygon is visible (of course). Well, this means that we only have to find out if the polygon points are in a clockwise direction after rotation of the polygon. And, like said before, if they are clockwise, we draw the polygon. Otherwise we don't! Now how do we code something like this? Ok, to check if the 3d points are in a clockwise direction, we need to find the normal of the polygon. The normal of a polygon is at 90 degrees to the surface of the polygon. Like this: � Normal � � � 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Polygon surface (note: you should imagine this polygon in 3d, of course) Remember we talked about normals in the previous trainer on lightsourcing? Read that doc for more info on normals. Anyway, we are working in 3d so the normal consist of x,y,z points also. Now we need three (not four) 3d points from the polygon to find the normal. The normal can be found like this: Xn=(y2-y1)*(z1-z3)-(z2-z1)*(y1-y3) Yn=(z2-z1)*(x1-x3)-(x2-x1)*(z1-z3) Zn=(x2-x1)*(y1-y3)-(y2-y1)*(x1-x3) Don't ask me to explain how these formulas work cos I don't understand them either. My math really sux! I just know they work and that's enough... :-) If you want to know more about normals, go read any mathbook. There should be something in it about normals and stuff like that. And again, read the previous trainer for more info. Anyway, we don't even need to calculate the entire normal vector, that is, all three (x,y,z) components. We only need the Z (depth) component so our normal is determined by: Normal := (x2-x1)*(y1-y3)-(y2-y1)*(x1-x3); Now when we rotate the polygon on all three axis, the polygon is visible when the normal is a positive value. The polygon isn't visible when the normal is a negative value. Thus, if the normal is positive, the polygons 3d points are clockwise. Otherwise they are anti clockwise. And that's all there is to it! Just remember: - Setup 3d points of visible polygons in a clockwise direction - Setup 3d points of nonvisible polygons anti clockwise - Now rotate object polygons - Determine Z normal of polygon - If Z normal > 0, draw polygon If you implement this correctly, your engine will be a LOT faster. See the example source for the result. Compare this with the previous trainers to see the difference in speed! The source is simply the previous trainer on light sourcing with these particular Z normal calculations added to it. Hint: In a previous trainer (#12), we calculated the entire face normal in order to find the color of a polygon. Now, using that facenormal, you take the z-component. If it's BELOW zero, don't draw the polygon. That's all. Saves you a couple of calculations too. So why don't you try to implement that method instead? Shouldn't be too hard... For questions, chatting or for suggestions for future trainers, mail me. If you spot inaccuracies, please mail me at once so I can correct anything wrong in these textfiles! Don't hesitate to contact me (or any other member of OT) cos we're always in for a chat... :-) That's all for now. Happy coding! -Vulture/Outlaw Triad- 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴퀼 Distro Sites �컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� All our releases are available at these fine boards: BlueNose World HQ +31 (0)345-619401 The Force Distrosite +31 (0)36-5346967 Bugs'R'Us Distrosite +31 (0)252-686092 The 7 Angels Distrosite +31 (0)715-148377 More distros wanted! ShockWave South African HQ +27 (011)888-6345 (preferably outside Society HQ United States HQ +1 (518)465-6721 of the Netherlands) ACe World Brazilian HQ +55 (21)-259-8847 Corps Elite Canadian HQ +403 (ITS)-PRIVATE Dark Genesis Canadian Distro +1 (250)561-2850 Also check the major FTP/WWW sites for Outlaw Triad productions. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Contact �컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� Want to contact Outlaw Triad for some reason? You can reach us at our distrosites in Holland. Or if you have e-mail access, mail us: Vulture (coder/pr) comma400@tem.nhl.nl Our internet homepage: http://www.tem.nhl.nl/~comma400/vulture.html These internet adresses should be valid at least till june 1997. 컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 Quote: Anybody can win, unless there happens to be a second entry