xenocara/xserver/mi/miwideline.c

/*

Copyright 1988, 1998  The Open Group

Permission to use, copy, modify, distribute, and sell this software and its
documentation for any purpose is hereby granted without fee, provided that
the above copyright notice appear in all copies and that both that
copyright notice and this permission notice appear in supporting
documentation.

The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE OPEN GROUP BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.

Except as contained in this notice, the name of The Open Group shall
not be used in advertising or otherwise to promote the sale, use or
other dealings in this Software without prior written authorization
from The Open Group.

*/

/* Author:  Keith Packard, MIT X Consortium */

/*
 * Mostly integer wideline code.  Uses a technique similar to
 * bresenham zero-width lines, except walks an X edge
 */

#ifdef HAVE_DIX_CONFIG_H
#include <dix-config.h>
#endif

#include <stdio.h>
#ifdef _XOPEN_SOURCE
#include <math.h>
#else
#define _XOPEN_SOURCE	/* to get prototype for hypot on some systems */
#include <math.h>
#undef _XOPEN_SOURCE
#endif
#include <X11/X.h>
#include "windowstr.h"
#include "gcstruct.h"
#include "regionstr.h"
#include "miwideline.h"
#include "mi.h"

static void miLineArc(DrawablePtr pDraw, GCPtr pGC,
		      unsigned long pixel, SpanDataPtr spanData,
		      LineFacePtr leftFace,
		      LineFacePtr rightFace,
		      double xorg, double yorg, Bool isInt);


/*
 * spans-based polygon filler
 */

static void
miFillPolyHelper (DrawablePtr pDrawable, GCPtr pGC, unsigned long pixel,
		  SpanDataPtr spanData, int y, int overall_height,
		  PolyEdgePtr left, PolyEdgePtr right,
		  int left_count, int right_count)
{
    int left_x = 0, left_e = 0;
    int	left_stepx = 0;
    int	left_signdx = 0;
    int	left_dy = 0, left_dx = 0;

    int right_x = 0, right_e = 0;
    int	right_stepx = 0;
    int	right_signdx = 0;
    int	right_dy = 0, right_dx = 0;

    int	height = 0;
    int	left_height = 0, right_height = 0;

    DDXPointPtr ppt;
    DDXPointPtr pptInit = NULL;
    int 	*pwidth;
    int 	*pwidthInit = NULL;
    XID		oldPixel;
    int		xorg;
    Spans	spanRec;

    left_height = 0;
    right_height = 0;
    
    if (!spanData)
    {
    	pptInit = xalloc (overall_height * sizeof(*ppt));
    	if (!pptInit)
	    return;
    	pwidthInit = xalloc (overall_height * sizeof(*pwidth));
    	if (!pwidthInit)
    	{
	    xfree (pptInit);
	    return;
    	}
	ppt = pptInit;
	pwidth = pwidthInit;
    	oldPixel = pGC->fgPixel;
    	if (pixel != oldPixel)
    	{
	    XID tmpPixel = (XID)pixel;
    	    DoChangeGC (pGC, GCForeground, &tmpPixel, FALSE);
    	    ValidateGC (pDrawable, pGC);
    	}
    }
    else
    {
	spanRec.points = xalloc (overall_height * sizeof (*ppt));
	if (!spanRec.points)
	    return;
	spanRec.widths = xalloc (overall_height * sizeof (int));
	if (!spanRec.widths)
	{
	    xfree (spanRec.points);
	    return;
	}
	ppt = spanRec.points;
	pwidth = spanRec.widths;
    }

    xorg = 0;
    if (pGC->miTranslate)
    {
	y += pDrawable->y;
	xorg = pDrawable->x;
    }
    while ((left_count || left_height) &&
	   (right_count || right_height))
    {
	MIPOLYRELOADLEFT
	MIPOLYRELOADRIGHT

	height = left_height;
	if (height > right_height)
	    height = right_height;

	left_height -= height;
	right_height -= height;

	while (--height >= 0)
	{
	    if (right_x >= left_x)
	    {
		ppt->y = y;
		ppt->x = left_x + xorg;
		ppt++;
		*pwidth++ = right_x - left_x + 1;
	    }
    	    y++;
    	
	    MIPOLYSTEPLEFT

	    MIPOLYSTEPRIGHT
	}
    }
    if (!spanData)
    {
    	(*pGC->ops->FillSpans) (pDrawable, pGC, ppt - pptInit, pptInit, pwidthInit, TRUE);
    	xfree (pwidthInit);
    	xfree (pptInit);
    	if (pixel != oldPixel)
    	{
	    DoChangeGC (pGC, GCForeground, &oldPixel, FALSE);
	    ValidateGC (pDrawable, pGC);
    	}
    }
    else
    {
	spanRec.count = ppt - spanRec.points;
	AppendSpanGroup (pGC, pixel, &spanRec, spanData)
    }
}

static void
miFillRectPolyHelper (
    DrawablePtr	pDrawable,
    GCPtr	pGC,
    unsigned long   pixel,
    SpanDataPtr	spanData,
    int		x,
    int		y,
    int		w,
    int		h)
{
    DDXPointPtr ppt;
    int 	*pwidth;
    XID		oldPixel;
    Spans	spanRec;
    xRectangle  rect;

    if (!spanData)
    {
	rect.x = x;
	rect.y = y;
	rect.width = w;
	rect.height = h;
    	oldPixel = pGC->fgPixel;
    	if (pixel != oldPixel)
    	{
	    XID tmpPixel = (XID)pixel;
    	    DoChangeGC (pGC, GCForeground, &tmpPixel, FALSE);
    	    ValidateGC (pDrawable, pGC);
    	}
	(*pGC->ops->PolyFillRect) (pDrawable, pGC, 1, &rect);
    	if (pixel != oldPixel)
    	{
	    DoChangeGC (pGC, GCForeground, &oldPixel, FALSE);
	    ValidateGC (pDrawable, pGC);
    	}
    }
    else
    {
	spanRec.points = xalloc (h * sizeof (*ppt));
	if (!spanRec.points)
	    return;
	spanRec.widths = xalloc (h * sizeof (int));
	if (!spanRec.widths)
	{
	    xfree (spanRec.points);
	    return;
	}
	ppt = spanRec.points;
	pwidth = spanRec.widths;

    	if (pGC->miTranslate)
    	{
	    y += pDrawable->y;
	    x += pDrawable->x;
    	}
	while (h--)
	{
	    ppt->x = x;
	    ppt->y = y;
	    ppt++;
	    *pwidth++ = w;
	    y++;
	}
	spanRec.count = ppt - spanRec.points;
	AppendSpanGroup (pGC, pixel, &spanRec, spanData)
    }
}

/* static */ int
miPolyBuildEdge (
    double	x0,
    double	y0,
    double	k,  /* x0 * dy - y0 * dx */
    int		dx,
    int		dy,
    int		xi,
    int		yi,
    int		left,
    PolyEdgePtr edge)
{
    int	    x, y, e;
    int	    xady;

    if (dy < 0)
    {
	dy = -dy;
	dx = -dx;
	k = -k;
    }

#ifdef NOTDEF
    {
	double	realk, kerror;
    	realk = x0 * dy - y0 * dx;
    	kerror = Fabs (realk - k);
    	if (kerror > .1)
	    printf ("realk: %g k: %g\n", realk, k);
    }
#endif
    y = ICEIL (y0);
    xady = ICEIL (k) + y * dx;

    if (xady <= 0)
	x = - (-xady / dy) - 1;
    else
	x = (xady - 1) / dy;

    e = xady - x * dy;

    if (dx >= 0)
    {
	edge->signdx = 1;
	edge->stepx = dx / dy;
	edge->dx = dx % dy;
    }
    else
    {
	edge->signdx = -1;
	edge->stepx = - (-dx / dy);
	edge->dx = -dx % dy;
	e = dy - e + 1;
    }
    edge->dy = dy;
    edge->x = x + left + xi;
    edge->e = e - dy;	/* bias to compare against 0 instead of dy */
    return y + yi;
}

#define StepAround(v, incr, max) (((v) + (incr) < 0) ? (max - 1) : ((v) + (incr) == max) ? 0 : ((v) + (incr)))

/* static */ int
miPolyBuildPoly (
    PolyVertexPtr	vertices,
    PolySlopePtr	slopes,
    int			count,
    int			xi,
    int			yi,
    PolyEdgePtr		left,
    PolyEdgePtr		right,
    int			*pnleft,
    int			*pnright,
    int			*h)
{
    int 	top, bottom;
    double 	miny, maxy;
    int 	i;
    int		j;
    int		clockwise;
    int		slopeoff;
    int 	s;
    int 	nright, nleft;
    int	   	y, lasty = 0, bottomy, topy = 0;

    /* find the top of the polygon */
    maxy = miny = vertices[0].y;
    bottom = top = 0;
    for (i = 1; i < count; i++)
    {
	if (vertices[i].y < miny)
	{
	    top = i;
	    miny = vertices[i].y;
	}
	if (vertices[i].y >= maxy)
	{
	    bottom = i;
	    maxy = vertices[i].y;
	}
    }
    clockwise = 1;
    slopeoff = 0;

    i = top;
    j = StepAround (top, -1, count);

    if (slopes[j].dy * slopes[i].dx > slopes[i].dy * slopes[j].dx)
    {
	clockwise = -1;
	slopeoff = -1;
    }

    bottomy = ICEIL (maxy) + yi;

    nright = 0;

    s = StepAround (top, slopeoff, count);
    i = top;
    while (i != bottom)
    {
	if (slopes[s].dy != 0)
	{
	    y = miPolyBuildEdge (vertices[i].x, vertices[i].y,
			slopes[s].k,
			slopes[s].dx, slopes[s].dy,
			xi, yi, 0,
			&right[nright]);
	    if (nright != 0)
	    	right[nright-1].height = y - lasty;
	    else
	    	topy = y;
	    nright++;
	    lasty = y;
	}

	i = StepAround (i, clockwise, count);
	s = StepAround (s, clockwise, count);
    }
    if (nright != 0)
	right[nright-1].height = bottomy - lasty;

    if (slopeoff == 0)
	slopeoff = -1;
    else
	slopeoff = 0;

    nleft = 0;
    s = StepAround (top, slopeoff, count);
    i = top;
    while (i != bottom)
    {
	if (slopes[s].dy != 0)
	{
	    y = miPolyBuildEdge (vertices[i].x, vertices[i].y,
			   slopes[s].k,
		       	   slopes[s].dx,  slopes[s].dy, xi, yi, 1,
		       	   &left[nleft]);
    
	    if (nleft != 0)
	    	left[nleft-1].height = y - lasty;
	    nleft++;
	    lasty = y;
	}
	i = StepAround (i, -clockwise, count);
	s = StepAround (s, -clockwise, count);
    }
    if (nleft != 0)
	left[nleft-1].height = bottomy - lasty;
    *pnleft = nleft;
    *pnright = nright;
    *h = bottomy - topy;
    return topy;
}

static void
miLineOnePoint (
    DrawablePtr	    pDrawable,
    GCPtr	    pGC,
    unsigned long   pixel,
    SpanDataPtr	    spanData,
    int		    x,
    int		    y)
{
    DDXPointRec pt;
    int	    wid;
    unsigned long	oldPixel;

    MILINESETPIXEL (pDrawable, pGC, pixel, oldPixel);
    if (pGC->fillStyle == FillSolid)
    {
	pt.x = x;
	pt.y = y;
	(*pGC->ops->PolyPoint) (pDrawable, pGC, CoordModeOrigin, 1, &pt);
    }
    else
    {
	wid = 1;
	if (pGC->miTranslate) 
	{
	    x += pDrawable->x;
	    y += pDrawable->y;
	}
	pt.x = x;
	pt.y = y;
	(*pGC->ops->FillSpans) (pDrawable, pGC, 1, &pt, &wid, TRUE);
    }
    MILINERESETPIXEL (pDrawable, pGC, pixel, oldPixel);
}

static void
miLineJoin (
    DrawablePtr 	pDrawable,
    GCPtr		pGC,
    unsigned long	pixel,
    SpanDataPtr		spanData,
    LineFacePtr		pLeft,
    LineFacePtr 	pRight)
{
    double	    mx = 0, my = 0;
    double	    denom = 0.0;
    PolyVertexRec   vertices[4];
    PolySlopeRec    slopes[4];
    int		    edgecount;
    PolyEdgeRec	    left[4], right[4];
    int		    nleft, nright;
    int		    y, height;
    int		    swapslopes;
    int		    joinStyle = pGC->joinStyle;
    int		    lw = pGC->lineWidth;

    if (lw == 1 && !spanData) {
	/* See if one of the lines will draw the joining pixel */
	if (pLeft->dx > 0 || (pLeft->dx == 0 && pLeft->dy > 0))
	    return;
	if (pRight->dx > 0 || (pRight->dx == 0 && pRight->dy > 0))
	    return;
	if (joinStyle != JoinRound) {
    	    denom = - pLeft->dx * (double)pRight->dy + pRight->dx * (double)pLeft->dy;
    	    if (denom == 0)
	    	return;	/* no join to draw */
	}
	if (joinStyle != JoinMiter) {
	    miLineOnePoint (pDrawable, pGC, pixel, spanData, pLeft->x, pLeft->y);
	    return;
	}
    } else {
    	if (joinStyle == JoinRound)
    	{
	    miLineArc(pDrawable, pGC, pixel, spanData,
		      pLeft, pRight,
		      (double)0.0, (double)0.0, TRUE);
	    return;
    	}
    	denom = - pLeft->dx * (double)pRight->dy + pRight->dx * (double)pLeft->dy;
    	if (denom == 0.0)
	    return;	/* no join to draw */
    }

    swapslopes = 0;
    if (denom > 0)
    {
	pLeft->xa = -pLeft->xa;
	pLeft->ya = -pLeft->ya;
	pLeft->dx = -pLeft->dx;
	pLeft->dy = -pLeft->dy;
    }
    else
    {
	swapslopes = 1;
	pRight->xa = -pRight->xa;
	pRight->ya = -pRight->ya;
	pRight->dx = -pRight->dx;
	pRight->dy = -pRight->dy;
    }

    vertices[0].x = pRight->xa;
    vertices[0].y = pRight->ya;
    slopes[0].dx = -pRight->dy;
    slopes[0].dy =  pRight->dx;
    slopes[0].k = 0;

    vertices[1].x = 0;
    vertices[1].y = 0;
    slopes[1].dx =  pLeft->dy;
    slopes[1].dy = -pLeft->dx;
    slopes[1].k = 0;

    vertices[2].x = pLeft->xa;
    vertices[2].y = pLeft->ya;

    if (joinStyle == JoinMiter)
    {
    	my = (pLeft->dy  * (pRight->xa * pRight->dy - pRight->ya * pRight->dx) -
              pRight->dy * (pLeft->xa  * pLeft->dy  - pLeft->ya  * pLeft->dx )) /
	      denom;
    	if (pLeft->dy != 0)
    	{
	    mx = pLeft->xa + (my - pLeft->ya) *
			    (double) pLeft->dx / (double) pLeft->dy;
    	}
    	else
    	{
	    mx = pRight->xa + (my - pRight->ya) *
			    (double) pRight->dx / (double) pRight->dy;
    	}
	/* check miter limit */
	if ((mx * mx + my * my) * 4 > SQSECANT * lw * lw)
	    joinStyle = JoinBevel;
    }

    if (joinStyle == JoinMiter)
    {
	slopes[2].dx = pLeft->dx;
	slopes[2].dy = pLeft->dy;
	slopes[2].k =  pLeft->k;
	if (swapslopes)
	{
	    slopes[2].dx = -slopes[2].dx;
	    slopes[2].dy = -slopes[2].dy;
	    slopes[2].k  = -slopes[2].k;
	}
	vertices[3].x = mx;
	vertices[3].y = my;
	slopes[3].dx = pRight->dx;
	slopes[3].dy = pRight->dy;
	slopes[3].k  = pRight->k;
	if (swapslopes)
	{
	    slopes[3].dx = -slopes[3].dx;
	    slopes[3].dy = -slopes[3].dy;
	    slopes[3].k  = -slopes[3].k;
	}
	edgecount = 4;
    }
    else
    {
	double	scale, dx, dy, adx, ady;

	adx = dx = pRight->xa - pLeft->xa;
	ady = dy = pRight->ya - pLeft->ya;
	if (adx < 0)
	    adx = -adx;
	if (ady < 0)
	    ady = -ady;
	scale = ady;
	if (adx > ady)
	    scale = adx;
	slopes[2].dx = (dx * 65536) / scale;
	slopes[2].dy = (dy * 65536) / scale;
	slopes[2].k = ((pLeft->xa + pRight->xa) * slopes[2].dy -
		       (pLeft->ya + pRight->ya) * slopes[2].dx) / 2.0;
	edgecount = 3;
    }

    y = miPolyBuildPoly (vertices, slopes, edgecount, pLeft->x, pLeft->y,
		   left, right, &nleft, &nright, &height);
    miFillPolyHelper (pDrawable, pGC, pixel, spanData, y, height, left, right, nleft, nright);
}

static int
miLineArcI (
    DrawablePtr	    pDraw,
    GCPtr	    pGC,
    int		    xorg,
    int		    yorg,
    DDXPointPtr	    points,
    int		    *widths)
{
    DDXPointPtr tpts, bpts;
    int *twids, *bwids;
    int x, y, e, ex, slw;

    tpts = points;
    twids = widths;
    if (pGC->miTranslate)
    {
	xorg += pDraw->x;
	yorg += pDraw->y;
    }
    slw = pGC->lineWidth;
    if (slw == 1)
    {
	tpts->x = xorg;
	tpts->y = yorg;
	*twids = 1;
	return 1;
    }
    bpts = tpts + slw;
    bwids = twids + slw;
    y = (slw >> 1) + 1;
    if (slw & 1)
	e = - ((y << 2) + 3);
    else
	e = - (y << 3);
    ex = -4;
    x = 0;
    while (y)
    {
	e += (y << 3) - 4;
	while (e >= 0)
	{
	    x++;
	    e += (ex = -((x << 3) + 4));
	}
	y--;
	slw = (x << 1) + 1;
	if ((e == ex) && (slw > 1))
	    slw--;
	tpts->x = xorg - x;
	tpts->y = yorg - y;
	tpts++;
	*twids++ = slw;
	if ((y != 0) && ((slw > 1) || (e != ex)))
	{
	    bpts--;
	    bpts->x = xorg - x;
	    bpts->y = yorg + y;
	    *--bwids = slw;
	}
    }
    return (pGC->lineWidth);
}

#define CLIPSTEPEDGE(edgey,edge,edgeleft) \
    if (ybase == edgey) \
    { \
	if (edgeleft) \
	{ \
	    if (edge->x > xcl) \
		xcl = edge->x; \
	} \
	else \
	{ \
	    if (edge->x < xcr) \
		xcr = edge->x; \
	} \
	edgey++; \
	edge->x += edge->stepx; \
	edge->e += edge->dx; \
	if (edge->e > 0) \
	{ \
	    edge->x += edge->signdx; \
	    edge->e -= edge->dy; \
	} \
    }

static int
miLineArcD (
    DrawablePtr	    pDraw,
    GCPtr	    pGC,
    double	    xorg,
    double	    yorg,
    DDXPointPtr	    points,
    int		    *widths,
    PolyEdgePtr	    edge1,
    int		    edgey1,
    Bool	    edgeleft1,
    PolyEdgePtr	    edge2,
    int		    edgey2,
    Bool	    edgeleft2)
{
    DDXPointPtr pts;
    int *wids;
    double radius, x0, y0, el, er, yk, xlk, xrk, k;
    int xbase, ybase, y, boty, xl, xr, xcl, xcr;
    int ymin, ymax;
    Bool edge1IsMin, edge2IsMin;
    int ymin1, ymin2;

    pts = points;
    wids = widths;
    xbase = floor(xorg);
    x0 = xorg - xbase;
    ybase = ICEIL (yorg);
    y0 = yorg - ybase;
    if (pGC->miTranslate)
    {
	xbase += pDraw->x;
	ybase += pDraw->y;
	edge1->x += pDraw->x;
	edge2->x += pDraw->x;
	edgey1 += pDraw->y;
	edgey2 += pDraw->y;
    }
    xlk = x0 + x0 + 1.0;
    xrk = x0 + x0 - 1.0;
    yk = y0 + y0 - 1.0;
    radius = ((double)pGC->lineWidth) / 2.0;
    y = floor(radius - y0 + 1.0);
    ybase -= y;
    ymin = ybase;
    ymax = 65536;
    edge1IsMin = FALSE;
    ymin1 = edgey1;
    if (edge1->dy >= 0)
    {
    	if (!edge1->dy)
    	{
	    if (edgeleft1)
	    	edge1IsMin = TRUE;
	    else
	    	ymax = edgey1;
	    edgey1 = 65536;
    	}
    	else
    	{
	    if ((edge1->signdx < 0) == edgeleft1)
	    	edge1IsMin = TRUE;
    	}
    }
    edge2IsMin = FALSE;
    ymin2 = edgey2;
    if (edge2->dy >= 0)
    {
    	if (!edge2->dy)
    	{
	    if (edgeleft2)
	    	edge2IsMin = TRUE;
	    else
	    	ymax = edgey2;
	    edgey2 = 65536;
    	}
    	else
    	{
	    if ((edge2->signdx < 0) == edgeleft2)
	    	edge2IsMin = TRUE;
    	}
    }
    if (edge1IsMin)
    {
	ymin = ymin1;
	if (edge2IsMin && ymin1 > ymin2)
	    ymin = ymin2;
    } else if (edge2IsMin)
	ymin = ymin2;
    el = radius * radius - ((y + y0) * (y + y0)) - (x0 * x0);
    er = el + xrk;
    xl = 1;
    xr = 0;
    if (x0 < 0.5)
    {
	xl = 0;
	el -= xlk;
    }
    boty = (y0 < -0.5) ? 1 : 0;
    if (ybase + y - boty > ymax)
	boty = ymax - ybase - y;
    while (y > boty)
    {
	k = (y << 1) + yk;
	er += k;
	while (er > 0.0)
	{
	    xr++;
	    er += xrk - (xr << 1);
	}
	el += k;
	while (el >= 0.0)
	{
	    xl--;
	    el += (xl << 1) - xlk;
	}
	y--;
	ybase++;
	if (ybase < ymin)
	    continue;
	xcl = xl + xbase;
	xcr = xr + xbase;
	CLIPSTEPEDGE(edgey1, edge1, edgeleft1);
	CLIPSTEPEDGE(edgey2, edge2, edgeleft2);
	if (xcr >= xcl)
	{
	    pts->x = xcl;
	    pts->y = ybase;
	    pts++;
	    *wids++ = xcr - xcl + 1;
	}
    }
    er = xrk - (xr << 1) - er;
    el = (xl << 1) - xlk - el;
    boty = floor(-y0 - radius + 1.0);
    if (ybase + y - boty > ymax)
	boty = ymax - ybase - y;
    while (y > boty)
    {
	k = (y << 1) + yk;
	er -= k;
	while ((er >= 0.0) && (xr >= 0))
	{
	    xr--;
	    er += xrk - (xr << 1);
	}
	el -= k;
	while ((el > 0.0) && (xl <= 0))
	{
	    xl++;
	    el += (xl << 1) - xlk;
	}
	y--;
	ybase++;
	if (ybase < ymin)
	    continue;
	xcl = xl + xbase;
	xcr = xr + xbase;
	CLIPSTEPEDGE(edgey1, edge1, edgeleft1);
	CLIPSTEPEDGE(edgey2, edge2, edgeleft2);
	if (xcr >= xcl)
	{
	    pts->x = xcl;
	    pts->y = ybase;
	    pts++;
	    *wids++ = xcr - xcl + 1;
	}
    }
    return (pts - points);
}

static int
miRoundJoinFace (LineFacePtr face, PolyEdgePtr edge, Bool *leftEdge)
{
    int	    y;
    int	    dx, dy;
    double  xa, ya;
    Bool	left;

    dx = -face->dy;
    dy = face->dx;
    xa = face->xa;
    ya = face->ya;
    left = 1;
    if (ya > 0)
    {
	ya = 0.0;
	xa = 0.0;
    }
    if (dy < 0 || (dy == 0 && dx > 0))
    {
	dx = -dx;
	dy = -dy;
	left = !left;
    }
    if (dx == 0 && dy == 0)
	dy = 1;
    if (dy == 0)
    {
	y = ICEIL (face->ya) + face->y;
	edge->x = -32767;
	edge->stepx = 0;
	edge->signdx = 0;
	edge->e = -1;
	edge->dy = 0;
	edge->dx = 0;
	edge->height = 0;
    }
    else
    {
	y = miPolyBuildEdge (xa, ya, 0.0, dx, dy, face->x, face->y, !left, edge);
	edge->height = 32767;
    }
    *leftEdge = !left;
    return y;
}

void
miRoundJoinClip (LineFacePtr pLeft, LineFacePtr pRight,
		 PolyEdgePtr edge1, PolyEdgePtr edge2,
		 int *y1, int *y2, Bool *left1, Bool *left2)
{
    double	denom;

    denom = - pLeft->dx * (double)pRight->dy + pRight->dx * (double)pLeft->dy;

    if (denom >= 0)
    {
	pLeft->xa = -pLeft->xa;
	pLeft->ya = -pLeft->ya;
    }
    else
    {
	pRight->xa = -pRight->xa;
	pRight->ya = -pRight->ya;
    }
    *y1 = miRoundJoinFace (pLeft, edge1, left1);
    *y2 = miRoundJoinFace (pRight, edge2, left2);
}

int
miRoundCapClip (LineFacePtr face, Bool isInt, PolyEdgePtr edge, Bool *leftEdge)
{
    int		y;
    int 	dx, dy;
    double	xa, ya, k;
    Bool	left;

    dx = -face->dy;
    dy = face->dx;
    xa = face->xa;
    ya = face->ya;
    k = 0.0;
    if (!isInt)
	k = face->k;
    left = 1;
    if (dy < 0 || (dy == 0 && dx > 0))
    {
	dx = -dx;
	dy = -dy;
	xa = -xa;
	ya = -ya;
	left = !left;
    }
    if (dx == 0 && dy == 0)
	dy = 1;
    if (dy == 0)
    {
	y = ICEIL (face->ya) + face->y;
	edge->x = -32767;
	edge->stepx = 0;
	edge->signdx = 0;
	edge->e = -1;
	edge->dy = 0;
	edge->dx = 0;
	edge->height = 0;
    }
    else
    {
	y = miPolyBuildEdge (xa, ya, k, dx, dy, face->x, face->y, !left, edge);
	edge->height = 32767;
    }
    *leftEdge = !left;
    return y;
}

static void
miLineArc (
    DrawablePtr		pDraw,
    GCPtr  		pGC,
    unsigned long	pixel,
    SpanDataPtr		spanData,
    LineFacePtr		leftFace,
    LineFacePtr 	rightFace,
    double	    	xorg,
    double          	yorg,
    Bool	    	isInt)
{
    DDXPointPtr points;
    int *widths;
    int xorgi = 0, yorgi = 0;
    XID		oldPixel;
    Spans spanRec;
    int n;
    PolyEdgeRec	edge1, edge2;
    int		edgey1, edgey2;
    Bool	edgeleft1, edgeleft2;

    if (isInt)
    {
	xorgi = leftFace ? leftFace->x : rightFace->x;
	yorgi = leftFace ? leftFace->y : rightFace->y;
    }
    edgey1 = 65536;
    edgey2 = 65536;
    edge1.x = 0; /* not used, keep memory checkers happy */
    edge1.dy = -1;
    edge2.x = 0; /* not used, keep memory checkers happy */
    edge2.dy = -1;
    edgeleft1 = FALSE;
    edgeleft2 = FALSE;
    if ((pGC->lineStyle != LineSolid || pGC->lineWidth > 2) &&
	((pGC->capStyle == CapRound && pGC->joinStyle != JoinRound) ||
	 (pGC->joinStyle == JoinRound && pGC->capStyle == CapButt)))
    {
	if (isInt)
	{
	    xorg = (double) xorgi;
	    yorg = (double) yorgi;
	}
	if (leftFace && rightFace)
	{
	    miRoundJoinClip (leftFace, rightFace, &edge1, &edge2,
			     &edgey1, &edgey2, &edgeleft1, &edgeleft2);
	}
	else if (leftFace)
	{
	    edgey1 = miRoundCapClip (leftFace, isInt, &edge1, &edgeleft1);
	}
	else if (rightFace)
	{
	    edgey2 = miRoundCapClip (rightFace, isInt, &edge2, &edgeleft2);
	}
	isInt = FALSE;
    }
    if (!spanData)
    {
    	points = xalloc(sizeof(DDXPointRec) * pGC->lineWidth);
    	if (!points)
	    return;
    	widths = xalloc(sizeof(int) * pGC->lineWidth);
    	if (!widths)
    	{
	    xfree(points);
	    return;
    	}
    	oldPixel = pGC->fgPixel;
    	if (pixel != oldPixel)
    	{
	    XID tmpPixel = (XID)pixel;
	    DoChangeGC(pGC, GCForeground, &tmpPixel, FALSE);
	    ValidateGC (pDraw, pGC);
    	}
    }
    else
    {
	points = xalloc (pGC->lineWidth * sizeof (DDXPointRec));
	if (!points)
	    return;
	widths = xalloc (pGC->lineWidth * sizeof (int));
	if (!widths)
	{
	    xfree (points);
	    return;
	}
	spanRec.points = points;
	spanRec.widths = widths;
    }
    if (isInt)
	n = miLineArcI(pDraw, pGC, xorgi, yorgi, points, widths);
    else
	n = miLineArcD(pDraw, pGC, xorg, yorg, points, widths,
		       &edge1, edgey1, edgeleft1,
		       &edge2, edgey2, edgeleft2);

    if (!spanData)
    {
    	(*pGC->ops->FillSpans)(pDraw, pGC, n, points, widths, TRUE);
    	xfree(widths);
    	xfree(points);
    	if (pixel != oldPixel)
    	{
	    DoChangeGC(pGC, GCForeground, &oldPixel, FALSE);
	    ValidateGC (pDraw, pGC);
    	}
    }
    else
    {
	spanRec.count = n;
	AppendSpanGroup (pGC, pixel, &spanRec, spanData)
    }
}

static void
miLineProjectingCap (DrawablePtr pDrawable, GCPtr pGC, unsigned long pixel,
		     SpanDataPtr spanData, LineFacePtr face, Bool isLeft,
		     double xorg, double yorg, Bool isInt)
{
    int	xorgi = 0, yorgi = 0;
    int	lw;
    PolyEdgeRec	lefts[2], rights[2];
    int		lefty, righty, topy, bottomy;
    PolyEdgePtr left, right;
    PolyEdgePtr	top, bottom;
    double	xa,ya;
    double	k;
    double	xap, yap;
    int		dx, dy;
    double	projectXoff, projectYoff;
    double	maxy;
    int		finaly;
    
    if (isInt)
    {
	xorgi = face->x;
	yorgi = face->y;
    }
    lw = pGC->lineWidth;
    dx = face->dx;
    dy = face->dy;
    k = face->k;
    if (dy == 0)
    {
	lefts[0].height = lw;
	lefts[0].x = xorgi;
	if (isLeft)
	    lefts[0].x -= (lw >> 1);
	lefts[0].stepx = 0;
	lefts[0].signdx = 1;
	lefts[0].e = -lw;
	lefts[0].dx = 0;
	lefts[0].dy = lw;
	rights[0].height = lw;
	rights[0].x = xorgi;
	if (!isLeft)
	    rights[0].x += ((lw + 1) >> 1);
	rights[0].stepx = 0;
	rights[0].signdx = 1;
	rights[0].e = -lw;
	rights[0].dx = 0;
	rights[0].dy = lw;
	miFillPolyHelper (pDrawable, pGC, pixel, spanData, yorgi - (lw >> 1), lw,
		     lefts, rights, 1, 1);
    }
    else if (dx == 0)
    {
	if (dy < 0) {
	    dy = -dy;
	    isLeft = !isLeft;
	}
	topy = yorgi;
	bottomy = yorgi + dy;
	if (isLeft)
	    topy -= (lw >> 1);
	else
	    bottomy += (lw >> 1);
	lefts[0].height = bottomy - topy;
	lefts[0].x = xorgi - (lw >> 1);
	lefts[0].stepx = 0;
	lefts[0].signdx = 1;
	lefts[0].e = -dy;
	lefts[0].dx = dx;
	lefts[0].dy = dy;

	rights[0].height = bottomy - topy;
	rights[0].x = lefts[0].x + (lw-1);
	rights[0].stepx = 0;
	rights[0].signdx = 1;
	rights[0].e = -dy;
	rights[0].dx = dx;
	rights[0].dy = dy;
	miFillPolyHelper (pDrawable, pGC, pixel, spanData, topy, bottomy - topy, lefts, rights, 1, 1);
    }
    else
    {
	xa = face->xa;
	ya = face->ya;
	projectXoff = -ya;
	projectYoff = xa;
	if (dx < 0)
	{
	    right = &rights[1];
	    left = &lefts[0];
	    top = &rights[0];
	    bottom = &lefts[1];
	}
	else
	{
	    right = &rights[0];
	    left = &lefts[1];
	    top = &lefts[0];
	    bottom = &rights[1];
	}
	if (isLeft)
	{
	    righty = miPolyBuildEdge (xa, ya,
		     k, dx, dy, xorgi, yorgi, 0, right);
	    
	    xa = -xa;
	    ya = -ya;
	    k = -k;
	    lefty = miPolyBuildEdge (xa - projectXoff, ya - projectYoff,
				     k, dx, dy, xorgi, yorgi, 1, left);
	    if (dx > 0)
	    {
		ya = -ya;
		xa = -xa;
	    }
	    xap = xa - projectXoff;
	    yap = ya - projectYoff;
	    topy = miPolyBuildEdge (xap, yap, xap * dx + yap * dy,
				    -dy, dx, xorgi, yorgi, dx > 0, top);
	    bottomy = miPolyBuildEdge (xa, ya,
				       0.0, -dy, dx, xorgi, yorgi, dx < 0, bottom);
	    maxy = -ya;
	}
	else
	{
	    righty = miPolyBuildEdge (xa - projectXoff, ya - projectYoff,
		     k, dx, dy, xorgi, yorgi, 0, right);
	    
	    xa = -xa;
	    ya = -ya;
	    k = -k;
	    lefty = miPolyBuildEdge (xa, ya,
		    k, dx, dy, xorgi, yorgi, 1, left);
	    if (dx > 0)
	    {
		ya = -ya;
		xa = -xa;
	    }
	    xap = xa - projectXoff;
	    yap = ya - projectYoff;
	    topy = miPolyBuildEdge (xa, ya, 0.0, -dy, dx, xorgi, xorgi, dx > 0, top);
	    bottomy = miPolyBuildEdge (xap, yap, xap * dx + yap * dy,
				       -dy, dx, xorgi, xorgi, dx < 0, bottom);
	    maxy = -ya + projectYoff;
	}
	finaly = ICEIL(maxy) + yorgi;
	if (dx < 0)
	{
	    left->height = bottomy - lefty;
	    right->height = finaly - righty;
	    top->height = righty - topy;
	}
	else
	{
	    right->height =  bottomy - righty;
	    left->height = finaly - lefty;
	    top->height = lefty - topy;
	}
	bottom->height = finaly - bottomy;
	miFillPolyHelper (pDrawable, pGC, pixel, spanData, topy,
		     bottom->height + bottomy - topy, lefts, rights, 2, 2);
    }
}

static void
miWideSegment (
    DrawablePtr		pDrawable,
    GCPtr		pGC,
    unsigned long	pixel,
    SpanDataPtr		spanData,
    int    		x1,
    int    		y1,
    int    		x2,
    int    		y2,
    Bool		projectLeft,
    Bool		projectRight,
    LineFacePtr 	leftFace,
    LineFacePtr 	rightFace)
{
    double	l, L, r;
    double	xa, ya;
    double	projectXoff = 0.0, projectYoff = 0.0;
    double	k;
    double	maxy;
    int		x, y;
    int		dx, dy;
    int		finaly;
    PolyEdgePtr left, right;
    PolyEdgePtr	top, bottom;
    int		lefty, righty, topy, bottomy;
    int		signdx;
    PolyEdgeRec	lefts[2], rights[2];
    LineFacePtr	tface;
    int		lw = pGC->lineWidth;

    /* draw top-to-bottom always */
    if (y2 < y1 || (y2 == y1 && x2 < x1))
    {
	x = x1;
	x1 = x2;
	x2 = x;

	y = y1;
	y1 = y2;
	y2 = y;

	x = projectLeft;
	projectLeft = projectRight;
	projectRight = x;

	tface = leftFace;
	leftFace = rightFace;
	rightFace = tface;
    }

    dy = y2 - y1;
    signdx = 1;
    dx = x2 - x1;
    if (dx < 0)
	signdx = -1;

    leftFace->x = x1;
    leftFace->y = y1;
    leftFace->dx = dx;
    leftFace->dy = dy;

    rightFace->x = x2;
    rightFace->y = y2;
    rightFace->dx = -dx;
    rightFace->dy = -dy;

    if (dy == 0)
    {
	rightFace->xa = 0;
	rightFace->ya = (double) lw / 2.0;
	rightFace->k = -(double) (lw * dx) / 2.0;
	leftFace->xa = 0;
	leftFace->ya = -rightFace->ya;
	leftFace->k = rightFace->k;
	x = x1;
	if (projectLeft)
	    x -= (lw >> 1);
	y = y1 - (lw >> 1);
	dx = x2 - x;
	if (projectRight)
	    dx += ((lw + 1) >> 1);
	dy = lw;
	miFillRectPolyHelper (pDrawable, pGC, pixel, spanData,
			      x, y, dx, dy);
    }
    else if (dx == 0)
    {
	leftFace->xa =  (double) lw / 2.0;
	leftFace->ya = 0;
	leftFace->k = (double) (lw * dy) / 2.0;
	rightFace->xa = -leftFace->xa;
	rightFace->ya = 0;
	rightFace->k = leftFace->k;
	y = y1;
	if (projectLeft)
	    y -= lw >> 1;
	x = x1 - (lw >> 1);
	dy = y2 - y;
	if (projectRight)
	    dy += ((lw + 1) >> 1);
	dx = lw;
	miFillRectPolyHelper (pDrawable, pGC, pixel, spanData,
			      x, y, dx, dy);
    }
    else
    {
    	l = ((double) lw) / 2.0;
    	L = hypot ((double) dx, (double) dy);

	if (dx < 0)
	{
	    right = &rights[1];
	    left = &lefts[0];
	    top = &rights[0];
	    bottom = &lefts[1];
	}
	else
	{
	    right = &rights[0];
	    left = &lefts[1];
	    top = &lefts[0];
	    bottom = &rights[1];
	}
	r = l / L;

	/* coord of upper bound at integral y */
	ya = -r * dx;
	xa = r * dy;

	if (projectLeft | projectRight)
	{
	    projectXoff = -ya;
	    projectYoff = xa;
	}

    	/* xa * dy - ya * dx */
	k = l * L;

	leftFace->xa = xa;
	leftFace->ya = ya;
	leftFace->k = k;
	rightFace->xa = -xa;
	rightFace->ya = -ya;
	rightFace->k = k;

	if (projectLeft)
	    righty = miPolyBuildEdge (xa - projectXoff, ya - projectYoff,
				      k, dx, dy, x1, y1, 0, right);
	else
	    righty = miPolyBuildEdge (xa, ya,
				      k, dx, dy, x1, y1, 0, right);

	/* coord of lower bound at integral y */
	ya = -ya;
	xa = -xa;

	/* xa * dy - ya * dx */
	k = - k;

	if (projectLeft)
	    lefty = miPolyBuildEdge (xa - projectXoff, ya - projectYoff,
				     k, dx, dy, x1, y1, 1, left);
	else
	    lefty = miPolyBuildEdge (xa, ya,
				     k, dx, dy, x1, y1, 1, left);

	/* coord of top face at integral y */

	if (signdx > 0)
	{
	    ya = -ya;
	    xa = -xa;
	}

	if (projectLeft)
	{
	    double xap = xa - projectXoff;
	    double yap = ya - projectYoff;
	    topy = miPolyBuildEdge (xap, yap, xap * dx + yap * dy,
				    -dy, dx, x1, y1, dx > 0, top);
	}
	else
	    topy = miPolyBuildEdge (xa, ya, 0.0, -dy, dx, x1, y1, dx > 0, top);

	/* coord of bottom face at integral y */

	if (projectRight)
	{
	    double xap = xa + projectXoff;
	    double yap = ya + projectYoff;
	    bottomy = miPolyBuildEdge (xap, yap, xap * dx + yap * dy,
				       -dy, dx, x2, y2, dx < 0, bottom);
	    maxy = -ya + projectYoff;
	}
	else
	{
	    bottomy = miPolyBuildEdge (xa, ya,
				       0.0, -dy, dx, x2, y2, dx < 0, bottom);
	    maxy = -ya;
	}

	finaly = ICEIL (maxy) + y2;

	if (dx < 0)
	{
	    left->height = bottomy - lefty;
	    right->height = finaly - righty;
	    top->height = righty - topy;
	}
	else
	{
	    right->height =  bottomy - righty;
	    left->height = finaly - lefty;
	    top->height = lefty - topy;
	}
	bottom->height = finaly - bottomy;
	miFillPolyHelper (pDrawable, pGC, pixel, spanData, topy,
		     bottom->height + bottomy - topy, lefts, rights, 2, 2);
    }
}

static SpanDataPtr
miSetupSpanData (GCPtr pGC, SpanDataPtr spanData, int npt)
{
    if ((npt < 3 && pGC->capStyle != CapRound) || miSpansEasyRop(pGC->alu))
	return (SpanDataPtr) NULL;
    if (pGC->lineStyle == LineDoubleDash)
	miInitSpanGroup (&spanData->bgGroup);
    miInitSpanGroup (&spanData->fgGroup);
    return spanData;
}

static void
miCleanupSpanData (DrawablePtr pDrawable, GCPtr pGC, SpanDataPtr spanData)
{
    if (pGC->lineStyle == LineDoubleDash)
    {
	XID oldPixel, pixel;
	
	pixel = pGC->bgPixel;
	oldPixel = pGC->fgPixel;
    	if (pixel != oldPixel)
    	{
    	    DoChangeGC (pGC, GCForeground, &pixel, FALSE);
    	    ValidateGC (pDrawable, pGC);
    	}
	miFillUniqueSpanGroup (pDrawable, pGC, &spanData->bgGroup);
	miFreeSpanGroup (&spanData->bgGroup);
    	if (pixel != oldPixel)
    	{
	    DoChangeGC (pGC, GCForeground, &oldPixel, FALSE);
	    ValidateGC (pDrawable, pGC);
    	}
    }
    miFillUniqueSpanGroup (pDrawable, pGC, &spanData->fgGroup);
    miFreeSpanGroup (&spanData->fgGroup);
}

void
miWideLine (DrawablePtr pDrawable, GCPtr pGC,
	    int mode, int npt, DDXPointPtr pPts)
{
 int x1, y1, x2, y2;
    SpanDataRec	spanDataRec;
    SpanDataPtr	spanData;
    long   	pixel;
    Bool	projectLeft, projectRight;
    LineFaceRec	leftFace, rightFace, prevRightFace;
    LineFaceRec	firstFace;
    int		first;
    Bool	somethingDrawn = FALSE;
    Bool	selfJoin;

    spanData = miSetupSpanData (pGC, &spanDataRec, npt);
    pixel = pGC->fgPixel;
    x2 = pPts->x;
    y2 = pPts->y;
    first = TRUE;
    selfJoin = FALSE;
    if (npt > 1)
    {
    	if (mode == CoordModePrevious)
    	{
	    int nptTmp;
	    DDXPointPtr pPtsTmp;
    
	    x1 = x2;
	    y1 = y2;
	    nptTmp = npt;
	    pPtsTmp = pPts + 1;
	    while (--nptTmp)
	    {
	    	x1 += pPtsTmp->x;
	    	y1 += pPtsTmp->y;
	    	++pPtsTmp;
	    }
	    if (x2 == x1 && y2 == y1)
	    	selfJoin = TRUE;
    	}
    	else if (x2 == pPts[npt-1].x && y2 == pPts[npt-1].y)
    	{
	    selfJoin = TRUE;
    	}
    }
    projectLeft = pGC->capStyle == CapProjecting && !selfJoin;
    projectRight = FALSE;
    while (--npt)
    {
	x1 = x2;
	y1 = y2;
	++pPts;
	x2 = pPts->x;
	y2 = pPts->y;
	if (mode == CoordModePrevious)
	{
	    x2 += x1;
	    y2 += y1;
	}
	if (x1 != x2 || y1 != y2)
	{
	    somethingDrawn = TRUE;
	    if (npt == 1 && pGC->capStyle == CapProjecting && !selfJoin)
	    	projectRight = TRUE;
	    miWideSegment (pDrawable, pGC, pixel, spanData, x1, y1, x2, y2,
		       	   projectLeft, projectRight, &leftFace, &rightFace);
	    if (first)
	    {
	    	if (selfJoin)
		    firstFace = leftFace;
	    	else if (pGC->capStyle == CapRound)
		{
		    if (pGC->lineWidth == 1 && !spanData)
			miLineOnePoint (pDrawable, pGC, pixel, spanData, x1, y1);
		    else
		    	miLineArc (pDrawable, pGC, pixel, spanData,
			       	   &leftFace, (LineFacePtr) NULL,
 			       	   (double)0.0, (double)0.0,
			       	   TRUE);
		}
	    }
	    else
	    {
	    	miLineJoin (pDrawable, pGC, pixel, spanData, &leftFace,
		            &prevRightFace);
	    }
	    prevRightFace = rightFace;
	    first = FALSE;
	    projectLeft = FALSE;
	}
	if (npt == 1 && somethingDrawn)
 	{
	    if (selfJoin)
		miLineJoin (pDrawable, pGC, pixel, spanData, &firstFace,
			    &rightFace);
	    else if (pGC->capStyle == CapRound)
	    {
		if (pGC->lineWidth == 1 && !spanData)
		    miLineOnePoint (pDrawable, pGC, pixel, spanData, x2, y2);
		else
		    miLineArc (pDrawable, pGC, pixel, spanData,
			       (LineFacePtr) NULL, &rightFace,
			       (double)0.0, (double)0.0,
			       TRUE);
	    }
	}
    }
    /* handle crock where all points are coincedent */
    if (!somethingDrawn)
    {
	projectLeft = pGC->capStyle == CapProjecting;
	miWideSegment (pDrawable, pGC, pixel, spanData,
		       x2, y2, x2, y2, projectLeft, projectLeft,
		       &leftFace, &rightFace);
	if (pGC->capStyle == CapRound)
	{
	    miLineArc (pDrawable, pGC, pixel, spanData,
		       &leftFace, (LineFacePtr) NULL,
		       (double)0.0, (double)0.0,
		       TRUE);
	    rightFace.dx = -1;	/* sleezy hack to make it work */
	    miLineArc (pDrawable, pGC, pixel, spanData,
		       (LineFacePtr) NULL, &rightFace,
 		       (double)0.0, (double)0.0,
		       TRUE);
	}
    }
    if (spanData)
	miCleanupSpanData (pDrawable, pGC, spanData);
}

#define V_TOP	    0
#define V_RIGHT	    1
#define V_BOTTOM    2
#define V_LEFT	    3

static void
miWideDashSegment (
    DrawablePtr	    pDrawable,
    GCPtr  	    pGC,
    SpanDataPtr	    spanData,
    int		    *pDashOffset,
    int		    *pDashIndex,
    int		    x1,
    int		    y1,
    int		    x2,
    int		    y2,
    Bool	    projectLeft,
    Bool	    projectRight,
    LineFacePtr	    leftFace,
    LineFacePtr	    rightFace)
{
    int		    dashIndex, dashRemain;
    unsigned char   *pDash;
    double	    L, l;
    double	    k;
    PolyVertexRec   vertices[4];
    PolyVertexRec   saveRight, saveBottom;
    PolySlopeRec    slopes[4];
    PolyEdgeRec	    left[2], right[2];
    LineFaceRec	    lcapFace, rcapFace;
    int		    nleft, nright;
    int		    h;
    int		    y;
    int		    dy, dx;
    unsigned long   pixel;
    double	    LRemain;
    double	    r;
    double	    rdx, rdy;
    double	    dashDx, dashDy;
    double	    saveK = 0.0;
    Bool	    first = TRUE;
    double	    lcenterx, lcentery, rcenterx = 0.0, rcentery = 0.0;
    unsigned long   fgPixel, bgPixel;
    
    dx = x2 - x1;
    dy = y2 - y1;
    dashIndex = *pDashIndex;
    pDash = pGC->dash;
    dashRemain = pDash[dashIndex] - *pDashOffset;
    fgPixel = pGC->fgPixel;
    bgPixel = pGC->bgPixel;
    if (pGC->fillStyle == FillOpaqueStippled ||
	pGC->fillStyle == FillTiled)
    {
	bgPixel = fgPixel;
    }

    l = ((double) pGC->lineWidth) / 2.0;
    if (dx == 0)
    {
	L = dy;
	rdx = 0;
	rdy = l;
	if (dy < 0)
	{
	    L = -dy;
	    rdy = -l;
	}
    }
    else if (dy == 0)
    {
	L = dx;
	rdx = l;
	rdy = 0;
	if (dx < 0)
	{
	    L = -dx;
	    rdx = -l;
	}
    }
    else
    {
	L = hypot ((double) dx, (double) dy);
	r = l / L;

	rdx = r * dx;
	rdy = r * dy;
    }
    k = l * L;
    LRemain = L;
    /* All position comments are relative to a line with dx and dy > 0,
     * but the code does not depend on this */
    /* top */
    slopes[V_TOP].dx = dx;
    slopes[V_TOP].dy = dy;
    slopes[V_TOP].k = k;
    /* right */
    slopes[V_RIGHT].dx = -dy;
    slopes[V_RIGHT].dy = dx;
    slopes[V_RIGHT].k = 0;
    /* bottom */
    slopes[V_BOTTOM].dx = -dx;
    slopes[V_BOTTOM].dy = -dy;
    slopes[V_BOTTOM].k = k;
    /* left */
    slopes[V_LEFT].dx = dy;
    slopes[V_LEFT].dy = -dx;
    slopes[V_LEFT].k = 0;

    /* preload the start coordinates */
    vertices[V_RIGHT].x = vertices[V_TOP].x = rdy;
    vertices[V_RIGHT].y = vertices[V_TOP].y = -rdx;

    vertices[V_BOTTOM].x = vertices[V_LEFT].x = -rdy;
    vertices[V_BOTTOM].y = vertices[V_LEFT].y = rdx;

    if (projectLeft)
    {
	vertices[V_TOP].x -= rdx;
	vertices[V_TOP].y -= rdy;

	vertices[V_LEFT].x -= rdx;
	vertices[V_LEFT].y -= rdy;

	slopes[V_LEFT].k = rdx * dx + rdy * dy;
    }

    lcenterx = x1;
    lcentery = y1;

    if (pGC->capStyle == CapRound)
    {
	lcapFace.dx = dx;
	lcapFace.dy = dy;
	lcapFace.x = x1;
	lcapFace.y = y1;

	rcapFace.dx = -dx;
	rcapFace.dy = -dy;
	rcapFace.x = x1;
	rcapFace.y = y1;
    }
    while (LRemain > dashRemain)
    {
	dashDx = (dashRemain * dx) / L;
	dashDy = (dashRemain * dy) / L;

	rcenterx = lcenterx + dashDx;
	rcentery = lcentery + dashDy;

	vertices[V_RIGHT].x += dashDx;
	vertices[V_RIGHT].y += dashDy;

	vertices[V_BOTTOM].x += dashDx;
	vertices[V_BOTTOM].y += dashDy;

	slopes[V_RIGHT].k = vertices[V_RIGHT].x * dx + vertices[V_RIGHT].y * dy;

	if (pGC->lineStyle == LineDoubleDash || !(dashIndex & 1))
	{
	    if (pGC->lineStyle == LineOnOffDash &&
 	        pGC->capStyle == CapProjecting)
	    {
		saveRight = vertices[V_RIGHT];
		saveBottom = vertices[V_BOTTOM];
		saveK = slopes[V_RIGHT].k;
		
		if (!first)
		{
		    vertices[V_TOP].x -= rdx;
		    vertices[V_TOP].y -= rdy;
    
		    vertices[V_LEFT].x -= rdx;
		    vertices[V_LEFT].y -= rdy;

		    slopes[V_LEFT].k = vertices[V_LEFT].x *
				       slopes[V_LEFT].dy -
				       vertices[V_LEFT].y *
				       slopes[V_LEFT].dx;
		}
		
		vertices[V_RIGHT].x += rdx;
		vertices[V_RIGHT].y += rdy;

		vertices[V_BOTTOM].x += rdx;
		vertices[V_BOTTOM].y += rdy;

		slopes[V_RIGHT].k = vertices[V_RIGHT].x *
				   slopes[V_RIGHT].dy -
				   vertices[V_RIGHT].y *
				   slopes[V_RIGHT].dx;
	    }
	    y = miPolyBuildPoly (vertices, slopes, 4, x1, y1,
			     	 left, right, &nleft, &nright, &h);
	    pixel = (dashIndex & 1) ? bgPixel : fgPixel;
	    miFillPolyHelper (pDrawable, pGC, pixel, spanData, y, h, left, right, nleft, nright);

	    if (pGC->lineStyle == LineOnOffDash)
	    {
		switch (pGC->capStyle)
		{
		case CapProjecting:
		    vertices[V_BOTTOM] = saveBottom;
		    vertices[V_RIGHT] = saveRight;
		    slopes[V_RIGHT].k = saveK;
		    break;
		case CapRound:
		    if (!first)
		    {
		    	if (dx < 0)
		    	{
		    	    lcapFace.xa = -vertices[V_LEFT].x;
		    	    lcapFace.ya = -vertices[V_LEFT].y;
			    lcapFace.k = slopes[V_LEFT].k;
		    	}
		    	else
		    	{
		    	    lcapFace.xa = vertices[V_TOP].x;
		    	    lcapFace.ya = vertices[V_TOP].y;
			    lcapFace.k = -slopes[V_LEFT].k;
		    	}
		    	miLineArc (pDrawable, pGC, pixel, spanData,
			       	   &lcapFace, (LineFacePtr) NULL,
			       	   lcenterx, lcentery, FALSE);
		    }
		    if (dx < 0)
		    {
		    	rcapFace.xa = vertices[V_BOTTOM].x;
		    	rcapFace.ya = vertices[V_BOTTOM].y;
			rcapFace.k = slopes[V_RIGHT].k;
		    }
		    else
		    {
		    	rcapFace.xa = -vertices[V_RIGHT].x;
		    	rcapFace.ya = -vertices[V_RIGHT].y;
			rcapFace.k = -slopes[V_RIGHT].k;
		    }
		    miLineArc (pDrawable, pGC, pixel, spanData,
			       (LineFacePtr) NULL, &rcapFace,
			       rcenterx, rcentery, FALSE);
		    break;
	    	}
	    }
	}
	LRemain -= dashRemain;
	++dashIndex;
	if (dashIndex == pGC->numInDashList)
	    dashIndex = 0;
	dashRemain = pDash[dashIndex];

	lcenterx = rcenterx;
	lcentery = rcentery;

	vertices[V_TOP] = vertices[V_RIGHT];
	vertices[V_LEFT] = vertices[V_BOTTOM];
	slopes[V_LEFT].k = -slopes[V_RIGHT].k;
	first = FALSE;
    }

    if (pGC->lineStyle == LineDoubleDash || !(dashIndex & 1))
    {
    	vertices[V_TOP].x -= dx;
    	vertices[V_TOP].y -= dy;

	vertices[V_LEFT].x -= dx;
	vertices[V_LEFT].y -= dy;

	vertices[V_RIGHT].x = rdy;
	vertices[V_RIGHT].y = -rdx;

	vertices[V_BOTTOM].x = -rdy;
	vertices[V_BOTTOM].y = rdx;

	
	if (projectRight)
	{
	    vertices[V_RIGHT].x += rdx;
	    vertices[V_RIGHT].y += rdy;
    
	    vertices[V_BOTTOM].x += rdx;
	    vertices[V_BOTTOM].y += rdy;
	    slopes[V_RIGHT].k = vertices[V_RIGHT].x *
				slopes[V_RIGHT].dy -
				vertices[V_RIGHT].y *
				slopes[V_RIGHT].dx;
	}
	else
	    slopes[V_RIGHT].k = 0;

	if (!first && pGC->lineStyle == LineOnOffDash &&
	    pGC->capStyle == CapProjecting)
	{
	    vertices[V_TOP].x -= rdx;
	    vertices[V_TOP].y -= rdy;

	    vertices[V_LEFT].x -= rdx;
	    vertices[V_LEFT].y -= rdy;
	    slopes[V_LEFT].k = vertices[V_LEFT].x *
			       slopes[V_LEFT].dy -
			       vertices[V_LEFT].y *
			       slopes[V_LEFT].dx;
	}
	else
	    slopes[V_LEFT].k += dx * dx + dy * dy;


	y = miPolyBuildPoly (vertices, slopes, 4, x2, y2,
			     left, right, &nleft, &nright, &h);

	pixel = (dashIndex & 1) ? pGC->bgPixel : pGC->fgPixel;
	miFillPolyHelper (pDrawable, pGC, pixel, spanData, y, h, left, right, nleft, nright);
	if (!first && pGC->lineStyle == LineOnOffDash &&
	    pGC->capStyle == CapRound)
	{
	    lcapFace.x = x2;
	    lcapFace.y = y2;
	    if (dx < 0)
	    {
		lcapFace.xa = -vertices[V_LEFT].x;
		lcapFace.ya = -vertices[V_LEFT].y;
		lcapFace.k = slopes[V_LEFT].k;
	    }
	    else
	    {
		lcapFace.xa = vertices[V_TOP].x;
		lcapFace.ya = vertices[V_TOP].y;
		lcapFace.k = -slopes[V_LEFT].k;
	    }
	    miLineArc (pDrawable, pGC, pixel, spanData,
		       &lcapFace, (LineFacePtr) NULL,
		       rcenterx, rcentery, FALSE);
	}
    }
    dashRemain = ((double) dashRemain) - LRemain;
    if (dashRemain == 0)
    {
	dashIndex++;
	if (dashIndex == pGC->numInDashList)
	    dashIndex = 0;
	dashRemain = pDash[dashIndex];
    }

    leftFace->x = x1;
    leftFace->y = y1;
    leftFace->dx = dx;
    leftFace->dy = dy;
    leftFace->xa = rdy;
    leftFace->ya = -rdx;
    leftFace->k = k;

    rightFace->x = x2;
    rightFace->y = y2;
    rightFace->dx = -dx;
    rightFace->dy = -dy;
    rightFace->xa = -rdy;
    rightFace->ya = rdx;
    rightFace->k = k;

    *pDashIndex = dashIndex;
    *pDashOffset = pDash[dashIndex] - dashRemain;
}

void
miWideDash (DrawablePtr pDrawable, GCPtr pGC,
	    int mode, int npt, DDXPointPtr pPts)
{
    int			x1, y1, x2, y2;
    unsigned long	pixel;
    Bool		projectLeft, projectRight;
    LineFaceRec		leftFace, rightFace, prevRightFace;
    LineFaceRec		firstFace;
    int			first;
    int			dashIndex, dashOffset;
    int			prevDashIndex;
    SpanDataRec		spanDataRec;
    SpanDataPtr		spanData;
    Bool		somethingDrawn = FALSE;
    Bool		selfJoin;
    Bool		endIsFg = FALSE, startIsFg = FALSE;
    Bool		firstIsFg = FALSE, prevIsFg = FALSE;

#if 0
    /* XXX backward compatibility */
    if (pGC->lineWidth == 0)
    {
	miZeroDashLine (pDrawable, pGC, mode, npt, pPts);
	return;
    }
#endif
    if (pGC->lineStyle == LineDoubleDash && 
	(pGC->fillStyle == FillOpaqueStippled || pGC->fillStyle == FillTiled))
    {
	miWideLine (pDrawable, pGC, mode, npt, pPts);
	return;
    }
    if (npt == 0)
	return;
    spanData = miSetupSpanData (pGC, &spanDataRec, npt);
    x2 = pPts->x;
    y2 = pPts->y;
    first = TRUE;
    selfJoin = FALSE;
    if (mode == CoordModePrevious)
    {
	int nptTmp;
	DDXPointPtr pPtsTmp;

	x1 = x2;
	y1 = y2;
	nptTmp = npt;
	pPtsTmp = pPts + 1;
	while (--nptTmp)
	{
	    x1 += pPtsTmp->x;
	    y1 += pPtsTmp->y;
	    ++pPtsTmp;
	}
	if (x2 == x1 && y2 == y1)
	    selfJoin = TRUE;
    }
    else if (x2 == pPts[npt-1].x && y2 == pPts[npt-1].y)
    {
	selfJoin = TRUE;
    }
    projectLeft = pGC->capStyle == CapProjecting && !selfJoin;
    projectRight = FALSE;
    dashIndex = 0;
    dashOffset = 0;
    miStepDash ((int)pGC->dashOffset, &dashIndex,
	        pGC->dash, (int)pGC->numInDashList, &dashOffset);
    while (--npt)
    {
	x1 = x2;
	y1 = y2;
	++pPts;
	x2 = pPts->x;
	y2 = pPts->y;
	if (mode == CoordModePrevious)
	{
	    x2 += x1;
	    y2 += y1;
	}
	if (x1 != x2 || y1 != y2)
	{
	    somethingDrawn = TRUE;
	    if (npt == 1 && pGC->capStyle == CapProjecting && 
		(!selfJoin || !firstIsFg))
		projectRight = TRUE;
	    prevDashIndex = dashIndex;
	    miWideDashSegment (pDrawable, pGC, spanData, &dashOffset, &dashIndex,
				x1, y1, x2, y2,
				projectLeft, projectRight, &leftFace, &rightFace);
	    startIsFg = !(prevDashIndex & 1);
	    endIsFg = (dashIndex & 1) ^ (dashOffset != 0);
	    if (pGC->lineStyle == LineDoubleDash || startIsFg)
	    {
	    	pixel = startIsFg ? pGC->fgPixel : pGC->bgPixel;
	    	if (first || (pGC->lineStyle == LineOnOffDash && !prevIsFg))
	    	{
	    	    if (first && selfJoin)
		    {
		    	firstFace = leftFace;
			firstIsFg = startIsFg;
		    }
	    	    else if (pGC->capStyle == CapRound)
		    	miLineArc (pDrawable, pGC, pixel, spanData,
			       	   &leftFace, (LineFacePtr) NULL,
			       	   (double)0.0, (double)0.0, TRUE);
	    	}
	    	else
	    	{
	    	    miLineJoin (pDrawable, pGC, pixel, spanData, &leftFace,
		            	&prevRightFace);
	    	}
	    }
	    prevRightFace = rightFace;
	    prevIsFg = endIsFg;
	    first = FALSE;
	    projectLeft = FALSE;
	}
	if (npt == 1 && somethingDrawn)
	{
	    if (pGC->lineStyle == LineDoubleDash || endIsFg)
	    {
		pixel = endIsFg ? pGC->fgPixel : pGC->bgPixel;
		if (selfJoin && (pGC->lineStyle == LineDoubleDash || firstIsFg))
		{
		    miLineJoin (pDrawable, pGC, pixel, spanData, &firstFace,
				&rightFace);
		}
		else 
		{
		    if (pGC->capStyle == CapRound)
			miLineArc (pDrawable, pGC, pixel, spanData,
				    (LineFacePtr) NULL, &rightFace,
				    (double)0.0, (double)0.0, TRUE);
		}
	    }
	    else
	    {
		/* glue a cap to the start of the line if
		 * we're OnOffDash and ended on odd dash
		 */
		if (selfJoin && firstIsFg)
		{
		    pixel = pGC->fgPixel;
		    if (pGC->capStyle == CapProjecting)
			miLineProjectingCap (pDrawable, pGC, pixel, spanData,
				    &firstFace, TRUE,
				    (double)0.0, (double)0.0, TRUE);
		    else if (pGC->capStyle == CapRound)
			miLineArc (pDrawable, pGC, pixel, spanData,
				    &firstFace, (LineFacePtr) NULL,
				    (double)0.0, (double)0.0, TRUE);
		}
	    }
	}
    }
    /* handle crock where all points are coincident */
    if (!somethingDrawn && (pGC->lineStyle == LineDoubleDash || !(dashIndex & 1)))
    {
	/* not the same as endIsFg computation above */
	pixel = (dashIndex & 1) ? pGC->bgPixel : pGC->fgPixel;
	switch (pGC->capStyle) {
	case CapRound:
	    miLineArc (pDrawable, pGC, pixel, spanData,
		       (LineFacePtr) NULL, (LineFacePtr) NULL,
		       (double)x2, (double)y2,
		       FALSE);
	    break;
	case CapProjecting:
	    x1 = pGC->lineWidth;
	    miFillRectPolyHelper (pDrawable, pGC, pixel, spanData,
				  x2 - (x1 >> 1), y2 - (x1 >> 1), x1, x1);
	    break;
	}
    }
    if (spanData)
	miCleanupSpanData (pDrawable, pGC, spanData);
}