miwideline.c   [plain text]

/*

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"

#ifdef ICEILTEMPDECL
ICEILTEMPDECL
#endif

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


/*
 * spans-based polygon filler
 */

void
miFillPolyHelper (pDrawable, pGC, pixel, spanData, y, overall_height,
		  left, right, left_count, right_count)
    DrawablePtr	pDrawable;
    GCPtr	pGC;
    unsigned long   pixel;
    SpanDataPtr	spanData;
    int		y;			/* start y coordinate */
    int		overall_height;		/* height of entire segment */
    PolyEdgePtr	left, right;
    int		left_count, right_count;
{
    register int left_x = 0, left_e = 0;
    int	left_stepx = 0;
    int	left_signdx = 0;
    int	left_dy = 0, left_dx = 0;

    register 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;

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

    left_height = 0;
    right_height = 0;
    
    if (!spanData)
    {
    	pptInit = (DDXPointPtr) ALLOCATE_LOCAL (overall_height * sizeof(*ppt));
    	if (!pptInit)
	    return;
    	pwidthInit = (int *) ALLOCATE_LOCAL (overall_height * sizeof(*pwidth));
    	if (!pwidthInit)
    	{
	    DEALLOCATE_LOCAL (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 = (DDXPointPtr) xalloc (overall_height * sizeof (*ppt));
	if (!spanRec.points)
	    return;
	spanRec.widths = (int *) 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);
    	DEALLOCATE_LOCAL (pwidthInit);
    	DEALLOCATE_LOCAL (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)
{
    register DDXPointPtr ppt;
    register 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 = (DDXPointPtr) xalloc (h * sizeof (*ppt));
	if (!spanRec.points)
	    return;
	spanRec.widths = (int *) 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)
    }
}

_X_EXPORT /* static */ int
miPolyBuildEdge (x0, y0, k, dx, dy, xi, yi, left, edge)
    double	x0, y0;
    double	k;  /* x0 * dy - y0 * dx */
    register int dx, dy;
    int		xi, yi;
    int		left;
    register 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)))

_X_EXPORT /* static */ int
miPolyBuildPoly (vertices, slopes, count, xi, yi, left, right, pnleft, pnright, h)
    register PolyVertexPtr vertices;
    register PolySlopePtr  slopes;
    int		    count;
    int		    xi, yi;
    PolyEdgePtr	    left, right;
    int		    *pnleft, *pnright;
    int		    *h;
{
    int	    top, bottom;
    double  miny, maxy;
    register int i;
    int	    j;
    int	    clockwise;
    int	    slopeoff;
    register int s;
    register 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,
    register LineFacePtr pLeft,
    register 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)
{
    register DDXPointPtr tpts, bpts;
    register int *twids, *bwids;
    register 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)
{
    register DDXPointPtr pts;
    register 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);
}

int
miRoundJoinFace (face, edge, leftEdge)
    register LineFacePtr face;
    register 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;
}

_X_EXPORT void
miRoundJoinClip (pLeft, pRight, edge1, edge2, y1, y2, left1, left2)
    register LineFacePtr pLeft, pRight;
    PolyEdgePtr	edge1, edge2;
    int		*y1, *y2;
    Bool	*left1, *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);
}

_X_EXPORT int
miRoundCapClip (face, isInt, edge, leftEdge)
    register LineFacePtr face;
    Bool	isInt;
    register PolyEdgePtr edge;
    Bool	*leftEdge;
{
    int	    y;
    register 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,
    register GCPtr  pGC,
    unsigned long   pixel,
    SpanDataPtr	    spanData,
    register LineFacePtr leftFace,
    register 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 = (DDXPointPtr)ALLOCATE_LOCAL(sizeof(DDXPointRec) * pGC->lineWidth);
    	if (!points)
	    return;
    	widths = (int *)ALLOCATE_LOCAL(sizeof(int) * pGC->lineWidth);
    	if (!widths)
    	{
	    DEALLOCATE_LOCAL(points);
	    return;
    	}
    	oldPixel = pGC->fgPixel;
    	if (pixel != oldPixel)
    	{
	    XID tmpPixel = (XID)pixel;
	    DoChangeGC(pGC, GCForeground, &tmpPixel, FALSE);
	    ValidateGC (pDraw, pGC);
    	}
    }
    else
    {
	points = (DDXPointPtr) xalloc (pGC->lineWidth * sizeof (DDXPointRec));
	if (!points)
	    return;
	widths = (int *) 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);
    	DEALLOCATE_LOCAL(widths);
    	DEALLOCATE_LOCAL(points);
    	if (pixel != oldPixel)
    	{
	    DoChangeGC(pGC, GCForeground, &oldPixel, FALSE);
	    ValidateGC (pDraw, pGC);
    	}
    }
    else
    {
	spanRec.count = n;
	AppendSpanGroup (pGC, pixel, &spanRec, spanData)
    }
}

void
miLineProjectingCap (pDrawable, pGC, pixel, spanData, face, isLeft, xorg, yorg, isInt)
    DrawablePtr	    pDrawable;
    register GCPtr  pGC;
    unsigned long   pixel;
    SpanDataPtr	    spanData;
    register LineFacePtr face;
    Bool	    isLeft;
    double	    xorg, 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,
    register int    x1,
    register int    y1,
    register int    x2,
    register int    y2,
    Bool	    projectLeft,
    Bool	    projectRight,
    register LineFacePtr leftFace,
    register 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);
    }
}

SpanDataPtr
miSetupSpanData (pGC, spanData, npt)
    register 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;
}

void
miCleanupSpanData (pDrawable, pGC, spanData)
    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);
}

_X_EXPORT void
miWideLine (pDrawable, pGC, mode, npt, pPts)
    DrawablePtr	pDrawable;
    register GCPtr pGC;
    int		mode;
    register int npt;
    register DDXPointPtr pPts;
{
    int		    x1, y1, x2, y2;
    SpanDataRec	    spanDataRec;
    SpanDataPtr	    spanData;
    unsigned long   pixel;
    Bool	    projectLeft, projectRight;
    LineFaceRec	    leftFace, rightFace, prevRightFace;
    LineFaceRec	    firstFace;
    register 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,
    register 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;
}

_X_EXPORT void
miWideDash (pDrawable, pGC, mode, npt, pPts)
    DrawablePtr	pDrawable;
    register GCPtr pGC;
    int		mode;
    register int npt;
    register DDXPointPtr pPts;
{
    int		    x1, y1, x2, y2;
    unsigned long   pixel;
    Bool	    projectLeft, projectRight;
    LineFaceRec	    leftFace, rightFace, prevRightFace;
    LineFaceRec	    firstFace;
    int		    first;
    int		    dashIndex, dashOffset;
    register 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);
}