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+Chapter 54\
+ 3-D Shading {#Heading1}
+------------
+
+### Putting Realistic Surfaces on Animated 3-D Objects {#Heading2}
+
+At the end of the previous chapter, X-Sharp had just acquired basic
+hidden-surface capability, and performance had been vastly improved
+through the use of fixed-point arithmetic. In this chapter, we’re going
+to add quite a bit more: support for 8088 and 80286 PCs, a general color
+model, and shading. That’s an awful lot to cover in one chapter
+(actually, it’ll spill over into the next chapter), so let’s get to it!
+
+### Support for Older Processors {#Heading3}
+
+To date, X-Sharp has run on only the 386 and 486, because it uses 32-bit
+multiply and divide instructions that sub-386 processors don’t support.
+I chose 32-bit instructions for two reasons: They’re much faster for
+16.16 fixed-point arithmetic than any approach that works on the 8088
+and 286; and they’re much easier to implement than any other approach.
+In short, I was after maximum performance, and I was perhaps just a
+little lazy.
+
+I should have known better than to try to sneak this one by you. The
+most common feedback I’ve gotten on X-Sharp is that I should make it
+support the 8088 and 286. Well, I can take a hint as well as the next
+guy. Listing 54.1 is an improved version of FIXED.ASM, containing dual
+386/8088 versions of **CosSin(), XformVec()**, and **ConcatXforms()**,
+as well as **FixedMul()** and **FixedDiv()**.
+
+Given the new version of FIXED.ASM, with **USE386** set to 0, X-Sharp
+will now run on any processor. That’s not to say that it will run fast
+on any processor, or at least not as fast as it used to. The switch to
+8088 instructions makes X-Sharp’s fixed-point calculations about 2.5
+times slower overall. Since a PC is perhaps 40 times slower than a
+486/33, we’re talking about a hundred-times speed difference between the
+low end and mainstream. A 486/33 can animate a 72-sided ball, complete
+with shading (as discussed later), at 60 frames per second (fps), with
+plenty of cycles to spare; an 8-MHz AT can animate the same ball at
+about 6 fps. Clearly, the level of animation an application uses must be
+tailored to the available CPU horsepower.
+
+The implementation of a 32-bit multiply using 8088 instructions is a
+simple matter of adding together four partial products. A 32-bit divide
+is not so simple, however. In fact, in Listing 54.1 I’ve chosen not to
+implement a full 32x32 divide, but rather only a 32x16 divide. The
+reason is simple: performance. A 32x16 divide can be implemented on an
+8088 with two **DIV** instructions, but a 32x32 divide takes a great
+deal more work, so far as I can see. (If anyone has a fast 32x32 divide,
+or has a faster way to handle signed multiplies and divides than the
+approach taken by Listing 54.1, please drop me a line care of the
+publisher.) In X-Sharp, division is used only to divide either X or Y by
+Z in the process of projecting from view space to screen space, so the
+cost of using a 32x16 divide is merely some inaccuracy in calculating
+screen coordinates, especially when objects get very close to the Z = 0
+plane. This error is not cumulative (that is, it doesn’t carry over to
+later frames), and in my experience doesn’t cause noticeable image
+degradation; therefore, given the already slow performance of the 8088
+and 286, I’ve opted for performance over precision.
+
+At any rate, please keep in mind that the non-386 version of
+**FixedDiv()** is *not* a general-purpose 32x32 fixed-point division
+routine. In fact, it will generate a divide-by-zero error if passed a
+fixed-point divisor between -1 and 1. As I’ve explained, the non-386
+version of **Fixed-Div()** is designed to do just what X-Sharp needs,
+and no more, as quickly as possible.
+
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+* * * * *
+
+Graphics Programming Black Book © 2001 Michael Abrash