/*************************************************************************\
* Module Name: Lines.c
*
* Contains the code for drawing short fractional endpoint lines and
* longer lines with strips. There is also a separate x86 Asm version
* of this code.
*
* Copyright (c) 1990-1994 Microsoft Corporation
* Copyright (c) 1992 Digital Equipment Corporation
\**************************************************************************/
#include "precomp.h"
///////////////////////////////////////////////////////////////////////
// We have to be careful of arithmetic overflow in a number of places.
// Fortunately, the compiler is guaranteed to natively support 64-bit
// signed LONGLONGs and 64-bit unsigned DWORDLONGs.
//
// UUInt32x32To64(a, b) is a macro defined in 'winnt.h' that multiplies
// two 32-bit ULONGs to produce a 64-bit DWORDLONG result.
//
// UInt64By32To32 is our own macro to divide a 64-bit DWORDLONG by
// a 32-bit ULONG to produce a 32-bit ULONG result.
//
// UInt64Mod32To32 is our own macro to modulus a 64-bit DWORDLONG by
// a 32-bit ULONG to produce a 32-bit ULONG result.
//
// 64 bit divides are usually very expensive. Since it's very rare
// that we'll get lines where the upper 32 bits of the 64 bit result
// are used, we can almost always use 32-bit ULONG divides. We still
// must correctly handle the larger cases:
#define UInt64Div32To32(a, b) \
((((DWORDLONG)(a)) > ULONG_MAX) ? \
(ULONG)((DWORDLONG)(a) / (ULONG)(b)) : \
(ULONG)((ULONG)(a) / (ULONG)(b)))
#define UInt64Mod32To32(a, b) \
((((DWORDLONG)(a)) > ULONG_MAX) ? \
(ULONG)((DWORDLONG)(a) % (ULONG)(b)) : \
(ULONG)((ULONG)(a) % (ULONG)(b)))
#define SWAPL(x,y,t) {t = x; x = y; y = t;}
FLONG gaflRound[] = {
FL_H_ROUND_DOWN | FL_V_ROUND_DOWN, // no flips
FL_H_ROUND_DOWN | FL_V_ROUND_DOWN, // FL_FLIP_D
FL_H_ROUND_DOWN, // FL_FLIP_V
FL_V_ROUND_DOWN, // FL_FLIP_V | FL_FLIP_D
FL_V_ROUND_DOWN, // FL_FLIP_SLOPE_ONE
0xbaadf00d, // FL_FLIP_SLOPE_ONE | FL_FLIP_D
FL_H_ROUND_DOWN, // FL_FLIP_SLOPE_ONE | FL_FLIP_V
0xbaadf00d // FL_FLIP_SLOPE_ONE | FL_FLIP_V | FL_FLIP_D
};
BOOL bIntegerLine(PDEV*, ULONG, ULONG, ULONG, ULONG);
BOOL bHardwareLine(PDEV*, POINTFIX*, POINTFIX*);
/******************************Public*Routine******************************\
* BOOL bLines(ppdev, pptfxFirst, pptfxBuf, cptfx, pls,
* prclClip, apfn[], flStart)
*
* Computes the DDA for the line and gets ready to draw it. Puts the
* pixel data into an array of strips, and calls a strip routine to
* do the actual drawing.
*
* Doing NT Lines Right
* --------------------
*
* In NT, all lines are given to the device driver in fractional
* coordinates, in a 28.4 fixed point format. The lower 4 bits are
* fractional for sub-pixel positioning.
*
* Note that you CANNOT! just round the coordinates to integers
* and pass the results to your favorite integer Bresenham routine!!
* (Unless, of course, you have such a high resolution device that
* nobody will notice -- not likely for a display device.) The
* fractions give a more accurate rendering of the line -- this is
* important for things like our Bezier curves, which would have 'kinks'
* if the points in its polyline approximation were rounded to integers.
*
* Unfortunately, for fractional lines there is more setup work to do
* a DDA than for integer lines. However, the main loop is exactly
* the same (and can be done entirely with 32 bit math).
*
* If You've Got Hardware That Does Bresenham
* ------------------------------------------
*
* A lot of hardware limits DDA error terms to 'n' bits. With fractional
* coordinates, 4 bits are given to the fractional part, letting
* you draw in hardware only those lines that lie entirely in a 2^(n-4)
* by 2^(n-4) pixel space.
*
* And you still have to correctly draw those lines with coordinates
* outside that space! Remember that the screen is only a viewport
* onto a 28.4 by 28.4 space -- if any part of the line is visible
* you MUST render it precisely, regardless of where the end points lie.
* So even if you do it in software, somewhere you'll have to have a
* 32 bit DDA routine.
*
* Our Implementation
* ------------------
*
* We employ a run length slice algorithm: our DDA calculates the
* number of pixels that are in each row (or 'strip') of pixels.
*
* We've separated the running of the DDA and the drawing of pixels:
* we run the DDA for several iterations and store the results in
* a 'strip' buffer (which are the lengths of consecutive pixel rows of
* the line), then we crank up a 'strip drawer' that will draw all the
* strips in the buffer.
*
* We also employ a 'half-flip' to reduce the number of strip
* iterations we need to do in the DDA and strip drawing loops: when a
* (normalized) line's slope is more than 1/2, we do a final flip
* about the line y = (1/2)x. So now, instead of each strip being
* consecutive horizontal or vertical pixel rows, each strip is composed
* of those pixels aligned in 45 degree rows. So a line like (0, 0) to
* (128, 128) would generate only one strip.
*
* We also always draw only left-to-right.
*
* Styled lines may have arbitrary style patterns. We specially
* optimize the default patterns (and call them 'masked' styles).
*
* The DDA Derivation
* ------------------
*
* Here is how I like to think of the DDA calculation.
*
* We employ Knuth's "diamond rule": rendering a one-pixel-wide line
* can be thought of as dragging a one-pixel-wide by one-pixel-high
* diamond along the true line. Pixel centers lie on the integer
* coordinates, and so we light any pixel whose center gets covered
* by the "drag" region (John D. Hobby, Journal of the Association
* for Computing Machinery, Vol. 36, No. 2, April 1989, pp. 209-229).
*
* We must define which pixel gets lit when the true line falls
* exactly half-way between two pixels. In this case, we follow
* the rule: when two pels are equidistant, the upper or left pel
* is illuminated, unless the slope is exactly one, in which case
* the upper or right pel is illuminated. (So we make the edges
* of the diamond exclusive, except for the top and left vertices,
* which are inclusive, unless we have slope one.)
*
* This metric decides what pixels should be on any line BEFORE it is
* flipped around for our calculation. Having a consistent metric
* this way will let our lines blend nicely with our curves. The
* metric also dictates that we will never have one pixel turned on
* directly above another that's turned on. We will also never have
* a gap; i.e., there will be exactly one pixel turned on for each
* column between the start and end points. All that remains to be
* done is to decide how many pixels should be turned on for each row.
*
* So lines we draw will consist of varying numbers of pixels on
* successive rows, for example:
*
* ******
* *****
* ******
* *****
*
* We'll call each set of pixels on a row a "strip".
*
* (Please remember that our coordinate space has the origin as the
* upper left pixel on the screen; postive y is down and positive x
* is right.)
*
* Device coordinates are specified as fixed point 28.4 numbers,
* where the first 28 bits are the integer coordinate, and the last
* 4 bits are the fraction. So coordinates may be thought of as
* having the form (x, y) = (M/F, N/F) where F is the constant scaling
* factor F = 2^4 = 16, and M and N are 32 bit integers.
*
* Consider the line from (M0/F, N0/F) to (M1/F, N1/F) which runs
* left-to-right and whose slope is in the first octant, and let
* dM = M1 - M0 and dN = N1 - N0. Then dM >= 0, dN >= 0 and dM >= dN.
*
* Since the slope of the line is less than 1, the edges of the
* drag region are created by the top and bottom vertices of the
* diamond. At any given pixel row y of the line, we light those
* pixels whose centers are between the left and right edges.
*
* Let mL(n) denote the line representing the left edge of the drag
* region. On pixel row j, the column of the first pixel to be
* lit is
*
* iL(j) = ceiling( mL(j * F) / F)
*
* Since the line's slope is less than one:
*
* iL(j) = ceiling( mL([j + 1/2] F) / F )
*
* Recall the formula for our line:
*
* n(m) = (dN / dM) (m - M0) + N0
*
* m(n) = (dM / dN) (n - N0) + M0
*
* Since the line's slope is less than one, the line representing
* the left edge of the drag region is the original line offset
* by 1/2 pixel in the y direction:
*
* mL(n) = (dM / dN) (n - F/2 - N0) + M0
*
* From this we can figure out the column of the first pixel that
* will be lit on row j, being careful of rounding (if the left
* edge lands exactly on an integer point, the pixel at that
* point is not lit because of our rounding convention):
*
* iL(j) = floor( mL(j F) / F ) + 1
*
* = floor( ((dM / dN) (j F - F/2 - N0) + M0) / F ) + 1
*
* = floor( F dM j - F/2 dM - N0 dM + dN M0) / F dN ) + 1
*
* F dM j - [ dM (N0 + F/2) - dN M0 ]
* = floor( ---------------------------------- ) + 1
* F dN
*
* dM j - [ dM (N0 + F/2) - dN M0 ] / F
* = floor( ------------------------------------ ) + 1 (1)
* dN
*
* = floor( (dM j + alpha) / dN ) + 1
*
* where
*
* alpha = - [ dM (N0 + F/2) - dN M0 ] / F
*
* We use equation (1) to calculate the DDA: there are iL(j+1) - iL(j)
* pixels in row j. Because we are always calculating iL(j) for
* integer quantities of j, we note that the only fractional term
* is constant, and so we can 'throw away' the fractional bits of
* alpha:
*
* beta = floor( - [ dM (N0 + F/2) - dN M0 ] / F ) (2)
*
* so
*
* iL(j) = floor( (dM j + beta) / dN ) + 1 (3)
*
* for integers j.
*
* Note if iR(j) is the line's rightmost pixel on row j, that
* iR(j) = iL(j + 1) - 1.
*
* Similarly, rewriting equation (1) as a function of column i,
* we can determine, given column i, on which pixel row j is the line
* lit:
*
* dN i + [ dM (N0 + F/2) - dN M0 ] / F
* j(i) = ceiling( ------------------------------------ ) - 1
* dM
*
* Floors are easier to compute, so we can rewrite this:
*
* dN i + [ dM (N0 + F/2) - dN M0 ] / F + dM - 1/F
* j(i) = floor( ----------------------------------------------- ) - 1
* dM
*
* dN i + [ dM (N0 + F/2) - dN M0 ] / F + dM - 1/F - dM
* = floor( ---------------------------------------------------- )
* dM
*
* dN i + [ dM (N0 + F/2) - dN M0 - 1 ] / F
* = floor( ---------------------------------------- )
* dM
*
* We can once again wave our hands and throw away the fractional bits
* of the remainder term:
*
* j(i) = floor( (dN i + gamma) / dM ) (4)
*
* where
*
* gamma = floor( [ dM (N0 + F/2) - dN M0 - 1 ] / F ) (5)
*
* We now note that
*
* beta = -gamma - 1 = ~gamma (6)
*
* To draw the pixels of the line, we could evaluate (3) on every scan
* line to determine where the strip starts. Of course, we don't want
* to do that because that would involve a multiply and divide for every
* scan. So we do everything incrementally.
*
* We would like to easily compute c , the number of pixels on scan j:
* j
*
* c = iL(j + 1) - iL(j)
* j
*
* = floor((dM (j + 1) + beta) / dN) - floor((dM j + beta) / dN) (7)
*
* This may be rewritten as
*
* c = floor(i + r / dN) - floor(i + r / dN) (8)
* j j+1 j+1 j j
*
* where i , i are integers and r < dN, r < dN.
* j j+1 j j+1
*
* Rewriting (7) again:
*
* c = floor(i + r / dN + dM / dN) - floor(i + r / dN)
* j j j j j
*
*
* = floor((r + dM) / dN) - floor(r / dN)
* j j
*
* This may be rewritten as
*
* c = dI + floor((r + dR) / dN) - floor(r / dN)
* j j j
*
* where dI + dR / dN = dM / dN, dI is an integer and dR < dN.
*
* r is the remainder (or "error") term in the DDA loop: r / dN
* j j
* is the exact fraction of a pixel at which the strip ends. To go
* on to the next scan and compute c we need to know r .
* j+1 j+1
*
* So in the main loop of the DDA:
*
* c = dI + floor((r + dR) / dN) and r = (r + dR) % dN
* j j j+1 j
*
* and we know r < dN, r < dN, and dR < dN.
* j j+1
*
* We have derived the DDA only for lines in the first octant; to
* handle other octants we do the common trick of flipping the line
* to the first octant by first making the line left-to-right by
* exchanging the end-points, then flipping about the lines y = 0 and
* y = x, as necessary. We must record the transformation so we can
* undo them later.
*
* We must also be careful of how the flips affect our rounding. If
* to get the line to the first octant we flipped about x = 0, we now
* have to be careful to round a y value of 1/2 up instead of down as
* we would for a line originally in the first octant (recall that
* "In the case where two pels are equidistant, the upper or left
* pel is illuminated...").
*
* To account for this rounding when running the DDA, we shift the line
* (or not) in the y direction by the smallest amount possible. That
* takes care of rounding for the DDA, but we still have to be careful
* about the rounding when determining the first and last pixels to be
* lit in the line.
*
* Determining The First And Last Pixels In The Line
* -------------------------------------------------
*
* Fractional coordinates also make it harder to determine which pixels
* will be the first and last ones in the line. We've already taken
* the fractional coordinates into account in calculating the DDA, but
* the DDA cannot tell us which are the end pixels because it is quite
* happy to calculate pixels on the line from minus infinity to positive
* infinity.
*
* The diamond rule determines the start and end pixels. (Recall that
* the sides are exclusive except for the left and top vertices.)
* This convention can be thought of in another way: there are diamonds
* around the pixels, and wherever the true line crosses a diamond,
* that pel is illuminated.
*
* Consider a line where we've done the flips to the first octant, and the
* floor of the start coordinates is the origin:
*
* +-----------------------> +x
* |
* | 0 1
* | 0123456789abcdef
* |
* | 0 00000000?1111111
* | 1 00000000 1111111
* | 2 0000000 111111
* | 3 000000 11111
* | 4 00000 ** 1111
* | 5 0000 ****1
* | 6 000 1***
* | 7 00 1 ****
* | 8 ? ***
* | 9 22 3 ****
* | a 222 33 ***
* | b 2222 333 ****
* | c 22222 3333 **
* | d 222222 33333
* | e 2222222 333333
* | f 22222222 3333333
* |
* | 2 3
* v
* +y
*
* If the start of the line lands on the diamond around pixel 0 (shown by
* the '0' region here), pixel 0 is the first pel in the line. The same
* is true for the other pels.
*
* A little more work has to be done if the line starts in the
* 'nether-land' between the diamonds (as illustrated by the '*' line):
* the first pel lit is the first diamond crossed by the line (pixel 1 in
* our example). This calculation is determined by the DDA or slope of
* the line.
*
* If the line starts exactly half way between two adjacent pixels
* (denoted here by the '?' spots), the first pixel is determined by our
* round-down convention (and is dependent on the flips done to
* normalize the line).
*
* Last Pel Exclusive
* ------------------
*
* To eliminate repeatedly lit pels between continuous connected lines,
* we employ a last-pel exclusive convention: if the line ends exactly on
* the diamond around a pel, that pel is not lit. (This eliminates the
* checks we had in the old code to see if we were re-lighting pels.)
*
* The Half Flip
* -------------
*
* To make our run length algorithm more efficient, we employ a "half
* flip". If after normalizing to the first octant, the slope is more
* than 1/2, we subtract the y coordinate from the x coordinate. This
* has the effect of reflecting the coordinates through the line of slope
* 1/2. Note that the diagonal gets mapped into the x-axis after a half
* flip.
*
* How Many Bits Do We Need, Anyway?
* ---------------------------------
*
* Note that if the line is visible on your screen, you must light up
* exactly the correct pixels, no matter where in the 28.4 x 28.4 device
* space the end points of the line lie (meaning you must handle 32 bit
* DDAs, you can certainly have optimized cases for lesser DDAs).
*
* We move the origin to (floor(M0 / F), floor(N0 / F)), so when we
* calculate gamma from (5), we know that 0 <= M0, N0 < F. And we
* are in the first octant, so dM >= dN. Then we know that gamma can
* be in the range [(-1/2)dM, (3/2)dM]. The DDI guarantees us that
* valid lines will have dM and dN values at most 31 bits (unsigned)
* of significance. So gamma requires 33 bits of significance (we store
* this as a 64 bit number for convenience).
*
* When running through the DDA loop, r + dR can have a value in the
* j
* range 0 <= r < 2 dN; thus the result must be a 32 bit unsigned value.
* j
*
* Testing Lines
* -------------
*
* To be NT compliant, a display driver must exactly adhere to GIQ,
* which means that for any given line, the driver must light exactly
* the same pels as does GDI. This can be tested using the Guiman tool
* provided elsewhere in the DDK, and 'ZTest', which draws random lines
* on the screen and to a bitmap, and compares the results.
*
* If You've Got Line Hardware
* ---------------------------
*
* If your hardware already adheres to GIQ, you're all set. Otherwise
* you'll want to look at the S3 sample code and read the following:
*
* 1) You'll want to special case integer-only lines, since they require
* less processing time and are more common (CAD programs will probably
* only ever give integer lines). GDI does not provide a flag saying
* that all lines in a path are integer lines; consequently, you will
* have to explicitly check every line.
*
* 2) You are required to correctly draw any line in the 28.4 device
* space that intersects the viewport. If you have less than 32 bits
* of significance in the hardware for the Bresenham terms, extremely
* long lines would overflow the hardware. For such (rare) cases, you
* can fall back to strip-drawing code (or if your display is a frame
* buffer, fall back to the engine).
*
* 3) If you can explicitly set the Bresenham terms in your hardware, you
* can draw non-integer lines using the hardware. If your hardware has
* 'n' bits of precision, you can draw GIQ lines that are up to 2^(n-5)
* pels long (4 bits are required for the fractional part, and one bit is
* used as a sign bit). Note that integer lines don't require the 4
* fractional bits, so if you special case them as in 1), you can do
* integer lines that are up to 2^(n - 1) pels long. See the
* 'bHardwareLine' routine for an example.
*
\**************************************************************************/
BOOL bLines(
PDEV* ppdev,
POINTFIX* pptfxFirst, // Start of first line
POINTFIX* pptfxBuf, // Pointer to buffer of all remaining lines
RUN* prun, // Pointer to runs if doing complex clipping
ULONG cptfx, // Number of points in pptfxBuf or number of runs
// in prun
LINESTATE* pls, // Colour and style info
RECTL* prclClip, // Pointer to clip rectangle if doing simple clipping
PFNSTRIP apfn[], // Array of strip functions
FLONG flStart) // Flags for each line, which is a combination of:
// FL_SIMPLE_CLIP
// FL_COMPLEX_CLIP
// FL_STYLED
// FL_LAST_PEL_INCLUSIVE
// - Should be set only for all integer lines,
// and can't be used with FL_COMPLEX_CLIP
{
ULONG M0;
ULONG dM;
ULONG N0;
ULONG dN;
ULONG dN_Original;
FLONG fl;
LONG x;
LONG y;
LONGLONG llBeta;
LONGLONG llGamma;
LONGLONG dl;
LONGLONG ll;
ULONG ulDelta;
ULONG x0;
ULONG y0;
ULONG x1;
ULONG cStylePels; // Major length of line in pixels for styling
ULONG xStart;
POINTL ptlStart;
STRIP strip;
PFNSTRIP pfn;
LONG cPels;
LONG* plStrip;
LONG* plStripEnd;
LONG cStripsInNextRun;
POINTFIX* pptfxBufEnd = pptfxBuf + cptfx; // Last point in path record
STYLEPOS spThis; // Style pos for this line
BOOL bW32p = (ppdev->ulChipID == W32P);
do {
/***********************************************************************\
* Start the DDA calculations. *
\***********************************************************************/
M0 = (LONG) pptfxFirst->x;
dM = (LONG) pptfxBuf->x;
N0 = (LONG) pptfxFirst->y;
dN = (LONG) pptfxBuf->y;
fl = flStart;
// Check for non-clipped, non-styled integer endpoint lines
if (bW32p)
{
if ((fl & (FL_CLIP | FL_STYLED)) == 0)
{
// Special-case integer end-point lines:
if (((M0 | dM | N0 | dN) & (F - 1)) == 0)
{
if (bIntegerLine(ppdev, M0, N0, dM, dN))
{
goto Next_Line;
}
}
}
}
if ((LONG) M0 > (LONG) dM)
{
// Ensure that we run left-to-right:
register ULONG ulTmp;
SWAPL(M0, dM, ulTmp);
SWAPL(N0, dN, ulTmp);
fl |= FL_FLIP_H;
}
// Compute the delta dx. The DDI says we can never have a valid delta
// with a magnitued more than 2^31 - 1, but GDI never actually checks
// its transforms. So we have to check for this case to avoid overflow:
dM -= M0;
if ((LONG) dM < 0)
{
goto Next_Line;
}
if ((LONG) dN < (LONG) N0)
{
// Line runs from bottom to top, so flip across y = 0:
N0 = -(LONG) N0;
dN = -(LONG) dN;
fl |= FL_FLIP_V;
}
dN -= N0;
if ((LONG) dN < 0)
{
goto Next_Line;
}
// We now have a line running left-to-right, top-to-bottom from (M0, N0)
// to (M0 + dM, N0 + dN):
if (dN >= dM)
{
if (dN == dM)
{
// Have to special case slopes of one:
fl |= FL_FLIP_SLOPE_ONE;
}
else
{
// Since line has slope greater than 1, flip across x = y:
register ULONG ulTmp;
SWAPL(dM, dN, ulTmp);
SWAPL(M0, N0, ulTmp);
fl |= FL_FLIP_D;
}
}
fl |= gaflRound[(fl & FL_ROUND_MASK) >> FL_ROUND_SHIFT];
x = LFLOOR((LONG) M0);
y = LFLOOR((LONG) N0);
M0 = FXFRAC(M0);
N0 = FXFRAC(N0);
// Calculate the remainder term [ dM * (N0 + F/2) - M0 * dN ]:
llGamma = UInt32x32To64(dM, N0 + F/2) - UInt32x32To64(M0, dN);
if (fl & FL_V_ROUND_DOWN) // Adjust so y = 1/2 rounds down
{
llGamma--;
}
llGamma >>= FLOG2;
llBeta = ~llGamma;
/***********************************************************************\
* Figure out which pixels are at the ends of the line. *
\***********************************************************************/
// The toughest part of GIQ is determining the start and end pels.
//
// Our approach here is to calculate x0 and x1 (the inclusive start
// and end columns of the line respectively, relative to our normalized
// origin). Then x1 - x0 + 1 is the number of pels in the line. The
// start point is easily calculated by plugging x0 into our line equation
// (which takes care of whether y = 1/2 rounds up or down in value)
// getting y0, and then undoing the normalizing flips to get back
// into device space.
//
// We look at the fractional parts of the coordinates of the start and
// end points, and call them (M0, N0) and (M1, N1) respectively, where
// 0 <= M0, N0, M1, N1 < 16. We plot (M0, N0) on the following grid
// to determine x0:
//
// +-----------------------> +x
// |
// | 0 1
// | 0123456789abcdef
// |
// | 0 ........?xxxxxxx
// | 1 ..........xxxxxx
// | 2 ...........xxxxx
// | 3 ............xxxx
// | 4 .............xxx
// | 5 ..............xx
// | 6 ...............x
// | 7 ................
// | 8 ................
// | 9 ......**........
// | a ........****...x
// | b ............****
// | c .............xxx****
// | d ............xxxx ****
// | e ...........xxxxx ****
// | f ..........xxxxxx
// |
// | 2 3
// v
//
// +y
//
// This grid accounts for the appropriate rounding of GIQ and last-pel
// exclusion. If (M0, N0) lands on an 'x', x0 = 2. If (M0, N0) lands
// on a '.', x0 = 1. If (M0, N0) lands on a '?', x0 rounds up or down,
// depending on what flips have been done to normalize the line.
//
// For the end point, if (M1, N1) lands on an 'x', x1 =
// floor((M0 + dM) / 16) + 1. If (M1, N1) lands on a '.', x1 =
// floor((M0 + dM)). If (M1, N1) lands on a '?', x1 rounds up or down,
// depending on what flips have been done to normalize the line.
//
// Lines of exactly slope one require a special case for both the start
// and end. For example, if the line ends such that (M1, N1) is (9, 1),
// the line has gone exactly through (8, 0) -- which may be considered
// to be part of 'x' because of rounding! So slopes of exactly slope
// one going through (8, 0) must also be considered as belonging in 'x'.
//
// For lines that go left-to-right, we have the following grid:
//
// +-----------------------> +x
// |
// | 0 1
// | 0123456789abcdef
// |
// | 0 xxxxxxxx?.......
// | 1 xxxxxxx.........
// | 2 xxxxxx..........
// | 3 xxxxx...........
// | 4 xxxx............
// | 5 xxx.............
// | 6 xx..............
// | 7 x...............
// | 8 x...............
// | 9 x.....**........
// | a xx......****....
// | b xxx.........****
// | c xxxx............****
// | d xxxxx........... ****
// | e xxxxxx.......... ****
// | f xxxxxxx.........
// |
// | 2 3
// v
//
// +y
//
// This grid accounts for the appropriate rounding of GIQ and last-pel
// exclusion. If (M0, N0) lands on an 'x', x0 = 0. If (M0, N0) lands
// on a '.', x0 = 1. If (M0, N0) lands on a '?', x0 rounds up or down,
// depending on what flips have been done to normalize the line.
//
// For the end point, if (M1, N1) lands on an 'x', x1 =
// floor((M0 + dM) / 16) - 1. If (M1, N1) lands on a '.', x1 =
// floor((M0 + dM)). If (M1, N1) lands on a '?', x1 rounds up or down,
// depending on what flips have been done to normalize the line.
//
// Lines of exactly slope one must be handled similarly to the right-to-
// left case.
{
// Calculate x0, x1
ULONG N1 = FXFRAC(N0 + dN);
ULONG M1 = FXFRAC(M0 + dM);
x1 = LFLOOR(M0 + dM);
if (fl & FL_LAST_PEL_INCLUSIVE)
{
// It sure is easy to compute the first pel when lines have only
// integer coordinates and are last-pel inclusive:
x0 = 0;
y0 = 0;
// Last-pel inclusive lines that are exactly one pixel long
// have a 'delta-x' and 'delta-y' equal to zero. The problem is
// that our clip code assumes that 'delta-x' is always non-zero
// (since it never happens with last-pel exclusive lines). As
// an inelegant solution, we simply modify 'delta-x' in this
// case -- because the line is exactly one pixel long, changing
// the slope will obviously have no effect on rasterization.
if (x1 == 0)
{
dM = 1;
llGamma = 0;
llBeta = ~llGamma;
}
}
else
{
if (fl & FL_FLIP_H)
{
// ---------------------------------------------------------------
// Line runs right-to-left: <----
// Compute x1:
if (N1 == 0)
{
if (LROUND(M1, fl & FL_H_ROUND_DOWN))
{
x1++;
}
}
else if (abs((LONG) (N1 - F/2)) + M1 > F)
{
x1++;
}
if ((fl & (FL_FLIP_SLOPE_ONE | FL_H_ROUND_DOWN))
== (FL_FLIP_SLOPE_ONE))
{
// Have to special-case diagonal lines going through our
// the point exactly equidistant between two horizontal
// pixels, if we're supposed to round x=1/2 down:
if ((N1 > 0) && (M1 == N1 + 8))
x1++;
// Don't you love special cases? Is this a rhetorical question?
if ((N0 > 0) && (M0 == N0 + 8))
{
x0 = 2;
ulDelta = dN;
goto right_to_left_compute_y0;
}
}
// Compute x0:
x0 = 1;
ulDelta = 0;
if (N0 == 0)
{
if (LROUND(M0, fl & FL_H_ROUND_DOWN))
{
x0 = 2;
ulDelta = dN;
}
}
else if (abs((LONG) (N0 - F/2)) + M0 > F)
{
x0 = 2;
ulDelta = dN;
}
// Compute y0:
right_to_left_compute_y0:
y0 = 0;
ll = llGamma + (LONGLONG) ulDelta;
if (ll >= (LONGLONG) (2 * dM - dN))
y0 = 2;
else if (ll >= (LONGLONG) (dM - dN))
y0 = 1;
}
else
{
// ---------------------------------------------------------------
// Line runs left-to-right: ---->
// Compute x1:
if (!(fl & FL_LAST_PEL_INCLUSIVE))
x1--;
if (M1 > 0)
{
if (N1 == 0)
{
if (LROUND(M1, fl & FL_H_ROUND_DOWN))
x1++;
}
else if (abs((LONG) (N1 - F/2)) <= (LONG) M1)
{
x1++;
}
}
if ((fl & (FL_FLIP_SLOPE_ONE | FL_H_ROUND_DOWN))
== (FL_FLIP_SLOPE_ONE | FL_H_ROUND_DOWN))
{
// Have to special-case diagonal lines going through our
// the point exactly equidistant between two horizontal
// pixels, if we're supposed to round x=1/2 down:
if ((M1 > 0) && (N1 == M1 + 8))
x1--;
if ((M0 > 0) && (N0 == M0 + 8))
{
x0 = 0;
goto left_to_right_compute_y0;
}
}
// Compute x0:
x0 = 0;
if (M0 > 0)
{
if (N0 == 0)
{
if (LROUND(M0, fl & FL_H_ROUND_DOWN))
x0 = 1;
}
else if (abs((LONG) (N0 - F/2)) <= (LONG) M0)
{
x0 = 1;
}
}
// Compute y0:
left_to_right_compute_y0:
y0 = 0;
if (llGamma >= (LONGLONG) (dM - (dN & (-(LONG) x0))))
{
y0 = 1;
}
}
}
}
cStylePels = x1 - x0 + 1;
if ((LONG) cStylePels <= 0)
goto Next_Line;
xStart = x0;
/***********************************************************************\
* Complex clipping. *
\***********************************************************************/
if (fl & FL_COMPLEX_CLIP)
{
dN_Original = dN;
Continue_Complex_Clipping:
if (fl & FL_FLIP_H)
{
// Line runs right-to-left <-----
x0 = xStart + cStylePels - prun->iStop - 1;
x1 = xStart + cStylePels - prun->iStart - 1;
}
else
{
// Line runs left-to-right ----->
x0 = xStart + prun->iStart;
x1 = xStart + prun->iStop;
}
prun++;
// Reset some variables we'll nuke a little later:
dN = dN_Original;
pls->spNext = pls->spComplex;
// No overflow since large integer math is used. Both values
// will be positive:
dl = UInt32x32To64(x0, dN) + llGamma;
// y0 = dl / dM:
y0 = UInt64Div32To32(dl, dM);
ASSERTDD((LONG) y0 >= 0, "y0 weird: Goofed up end pel calc?");
}
/***********************************************************************\
* Simple rectangular clipping. *
\***********************************************************************/
if (fl & FL_SIMPLE_CLIP)
{
ULONG y1;
LONG xRight;
LONG xLeft;
LONG yBottom;
LONG yTop;
// Note that y0 and y1 are actually the lower and upper bounds,
// respectively, of the y coordinates of the line (the line may
// have actually shrunk due to first/last pel clipping).
//
// Also note that x0, y0 are not necessarily zero.
RECTL* prcl = &prclClip[(fl & FL_RECTLCLIP_MASK) >>
FL_RECTLCLIP_SHIFT];
// Normalize to the same point we've normalized for the DDA
// calculations:
xRight = prcl->right - x;
xLeft = prcl->left - x;
yBottom = prcl->bottom - y;
yTop = prcl->top - y;
if (yBottom <= (LONG) y0 ||
xRight <= (LONG) x0 ||
xLeft > (LONG) x1)
{
Totally_Clipped:
if (fl & FL_STYLED)
{
pls->spNext += cStylePels;
if (pls->spNext >= pls->spTotal2)
pls->spNext %= pls->spTotal2;
}
goto Next_Line;
}
if ((LONG) x1 >= xRight)
x1 = xRight - 1;
// We have to know the correct y1, which we haven't bothered to
// calculate up until now. This multiply and divide is quite
// expensive; we could replace it with code similar to that which
// we used for computing y0.
//
// The reason why we need the actual value, and not an upper
// bounds guess like y1 = LFLOOR(dM) + 2 is that we have to be
// careful when calculating x(y) that y0 <= y <= y1, otherwise
// we can overflow on the divide (which, needless to say, is very
// bad).
dl = UInt32x32To64(x1, dN) + llGamma;
// y1 = dl / dM:
y1 = UInt64Div32To32(dl, dM);
if (yTop > (LONG) y1)
goto Totally_Clipped;
if (yBottom <= (LONG) y1)
{
y1 = yBottom;
dl = UInt32x32To64(y1, dM) + llBeta;
// x1 = dl / dN:
x1 = UInt64Div32To32(dl, dN);
}
// At this point, we've taken care of calculating the intercepts
// with the right and bottom edges. Now we work on the left and
// top edges:
if (xLeft > (LONG) x0)
{
x0 = xLeft;
dl = UInt32x32To64(x0, dN) + llGamma;
// y0 = dl / dM;
y0 = UInt64Div32To32(dl, dM);
if (yBottom <= (LONG) y0)
goto Totally_Clipped;
}
if (yTop > (LONG) y0)
{
y0 = yTop;
dl = UInt32x32To64(y0, dM) + llBeta;
// x0 = dl / dN + 1;
x0 = UInt64Div32To32(dl, dN) + 1;
if (xRight <= (LONG) x0)
goto Totally_Clipped;
}
ASSERTDD(x0 <= x1, "Improper rectangle clip");
}
/***********************************************************************\
* Done clipping. Unflip if necessary. *
\***********************************************************************/
ptlStart.x = x + x0;
ptlStart.y = y + y0;
if (fl & FL_FLIP_D)
{
register LONG lTmp;
SWAPL(ptlStart.x, ptlStart.y, lTmp);
}
if (fl & FL_FLIP_V)
{
ptlStart.y = -ptlStart.y;
}
cPels = x1 - x0 + 1;
/***********************************************************************\
* Style calculations. *
\***********************************************************************/
if (fl & FL_STYLED)
{
STYLEPOS sp;
spThis = pls->spNext;
pls->spNext += cStylePels;
{
if (pls->spNext >= pls->spTotal2)
pls->spNext %= pls->spTotal2;
if (fl & FL_FLIP_H)
sp = pls->spNext - x0 + xStart;
else
sp = spThis + x0 - xStart;
ASSERTDD(fl & FL_STYLED, "Oops");
// Normalize our target style position:
if ((sp < 0) || (sp >= pls->spTotal2))
{
sp %= pls->spTotal2;
// The modulus of a negative number is not well-defined
// in C -- if it's negative we'll adjust it so that it's
// back in the range [0, spTotal2):
if (sp < 0)
sp += pls->spTotal2;
}
// Since we always draw the line left-to-right, but styling is
// always done in the direction of the original line, we have
// to figure out where we are in the style array for the left
// edge of this line.
if (fl & FL_FLIP_H)
{
// Line originally ran right-to-left:
sp = -sp;
if (sp < 0)
sp += pls->spTotal2;
pls->ulStyleMask = ~pls->ulStartMask;
pls->pspStart = &pls->aspRtoL[0];
pls->pspEnd = &pls->aspRtoL[pls->cStyle - 1];
}
else
{
// Line originally ran left-to-right:
pls->ulStyleMask = pls->ulStartMask;
pls->pspStart = &pls->aspLtoR[0];
pls->pspEnd = &pls->aspLtoR[pls->cStyle - 1];
}
if (sp >= pls->spTotal)
{
sp -= pls->spTotal;
if (pls->cStyle & 1)
pls->ulStyleMask = ~pls->ulStyleMask;
}
pls->psp = pls->pspStart;
while (sp >= *pls->psp)
sp -= *pls->psp++;
ASSERTDD(pls->psp <= pls->pspEnd,
"Flew off into NeverNeverLand");
pls->spRemaining = *pls->psp - sp;
if ((pls->psp - pls->pspStart) & 1)
pls->ulStyleMask = ~pls->ulStyleMask;
}
}
plStrip = &strip.alStrips[0];
plStripEnd = &strip.alStrips[STRIP_MAX]; // Is exclusive
cStripsInNextRun = 0x7fffffff;
strip.ptlStart = ptlStart;
if (2 * dN > dM &&
!(fl & FL_STYLED))
{
// Do a half flip! Remember that we may doing this on the
// same line multiple times for complex clipping (meaning the
// affected variables should be reset for every clip run):
fl |= FL_FLIP_HALF;
llBeta = llGamma - (LONGLONG) ((LONG) dM);
dN = dM - dN;
y0 = x0 - y0; // Note this may overflow, but that's okay
}
// Now, run the DDA starting at (ptlStart.x, ptlStart.y)!
strip.flFlips = fl;
pfn = apfn[(fl & FL_STRIP_MASK) >> FL_STRIP_SHIFT];
// Now calculate the DDA variables needed to figure out how many pixels
// go in the very first strip:
{
register LONG i;
register ULONG dI;
register ULONG dR;
ULONG r;
if (dN == 0)
i = 0x7fffffff;
else
{
dl = UInt32x32To64(y0 + 1, dM) + llBeta;
ASSERTDD(dl >= 0, "Oops!");
// i = (dl / dN) - x0 + 1;
// r = (dl % dN);
i = UInt64Div32To32(dl, dN);
r = UInt64Mod32To32(dl, dN);
i = i - x0 + 1;
dI = dM / dN;
dR = dM % dN; // 0 <= dR < dN
ASSERTDD(dI > 0, "Weird dI");
}
ASSERTDD(i > 0 && i <= 0x7fffffff, "Weird initial strip length");
ASSERTDD(cPels > 0, "Zero pel line");
/***********************************************************************\
* Run the DDA! *
\***********************************************************************/
while(TRUE)
{
cPels -= i;
if (cPels <= 0)
break;
*plStrip++ = i;
if (plStrip == plStripEnd)
{
strip.cStrips = (LONG)(plStrip - &strip.alStrips[0]);
(*pfn)(ppdev, &strip, pls);
plStrip = &strip.alStrips[0];
}
i = dI;
r += dR;
if (r >= dN)
{
r -= dN;
i++;
}
}
*plStrip++ = cPels + i;
strip.cStrips = (LONG)(plStrip - &strip.alStrips[0]);
(*pfn)(ppdev, &strip, pls);
}
Next_Line:
if (fl & FL_COMPLEX_CLIP)
{
cptfx--;
if (cptfx != 0)
goto Continue_Complex_Clipping;
break;
}
else
{
pptfxFirst = pptfxBuf;
pptfxBuf++;
}
} while (pptfxBuf < pptfxBufEnd);
return(TRUE);
}
//////////////////////////////////////////////////////////////////////////
// General defines for bHardwareLine
#define HW_FLIP_D 0x0001L // Diagonal flip
#define HW_FLIP_V 0x0002L // Vertical flip
#define HW_FLIP_H 0x0004L // Horizontal flip
#define HW_FLIP_SLOPE_ONE 0x0008L // Normalized line has exactly slope one
#define HW_FLIP_MASK (HW_FLIP_D | HW_FLIP_V | HW_FLIP_H)
#define HW_X_ROUND_DOWN 0x0100L // x = 1/2 rounds down in value
#define HW_Y_ROUND_DOWN 0x0200L // y = 1/2 rounds down in value
LONG gaiDir[] = { 0, 1, 7, 6, 3, 2, 4, 5 };
FLONG gaflHardwareRound[] = {
HW_X_ROUND_DOWN | HW_Y_ROUND_DOWN, // | | |
HW_X_ROUND_DOWN | HW_Y_ROUND_DOWN, // | | | FLIP_D
HW_X_ROUND_DOWN, // | | FLIP_V |
HW_Y_ROUND_DOWN, // | | FLIP_V | FLIP_D
HW_Y_ROUND_DOWN, // | FLIP_H | |
HW_X_ROUND_DOWN, // | FLIP_H | | FLIP_D
0, // | FLIP_H | FLIP_V |
0, // | FLIP_H | FLIP_V | FLIP_D
HW_Y_ROUND_DOWN, // SLOPE_ONE | | |
0xffffffff, // SLOPE_ONE | | | FLIP_D
HW_X_ROUND_DOWN, // SLOPE_ONE | | FLIP_V |
0xffffffff, // SLOPE_ONE | | FLIP_V | FLIP_D
HW_Y_ROUND_DOWN, // SLOPE_ONE | FLIP_H | |
0xffffffff, // SLOPE_ONE | FLIP_H | | FLIP_D
HW_X_ROUND_DOWN, // SLOPE_ONE | FLIP_H | FLIP_V |
0xffffffff // SLOPE_ONE | FLIP_H | FLIP_V | FLIP_D
};
#if 0
//////////////////////////////////////////////////////////////////////////
// S3 specific defines
#define DEFAULT_DRAW_CMD (DRAW_LINE | DRAW | DIR_TYPE_XY | MULTIPLE_PIXELS | \
WRITE | LAST_PIXEL_OFF)
LONG gaiDrawCmd[] = {
DEFAULT_DRAW_CMD | PLUS_X | PLUS_Y | 0, // Octant 0
DEFAULT_DRAW_CMD | PLUS_X | PLUS_Y | MAJOR_Y, // Octant 1
DEFAULT_DRAW_CMD | PLUS_X | 0 | 0, // Octant 7
DEFAULT_DRAW_CMD | PLUS_X | 0 | MAJOR_Y, // Octant 6
DEFAULT_DRAW_CMD | 0 | PLUS_Y | 0, // Octant 3
DEFAULT_DRAW_CMD | 0 | PLUS_Y | MAJOR_Y, // Octant 2
DEFAULT_DRAW_CMD | 0 | 0 | 0, // Octant 4
DEFAULT_DRAW_CMD | 0 | 0 | MAJOR_Y, // Octant 5
};
#endif
// The S3's hardware can have 13 bits of significance for the error and
// step terms:
#define NUM_DDA_BITS 13
/******************************Public*Routine******************************\
* BOOL bHardwareLine(ppdev, pptfxStart, pptfxEnd)
*
* This routine is useful for folks who have line drawing hardware where
* they can explicitly set the Bresenham terms -- they can use this routine
* to draw fractional coordinate GIQ lines with the hardware.
*
* Fractional coordinate lines require an extra 4 bits of precision in the
* Bresenham terms. For example, if your hardware has 13 bits of precision
* for the terms, you can only draw GIQ lines up to 255 pels long using this
* routine.
*
* Input:
* pptfxStart - Points to GIQ coordinate of start of line
* pptfxEnd - Points to GIQ coordinate of end of line
* NUM_DDA_BITS- The number of bits of precision your hardware can support.
*
* Output:
* returns - TRUE if the line was drawn.
* FALSE if the line is too long, and the strips code must be
* used.
*
* DDALINE:
* iDir - Direction of the line, as an octant numbered as follows:
*
* \ 5 | 6 /
* \ | /
* 4 \ | / 7
* \ /
* -----+-----
* /|\
* 3 / | \ 0
* / | \
* / 2 | 1 \
*
* ptlStart - Start pixel of line.
* cPels - # of pels in line. *NOTE* You must check if this is <= 0!
* dMajor - Major axis delta.
* dMinor - Minor axis delta.
* lErrorTerm - Error term.
*
* What you do with the last 3 terms may be a little tricky. They are
* actually the terms for the formula of the normalized line
*
* dMinor * x + (lErrorTerm + dMajor)
* y(x) = floor( ---------------------------------- )
* dMajor
*
* where y(x) is the y coordinate of the pixel to be lit as a function of
* the x-coordinate.
*
* Every time the line advances one in the major direction 'x', dMinor
* gets added to the current error term. If the resulting value is >= 0,
* we know we have to move one pixel in the minor direction 'y', and
* dMajor must be subtracted from the current error term.
*
* If you're trying to figure out what this means for your hardware, you can
* think of the DDALINE terms as having been computed equivalently as
* follows:
*
* dMinor = 2 * (minor axis delta)
* dMajor = 2 * (major axis delta)
* lErrorTerm = - (major axis delta) - fixup
*
* That is, if your documentation tells you that for integer lines, a
* register is supposed to be initialized with the value
* '2 * (minor axis delta)', you'll actually use dMinor.
*
* Example: Setting up the 8514
*
* AXSTPSIGN is supposed to be the axial step constant register, defined
* as 2 * (minor axis delta). You set:
*
* AXSTPSIGN = dMinor
*
* DGSTPSIGN is supposed to be the diagonal step constant register,
* defined as 2 * (minor axis delta) - 2 * (major axis delta). You set:
*
* DGSTPSIGN = dMinor - dMajor
*
* ERR_TERM is supposed to be the adjusted error term, defined as
* 2 * (minor axis delta) - (major axis delta) - fixup. You set:
*
* ERR_TERM = lErrorTerm + dMinor
*
* Implementation:
*
* You'll want to special case integer lines before calling this routine
* (since they're very common, take less time to the computation of line
* terms, and can handle longer lines than this routine because 4 bits
* aren't being given to the fraction).
*
* If a GIQ line is too long to be handled by this routine, you can just
* use the slower strip routines for that line. Note that you cannot
* just fail the call -- you must be able to accurately draw any line
* in the 28.4 device space when it intersects the viewport.
*
* Testing:
*
* Use Guiman, or some other test that draws random fractional coordinate
* lines and compares them to what GDI itself draws to a bitmap.
*
\**************************************************************************/
BOOL bHardwareLine(
PDEV* ppdev,
POINTFIX* pptfxStart, // Start of line
POINTFIX* pptfxEnd) // End of line
{
FLONG fl; // Various flags
ULONG M0; // Normalized fractional unit x start coordinate (0 <= M0 < F)
ULONG N0; // Normalized fractional unit y start coordinate (0 <= N0 < F)
ULONG M1; // Normalized fractional unit x end coordinate (0 <= M1 < F)
ULONG N1; // Normalized fractional unit x end coordinate (0 <= N1 < F)
ULONG dM; // Normalized fractional unit x-delta (0 <= dM)
ULONG dN; // Normalized fractional unit y-delta (0 <= dN <= dM)
LONG x; // Normalized x coordinate of origin
LONG y; // Normalized y coordinate of origin
LONG x0; // Normalized x offset from origin to start pixel (inclusive)
LONG y0; // Normalized y offset from origin to start pixel (inclusive)
LONG x1; // Normalized x offset from origin to end pixel (inclusive)
LONG lGamma;// Bresenham error term at origin
LONG cPels; // Number of pixels in line
/***********************************************************************\
* Normalize line to the first octant.
\***********************************************************************/
fl = 0;
M0 = pptfxStart->x;
dM = pptfxEnd->x;
if ((LONG) dM < (LONG) M0)
{
// Line runs from right to left, so flip across x = 0:
M0 = -(LONG) M0;
dM = -(LONG) dM;
fl |= HW_FLIP_H;
}
// Compute the delta. The DDI says we can never have a valid delta
// with a magnitude more than 2^31 - 1, but the engine never actually
// checks its transforms. To ensure that we'll never puke on our shoes,
// we check for that case and simply refuse to draw the line:
dM -= M0;
if ((LONG) dM < 0)
return(FALSE);
N0 = pptfxStart->y;
dN = pptfxEnd->y;
if ((LONG) dN < (LONG) N0)
{
// Line runs from bottom to top, so flip across y = 0:
N0 = -(LONG) N0;
dN = -(LONG) dN;
fl |= HW_FLIP_V;
}
// Compute another delta:
dN -= N0;
if ((LONG) dN < 0)
return(FALSE);
if (dN >= dM)
{
if (dN == dM)
{
// Have to special case slopes of one:
fl |= HW_FLIP_SLOPE_ONE;
}
else
{
// Since line has slope greater than 1, flip across x = y:
register ULONG ulTmp;
ulTmp = dM; dM = dN; dN = ulTmp;
ulTmp = M0; M0 = N0; N0 = ulTmp;
fl |= HW_FLIP_D;
}
}
// Figure out if we can do the line in hardware, given that we have a
// limited number of bits of precision for the Bresenham terms.
//
// Remember that one bit has to be kept as a sign bit:
if ((LONG) dM >= (1L << (NUM_DDA_BITS - 1)))
return(FALSE);
fl |= gaflHardwareRound[fl];
/***********************************************************************\
* Calculate the error term at pixel 0.
\***********************************************************************/
x = LFLOOR((LONG) M0);
y = LFLOOR((LONG) N0);
M0 = FXFRAC(M0);
N0 = FXFRAC(N0);
// NOTE NOTE NOTE: If this routine were to handle any line in the 28.4
// space, it will overflow its math (the following part requires 36 bits
// of precision)! But we get here for lines that the hardware can handle
// (see the expression (dM >= (1L << (NUM_DDA_BITS - 1))) above?), so if
// cBits is less than 28, we're safe.
//
// If you're going to use this routine to handle all lines in the 28.4
// device space, you will HAVE to make sure the math doesn't overflow,
// otherwise you won't be NT compliant! (See 'bHardwareLine' for an example
// how to do that. You don't have to worry about this if you simply
// default to the strips code for long lines, because those routines
// already do the math correctly.)
// Calculate the remainder term [ dM * (N0 + F/2) - M0 * dN ]. Note
// that M0 and N0 have at most 4 bits of significance (and if the
// arguments are properly ordered, on a 486 each multiply would be no
// more than 13 cycles):
lGamma = (N0 + F/2) * dM - M0 * dN;
if (fl & HW_Y_ROUND_DOWN)
lGamma--;
lGamma >>= FLOG2;
/***********************************************************************\
* Figure out which pixels are at the ends of the line.
\***********************************************************************/
// The toughest part of GIQ is determining the start and end pels.
//
// Our approach here is to calculate x0 and x1 (the inclusive start
// and end columns of the line respectively, relative to our normalized
// origin). Then x1 - x0 + 1 is the number of pels in the line. The
// start point is easily calculated by plugging x0 into our line equation
// (which takes care of whether y = 1/2 rounds up or down in value)
// getting y0, and then undoing the normalizing flips to get back
// into device space.
//
// We look at the fractional parts of the coordinates of the start and
// end points, and call them (M0, N0) and (M1, N1) respectively, where
// 0 <= M0, N0, M1, N1 < 16. We plot (M0, N0) on the following grid
// to determine x0:
//
// +-----------------------> +x
// |
// | 0 1
// | 0123456789abcdef
// |
// | 0 ........?xxxxxxx
// | 1 ..........xxxxxx
// | 2 ...........xxxxx
// | 3 ............xxxx
// | 4 .............xxx
// | 5 ..............xx
// | 6 ...............x
// | 7 ................
// | 8 ................
// | 9 ......**........
// | a ........****...x
// | b ............****
// | c .............xxx****
// | d ............xxxx ****
// | e ...........xxxxx ****
// | f ..........xxxxxx
// |
// | 2 3
// v
//
// +y
//
// This grid accounts for the appropriate rounding of GIQ and last-pel
// exclusion. If (M0, N0) lands on an 'x', x0 = 2. If (M0, N0) lands
// on a '.', x0 = 1. If (M0, N0) lands on a '?', x0 rounds up or down,
// depending on what flips have been done to normalize the line.
//
// For the end point, if (M1, N1) lands on an 'x', x1 =
// floor((M0 + dM) / 16) + 1. If (M1, N1) lands on a '.', x1 =
// floor((M0 + dM)). If (M1, N1) lands on a '?', x1 rounds up or down,
// depending on what flips have been done to normalize the line.
//
// Lines of exactly slope one require a special case for both the start
// and end. For example, if the line ends such that (M1, N1) is (9, 1),
// the line has gone exactly through (8, 0) -- which may be considered
// to be part of 'x' because of rounding! So slopes of exactly slope
// one going through (8, 0) must also be considered as belonging in 'x'
// when an x value of 1/2 is supposed to round up in value.
// Calculate x0, x1:
N1 = FXFRAC(N0 + dN);
M1 = FXFRAC(M0 + dM);
x1 = LFLOOR(M0 + dM);
// Line runs left-to-right:
// Compute x1:
x1--;
if (M1 > 0)
{
if (N1 == 0)
{
if (LROUND(M1, fl & HW_X_ROUND_DOWN))
x1++;
}
else if (abs((LONG) (N1 - F/2)) <= (LONG) M1)
{
x1++;
}
}
if ((fl & (HW_FLIP_SLOPE_ONE | HW_X_ROUND_DOWN))
== (HW_FLIP_SLOPE_ONE | HW_X_ROUND_DOWN))
{
// Have to special-case diagonal lines going through our
// the point exactly equidistant between two horizontal
// pixels, if we're supposed to round x=1/2 down:
if ((M1 > 0) && (N1 == M1 + 8))
x1--;
if ((M0 > 0) && (N0 == M0 + 8))
{
x0 = 0;
goto left_to_right_compute_y0;
}
}
// Compute x0:
x0 = 0;
if (M0 > 0)
{
if (N0 == 0)
{
if (LROUND(M0, fl & HW_X_ROUND_DOWN))
x0 = 1;
}
else if (abs((LONG) (N0 - F/2)) <= (LONG) M0)
{
x0 = 1;
}
}
left_to_right_compute_y0:
/***********************************************************************\
* Calculate the start pixel.
\***********************************************************************/
// We now compute y0 and adjust the error term. We know x0, and we know
// the current formula for the pixels to be lit on the line:
//
// dN * x + lGamma
// y(x) = floor( --------------- )
// dM
//
// The remainder of this expression is the new error term at (x0, y0).
// Since x0 is going to be either 0 or 1, we don't actually have to do a
// multiply or divide to compute y0. Finally, we subtract dM from the
// new error term so that it is in the range [-dM, 0).
y0 = 0;
lGamma += (dN & (-x0));
lGamma -= dM;
if (lGamma >= 0)
{
y0 = 1;
lGamma -= dM;
}
// Undo our flips to get the start coordinate:
x += x0;
y += y0;
if (fl & HW_FLIP_D)
{
register LONG lTmp;
lTmp = x; x = y; y = lTmp;
}
if (fl & HW_FLIP_V)
{
y = -y;
}
if (fl & HW_FLIP_H)
{
x = -x;
}
/***********************************************************************\
* Return the Bresenham terms:
\***********************************************************************/
// iDir = gaiDir[fl & HW_FLIP_MASK];
// ptlStart.x = x;
// ptlStart.y = y;
// cPels = x1 - x0 + 1; // NOTE: You'll have to check if cPels <= 0!
// dMajor = dM;
// dMinor = dN;
// lErrorTerm = lGamma;
/***********************************************************************\
* Draw the line. S3 specific code follows:
\***********************************************************************/
cPels = x1 - x0 + 1;
#if 0
if (cPels > 0)
{
IO_FIFO_WAIT(ppdev, 7);
IO_CUR_X(ppdev, x);
IO_CUR_Y(ppdev, y);
IO_MAJ_AXIS_PCNT(ppdev, cPels);
IO_AXSTP(ppdev, dN);
IO_DIASTP(ppdev, dN - dM);
IO_ERR_TERM(ppdev, dN + lGamma);
IO_CMD(ppdev, gaiDrawCmd[fl & HW_FLIP_MASK]);
}
#endif
return(TRUE);
}