78 lines
4.2 KiB
Markdown
78 lines
4.2 KiB
Markdown
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[Previous](53-04.html) [Table of Contents](index.html) [Next](54-02.html)
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Chapter 54\
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3-D Shading {#Heading1}
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------------
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### Putting Realistic Surfaces on Animated 3-D Objects {#Heading2}
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At the end of the previous chapter, X-Sharp had just acquired basic
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hidden-surface capability, and performance had been vastly improved
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through the use of fixed-point arithmetic. In this chapter, we’re going
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to add quite a bit more: support for 8088 and 80286 PCs, a general color
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model, and shading. That’s an awful lot to cover in one chapter
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(actually, it’ll spill over into the next chapter), so let’s get to it!
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### Support for Older Processors {#Heading3}
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To date, X-Sharp has run on only the 386 and 486, because it uses 32-bit
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multiply and divide instructions that sub-386 processors don’t support.
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I chose 32-bit instructions for two reasons: They’re much faster for
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16.16 fixed-point arithmetic than any approach that works on the 8088
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and 286; and they’re much easier to implement than any other approach.
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In short, I was after maximum performance, and I was perhaps just a
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little lazy.
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I should have known better than to try to sneak this one by you. The
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most common feedback I’ve gotten on X-Sharp is that I should make it
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support the 8088 and 286. Well, I can take a hint as well as the next
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guy. Listing 54.1 is an improved version of FIXED.ASM, containing dual
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386/8088 versions of **CosSin(), XformVec()**, and **ConcatXforms()**,
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as well as **FixedMul()** and **FixedDiv()**.
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Given the new version of FIXED.ASM, with **USE386** set to 0, X-Sharp
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will now run on any processor. That’s not to say that it will run fast
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on any processor, or at least not as fast as it used to. The switch to
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8088 instructions makes X-Sharp’s fixed-point calculations about 2.5
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times slower overall. Since a PC is perhaps 40 times slower than a
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486/33, we’re talking about a hundred-times speed difference between the
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low end and mainstream. A 486/33 can animate a 72-sided ball, complete
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with shading (as discussed later), at 60 frames per second (fps), with
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plenty of cycles to spare; an 8-MHz AT can animate the same ball at
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about 6 fps. Clearly, the level of animation an application uses must be
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tailored to the available CPU horsepower.
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The implementation of a 32-bit multiply using 8088 instructions is a
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simple matter of adding together four partial products. A 32-bit divide
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is not so simple, however. In fact, in Listing 54.1 I’ve chosen not to
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implement a full 32x32 divide, but rather only a 32x16 divide. The
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reason is simple: performance. A 32x16 divide can be implemented on an
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8088 with two **DIV** instructions, but a 32x32 divide takes a great
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deal more work, so far as I can see. (If anyone has a fast 32x32 divide,
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or has a faster way to handle signed multiplies and divides than the
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approach taken by Listing 54.1, please drop me a line care of the
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publisher.) In X-Sharp, division is used only to divide either X or Y by
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Z in the process of projecting from view space to screen space, so the
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cost of using a 32x16 divide is merely some inaccuracy in calculating
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screen coordinates, especially when objects get very close to the Z = 0
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plane. This error is not cumulative (that is, it doesn’t carry over to
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later frames), and in my experience doesn’t cause noticeable image
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degradation; therefore, given the already slow performance of the 8088
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and 286, I’ve opted for performance over precision.
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At any rate, please keep in mind that the non-386 version of
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**FixedDiv()** is *not* a general-purpose 32x32 fixed-point division
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routine. In fact, it will generate a divide-by-zero error if passed a
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fixed-point divisor between -1 and 1. As I’ve explained, the non-386
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version of **Fixed-Div()** is designed to do just what X-Sharp needs,
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and no more, as quickly as possible.
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------------------------ --------------------------------- --------------------
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[Previous](53-04.html) [Table of Contents](index.html) [Next](54-02.html)
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------------------------ --------------------------------- --------------------
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* * * * *
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Graphics Programming Black Book © 2001 Michael Abrash
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