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+/***********************************************************
+
+Copyright 1987, 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.
+
+
+Copyright 1987 by Digital Equipment Corporation, Maynard, Massachusetts.
+
+ All Rights Reserved
+
+Permission to use, copy, modify, and distribute this software and its
+documentation for any purpose and without fee is hereby granted,
+provided that the above copyright notice appear in all copies and that
+both that copyright notice and this permission notice appear in
+supporting documentation, and that the name of Digital not be
+used in advertising or publicity pertaining to distribution of the
+software without specific, written prior permission.
+
+DIGITAL DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING
+ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL
+DIGITAL BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR
+ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
+WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
+ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
+SOFTWARE.
+
+******************************************************************/
+/* $Xorg: miarc.c,v 1.4 2001/02/09 02:05:20 xorgcvs Exp $ */
+/* Author: Keith Packard and Bob Scheifler */
+/* Warning: this code is toxic, do not dally very long here. */
+
+#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 "X.h"
+#include "Xprotostr.h"
+#include "misc.h"
+#include "gcstruct.h"
+#include "scrnintstr.h"
+#include "pixmapstr.h"
+#include "windowstr.h"
+#include "mifpoly.h"
+#include "mi.h"
+#include "mifillarc.h"
+#include "Xfuncproto.h"
+
+static double miDsin(), miDcos(), miDasin(), miDatan2();
+double cbrt(
+#if NeedFunctionPrototypes
+ double
+#endif
+);
+
+#ifdef ICEILTEMPDECL
+ICEILTEMPDECL
+#endif
+
+/*
+ * some interesting sematic interpretation of the protocol:
+ *
+ * Self intersecting arcs (i.e. those spanning 360 degrees)
+ * never join with other arcs, and are drawn without caps
+ * (unless on/off dashed, in which case each dash segment
+ * is capped, except when the last segment meets the
+ * first segment, when no caps are drawn)
+ *
+ * double dash arcs are drawn in two parts, first the
+ * odd dashes (drawn in background) then the even dashes
+ * (drawn in foreground). This means that overlapping
+ * sections of foreground/background are drawn twice,
+ * first in background then in foreground. The double-draw
+ * occurs even when the function uses the destination values
+ * (e.g. xor mode). This is the same way the wide-line
+ * code works and should be "fixed".
+ *
+ */
+
+#undef max
+#undef min
+
+#if defined (__GNUC__) && defined (__STDC__) && !defined (__STRICT_ANSI__)
+#define USE_INLINE
+#endif
+
+#ifdef USE_INLINE
+inline static const int max (const int x, const int y)
+{
+ return x>y? x:y;
+}
+
+inline static const int min (const int x, const int y)
+{
+ return x<y? x:y;
+}
+
+#else
+
+static int
+max (x, y)
+{
+ return x>y? x:y;
+}
+
+static int
+min (x, y)
+{
+ return x<y? x:y;
+}
+
+#endif
+
+struct bound {
+ double min, max;
+};
+
+struct ibound {
+ int min, max;
+};
+
+#define boundedLe(value, bounds)\
+ ((bounds).min <= (value) && (value) <= (bounds).max)
+
+struct line {
+ double m, b;
+ int valid;
+};
+
+#define intersectLine(y,line) (line.m * (y) + line.b)
+
+/*
+ * these are all y value bounds
+ */
+
+struct arc_bound {
+ struct bound ellipse;
+ struct bound inner;
+ struct bound outer;
+ struct bound right;
+ struct bound left;
+ struct ibound inneri;
+ struct ibound outeri;
+};
+
+struct accelerators {
+ double tail_y;
+ double h2;
+ double w2;
+ double h4;
+ double w4;
+ double h2mw2;
+ double h2l;
+ double w2l;
+ double fromIntX;
+ double fromIntY;
+ struct line left, right;
+ int yorgu;
+ int yorgl;
+ int xorg;
+};
+
+struct arc_def {
+ double w, h, l;
+ double a0, a1;
+};
+
+# define todeg(xAngle) (((double) (xAngle)) / 64.0)
+
+# define RIGHT_END 0
+# define LEFT_END 1
+
+typedef struct _miArcJoin {
+ int arcIndex0, arcIndex1;
+ int phase0, phase1;
+ int end0, end1;
+} miArcJoinRec, *miArcJoinPtr;
+
+typedef struct _miArcCap {
+ int arcIndex;
+ int end;
+} miArcCapRec, *miArcCapPtr;
+
+typedef struct _miArcFace {
+ SppPointRec clock;
+ SppPointRec center;
+ SppPointRec counterClock;
+} miArcFaceRec, *miArcFacePtr;
+
+typedef struct _miArcData {
+ xArc arc;
+ int render; /* non-zero means render after drawing */
+ int join; /* related join */
+ int cap; /* related cap */
+ int selfJoin; /* final dash meets first dash */
+ miArcFaceRec bounds[2];
+ double x0, y0, x1, y1;
+} miArcDataRec, *miArcDataPtr;
+
+/*
+ * This is an entire sequence of arcs, computed and categorized according
+ * to operation. miDashArcs generates either one or two of these.
+ */
+
+typedef struct _miPolyArc {
+ int narcs;
+ miArcDataPtr arcs;
+ int ncaps;
+ miArcCapPtr caps;
+ int njoins;
+ miArcJoinPtr joins;
+} miPolyArcRec, *miPolyArcPtr;
+
+#define GCValsFunction 0
+#define GCValsForeground 1
+#define GCValsBackground 2
+#define GCValsLineWidth 3
+#define GCValsCapStyle 4
+#define GCValsJoinStyle 5
+#define GCValsMask (GCFunction | GCForeground | GCBackground | \
+ GCLineWidth | GCCapStyle | GCJoinStyle)
+static CARD32 gcvals[6];
+
+static void fillSpans(), newFinalSpan();
+static void drawArc(), drawQuadrant(), drawZeroArc();
+static void miArcJoin(), miArcCap(), miRoundCap(), miFreeArcs();
+static int computeAngleFromPath();
+static miPolyArcPtr miComputeArcs ();
+static int miGetArcPts();
+
+# define CUBED_ROOT_2 1.2599210498948732038115849718451499938964
+# define CUBED_ROOT_4 1.5874010519681993173435330390930175781250
+
+/*
+ * draw one segment of the arc using the arc spans generation routines
+ */
+
+static void
+miArcSegment(pDraw, pGC, tarc, right, left)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ xArc tarc;
+ miArcFacePtr right, left;
+{
+ int l = pGC->lineWidth;
+ int a0, a1, startAngle, endAngle;
+ miArcFacePtr temp;
+
+ if (!l)
+ l = 1;
+
+ if (tarc.width == 0 || tarc.height == 0) {
+ drawZeroArc (pDraw, pGC, &tarc, l, left, right);
+ return;
+ }
+
+ if (pGC->miTranslate) {
+ tarc.x += pDraw->x;
+ tarc.y += pDraw->y;
+ }
+
+ a0 = tarc.angle1;
+ a1 = tarc.angle2;
+ if (a1 > FULLCIRCLE)
+ a1 = FULLCIRCLE;
+ else if (a1 < -FULLCIRCLE)
+ a1 = -FULLCIRCLE;
+ if (a1 < 0) {
+ startAngle = a0 + a1;
+ endAngle = a0;
+ temp = right;
+ right = left;
+ left = temp;
+ } else {
+ startAngle = a0;
+ endAngle = a0 + a1;
+ }
+ /*
+ * bounds check the two angles
+ */
+ if (startAngle < 0)
+ startAngle = FULLCIRCLE - (-startAngle) % FULLCIRCLE;
+ if (startAngle >= FULLCIRCLE)
+ startAngle = startAngle % FULLCIRCLE;
+ if (endAngle < 0)
+ endAngle = FULLCIRCLE - (-endAngle) % FULLCIRCLE;
+ if (endAngle > FULLCIRCLE)
+ endAngle = (endAngle-1) % FULLCIRCLE + 1;
+ if ((startAngle == endAngle) && a1) {
+ startAngle = 0;
+ endAngle = FULLCIRCLE;
+ }
+
+ drawArc (&tarc, l, startAngle, endAngle, right, left);
+}
+
+/*
+
+Three equations combine to describe the boundaries of the arc
+
+x^2/w^2 + y^2/h^2 = 1 ellipse itself
+(X-x)^2 + (Y-y)^2 = r^2 circle at (x, y) on the ellipse
+(Y-y) = (X-x)*w^2*y/(h^2*x) normal at (x, y) on the ellipse
+
+These lead to a quartic relating Y and y
+
+y^4 - (2Y)y^3 + (Y^2 + (h^4 - w^2*r^2)/(w^2 - h^2))y^2
+ - (2Y*h^4/(w^2 - h^2))y + (Y^2*h^4)/(w^2 - h^2) = 0
+
+The reducible cubic obtained from this quartic is
+
+z^3 - (3N)z^2 - 2V = 0
+
+where
+
+N = (Y^2 + (h^4 - w^2*r^2/(w^2 - h^2)))/6
+V = w^2*r^2*Y^2*h^4/(4 *(w^2 - h^2)^2)
+
+Let
+
+t = z - N
+p = -N^2
+q = -N^3 - V
+
+Then we get
+
+t^3 + 3pt + 2q = 0
+
+The discriminant of this cubic is
+
+D = q^2 + p^3
+
+When D > 0, a real root is obtained as
+
+z = N + cbrt(-q+sqrt(D)) + cbrt(-q-sqrt(D))
+
+When D < 0, a real root is obtained as
+
+z = N - 2m*cos(acos(-q/m^3)/3)
+
+where
+
+m = sqrt(|p|) * sign(q)
+
+Given a real root Z of the cubic, the roots of the quartic are the roots
+of the two quadratics
+
+y^2 + ((b+A)/2)y + (Z + (bZ - d)/A) = 0
+
+where
+
+A = +/- sqrt(8Z + b^2 - 4c)
+b, c, d are the cubic, quadratic, and linear coefficients of the quartic
+
+Some experimentation is then required to determine which solutions
+correspond to the inner and outer boundaries.
+
+*/
+
+typedef struct {
+ short lx, lw, rx, rw;
+} miArcSpan;
+
+typedef struct {
+ miArcSpan *spans;
+ int count1, count2, k;
+ char top, bot, hole;
+} miArcSpanData;
+
+typedef struct {
+ unsigned long lrustamp;
+ unsigned short lw;
+ unsigned short width, height;
+ miArcSpanData *spdata;
+} arcCacheRec;
+
+#define CACHESIZE 25
+
+static arcCacheRec arcCache[CACHESIZE];
+static unsigned long lrustamp;
+static arcCacheRec *lastCacheHit = &arcCache[0];
+static RESTYPE cacheType;
+
+/*
+ * External so it can be called when low on memory.
+ * Call with a zero ID in that case.
+ */
+/*ARGSUSED*/
+int
+miFreeArcCache (data, id)
+ pointer data;
+ XID id;
+{
+ int k;
+ arcCacheRec *cent;
+
+ if (id)
+ cacheType = 0;
+
+ for (k = CACHESIZE, cent = &arcCache[0]; --k >= 0; cent++)
+ {
+ if (cent->spdata)
+ {
+ cent->lrustamp = 0;
+ cent->lw = 0;
+ xfree(cent->spdata);
+ cent->spdata = NULL;
+ }
+ }
+ lrustamp = 0;
+ return Success;
+}
+
+static void
+miComputeCircleSpans(lw, parc, spdata)
+ int lw;
+ xArc *parc;
+ miArcSpanData *spdata;
+{
+ register miArcSpan *span;
+ int doinner;
+ register int x, y, e;
+ int xk, yk, xm, ym, dx, dy;
+ register int slw, inslw;
+ int inx, iny, ine;
+ int inxk, inyk, inxm, inym;
+
+ doinner = -lw;
+ slw = parc->width - doinner;
+ y = parc->height >> 1;
+ dy = parc->height & 1;
+ dx = 1 - dy;
+ MIWIDEARCSETUP(x, y, dy, slw, e, xk, xm, yk, ym);
+ inslw = parc->width + doinner;
+ if (inslw > 0)
+ {
+ spdata->hole = spdata->top;
+ MIWIDEARCSETUP(inx, iny, dy, inslw, ine, inxk, inxm, inyk, inym);
+ }
+ else
+ {
+ spdata->hole = FALSE;
+ doinner = -y;
+ }
+ spdata->count1 = -doinner - spdata->top;
+ spdata->count2 = y + doinner;
+ span = spdata->spans;
+ while (y)
+ {
+ MIFILLARCSTEP(slw);
+ span->lx = dy - x;
+ if (++doinner <= 0)
+ {
+ span->lw = slw;
+ span->rx = 0;
+ span->rw = span->lx + slw;
+ }
+ else
+ {
+ MIFILLINARCSTEP(inslw);
+ span->lw = x - inx;
+ span->rx = dy - inx + inslw;
+ span->rw = inx - x + slw - inslw;
+ }
+ span++;
+ }
+ if (spdata->bot)
+ {
+ if (spdata->count2)
+ spdata->count2--;
+ else
+ {
+ if (lw > (int)parc->height)
+ span[-1].rx = span[-1].rw = -((lw - (int)parc->height) >> 1);
+ else
+ span[-1].rw = 0;
+ spdata->count1--;
+ }
+ }
+}
+
+static void
+miComputeEllipseSpans(lw, parc, spdata)
+ int lw;
+ xArc *parc;
+ miArcSpanData *spdata;
+{
+ register miArcSpan *span;
+ double w, h, r, xorg;
+ double Hs, Hf, WH, K, Vk, Nk, Fk, Vr, N, Nc, Z, rs;
+ double A, T, b, d, x, y, t, inx, outx, hepp, hepm;
+ int flip, solution;
+
+ w = (double)parc->width / 2.0;
+ h = (double)parc->height / 2.0;
+ r = lw / 2.0;
+ rs = r * r;
+ Hs = h * h;
+ WH = w * w - Hs;
+ Nk = w * r;
+ Vk = (Nk * Hs) / (WH + WH);
+ Hf = Hs * Hs;
+ Nk = (Hf - Nk * Nk) / WH;
+ Fk = Hf / WH;
+ hepp = h + EPSILON;
+ hepm = h - EPSILON;
+ K = h + ((lw - 1) >> 1);
+ span = spdata->spans;
+ if (parc->width & 1)
+ xorg = .5;
+ else
+ xorg = 0.0;
+ if (spdata->top)
+ {
+ span->lx = 0;
+ span->lw = 1;
+ span++;
+ }
+ spdata->count1 = 0;
+ spdata->count2 = 0;
+ spdata->hole = (spdata->top &&
+ (int)parc->height * lw <= (int)(parc->width * parc->width) &&
+ lw < (int)parc->height);
+ for (; K > 0.0; K -= 1.0)
+ {
+ N = (K * K + Nk) / 6.0;
+ Nc = N * N * N;
+ Vr = Vk * K;
+ t = Nc + Vr * Vr;
+ d = Nc + t;
+ if (d < 0.0) {
+ d = Nc;
+ b = N;
+ if ( (b < 0.0) == (t < 0.0) )
+ {
+ b = -b;
+ d = -d;
+ }
+ Z = N - 2.0 * b * cos(acos(-t / d) / 3.0);
+ if ( (Z < 0.0) == (Vr < 0.0) )
+ flip = 2;
+ else
+ flip = 1;
+ }
+ else
+ {
+ d = Vr * sqrt(d);
+ Z = N + cbrt(t + d) + cbrt(t - d);
+ flip = 0;
+ }
+ A = sqrt((Z + Z) - Nk);
+ T = (Fk - Z) * K / A;
+ inx = 0.0;
+ solution = FALSE;
+ b = -A + K;
+ d = b * b - 4 * (Z + T);
+ if (d >= 0)
+ {
+ d = sqrt(d);
+ y = (b + d) / 2;
+ if ((y >= 0.0) && (y < hepp))
+ {
+ solution = TRUE;
+ if (y > hepm)
+ y = h;
+ t = y / h;
+ x = w * sqrt(1 - (t * t));
+ t = K - y;
+ t = sqrt(rs - (t * t));
+ if (flip == 2)
+ inx = x - t;
+ else
+ outx = x + t;
+ }
+ }
+ b = A + K;
+ d = b * b - 4 * (Z - T);
+ /* Because of the large magnitudes involved, we lose enough precision
+ * that sometimes we end up with a negative value near the axis, when
+ * it should be positive. This is a workaround.
+ */
+ if (d < 0 && !solution)
+ d = 0.0;
+ if (d >= 0) {
+ d = sqrt(d);
+ y = (b + d) / 2;
+ if (y < hepp)
+ {
+ if (y > hepm)
+ y = h;
+ t = y / h;
+ x = w * sqrt(1 - (t * t));
+ t = K - y;
+ inx = x - sqrt(rs - (t * t));
+ }
+ y = (b - d) / 2;
+ if (y >= 0.0)
+ {
+ if (y > hepm)
+ y = h;
+ t = y / h;
+ x = w * sqrt(1 - (t * t));
+ t = K - y;
+ t = sqrt(rs - (t * t));
+ if (flip == 1)
+ inx = x - t;
+ else
+ outx = x + t;
+ }
+ }
+ span->lx = ICEIL(xorg - outx);
+ if (inx <= 0.0)
+ {
+ spdata->count1++;
+ span->lw = ICEIL(xorg + outx) - span->lx;
+ span->rx = ICEIL(xorg + inx);
+ span->rw = -ICEIL(xorg - inx);
+ }
+ else
+ {
+ spdata->count2++;
+ span->lw = ICEIL(xorg - inx) - span->lx;
+ span->rx = ICEIL(xorg + inx);
+ span->rw = ICEIL(xorg + outx) - span->rx;
+ }
+ span++;
+ }
+ if (spdata->bot)
+ {
+ outx = w + r;
+ if (r >= h && r <= w)
+ inx = 0.0;
+ else if (Nk < 0.0 && -Nk < Hs)
+ {
+ inx = w * sqrt(1 + Nk / Hs) - sqrt(rs + Nk);
+ if (inx > w - r)
+ inx = w - r;
+ }
+ else
+ inx = w - r;
+ span->lx = ICEIL(xorg - outx);
+ if (inx <= 0.0)
+ {
+ span->lw = ICEIL(xorg + outx) - span->lx;
+ span->rx = ICEIL(xorg + inx);
+ span->rw = -ICEIL(xorg - inx);
+ }
+ else
+ {
+ span->lw = ICEIL(xorg - inx) - span->lx;
+ span->rx = ICEIL(xorg + inx);
+ span->rw = ICEIL(xorg + outx) - span->rx;
+ }
+ }
+ if (spdata->hole)
+ {
+ span = &spdata->spans[spdata->count1];
+ span->lw = -span->lx;
+ span->rx = 1;
+ span->rw = span->lw;
+ spdata->count1--;
+ spdata->count2++;
+ }
+}
+
+static double
+tailX(K, def, bounds, acc)
+ double K;
+ struct arc_def *def;
+ struct arc_bound *bounds;
+ struct accelerators *acc;
+{
+ double w, h, r;
+ double Hs, Hf, WH, Vk, Nk, Fk, Vr, N, Nc, Z, rs;
+ double A, T, b, d, x, y, t, hepp, hepm;
+ int flip, solution;
+ double xs[2];
+ double *xp;
+
+ w = def->w;
+ h = def->h;
+ r = def->l;
+ rs = r * r;
+ Hs = acc->h2;
+ WH = -acc->h2mw2;
+ Nk = def->w * r;
+ Vk = (Nk * Hs) / (WH + WH);
+ Hf = acc->h4;
+ Nk = (Hf - Nk * Nk) / WH;
+ if (K == 0.0) {
+ if (Nk < 0.0 && -Nk < Hs) {
+ xs[0] = w * sqrt(1 + Nk / Hs) - sqrt(rs + Nk);
+ xs[1] = w - r;
+ if (acc->left.valid && boundedLe(K, bounds->left) &&
+ !boundedLe(K, bounds->outer) && xs[0] >= 0.0 && xs[1] >= 0.0)
+ return xs[1];
+ if (acc->right.valid && boundedLe(K, bounds->right) &&
+ !boundedLe(K, bounds->inner) && xs[0] <= 0.0 && xs[1] <= 0.0)
+ return xs[1];
+ return xs[0];
+ }
+ return w - r;
+ }
+ Fk = Hf / WH;
+ hepp = h + EPSILON;
+ hepm = h - EPSILON;
+ N = (K * K + Nk) / 6.0;
+ Nc = N * N * N;
+ Vr = Vk * K;
+ xp = xs;
+ xs[0] = 0.0;
+ t = Nc + Vr * Vr;
+ d = Nc + t;
+ if (d < 0.0) {
+ d = Nc;
+ b = N;
+ if ( (b < 0.0) == (t < 0.0) )
+ {
+ b = -b;
+ d = -d;
+ }
+ Z = N - 2.0 * b * cos(acos(-t / d) / 3.0);
+ if ( (Z < 0.0) == (Vr < 0.0) )
+ flip = 2;
+ else
+ flip = 1;
+ }
+ else
+ {
+ d = Vr * sqrt(d);
+ Z = N + cbrt(t + d) + cbrt(t - d);
+ flip = 0;
+ }
+ A = sqrt((Z + Z) - Nk);
+ T = (Fk - Z) * K / A;
+ solution = FALSE;
+ b = -A + K;
+ d = b * b - 4 * (Z + T);
+ if (d >= 0 && flip == 2)
+ {
+ d = sqrt(d);
+ y = (b + d) / 2;
+ if ((y >= 0.0) && (y < hepp))
+ {
+ solution = TRUE;
+ if (y > hepm)
+ y = h;
+ t = y / h;
+ x = w * sqrt(1 - (t * t));
+ t = K - y;
+ t = sqrt(rs - (t * t));
+ *xp++ = x - t;
+ }
+ }
+ b = A + K;
+ d = b * b - 4 * (Z - T);
+ /* Because of the large magnitudes involved, we lose enough precision
+ * that sometimes we end up with a negative value near the axis, when
+ * it should be positive. This is a workaround.
+ */
+ if (d < 0 && !solution)
+ d = 0.0;
+ if (d >= 0) {
+ d = sqrt(d);
+ y = (b + d) / 2;
+ if (y < hepp)
+ {
+ if (y > hepm)
+ y = h;
+ t = y / h;
+ x = w * sqrt(1 - (t * t));
+ t = K - y;
+ *xp++ = x - sqrt(rs - (t * t));
+ }
+ y = (b - d) / 2;
+ if (y >= 0.0 && flip == 1)
+ {
+ if (y > hepm)
+ y = h;
+ t = y / h;
+ x = w * sqrt(1 - (t * t));
+ t = K - y;
+ t = sqrt(rs - (t * t));
+ *xp++ = x - t;
+ }
+ }
+ if (xp > &xs[1]) {
+ if (acc->left.valid && boundedLe(K, bounds->left) &&
+ !boundedLe(K, bounds->outer) && xs[0] >= 0.0 && xs[1] >= 0.0)
+ return xs[1];
+ if (acc->right.valid && boundedLe(K, bounds->right) &&
+ !boundedLe(K, bounds->inner) && xs[0] <= 0.0 && xs[1] <= 0.0)
+ return xs[1];
+ }
+ return xs[0];
+}
+
+static miArcSpanData *
+miComputeWideEllipse(lw, parc, mustFree)
+ int lw;
+ register xArc *parc;
+ Bool *mustFree;
+{
+ register miArcSpanData *spdata;
+ register arcCacheRec *cent, *lruent;
+ register int k;
+ arcCacheRec fakeent;
+
+ if (!lw)
+ lw = 1;
+ if (parc->height <= 1500)
+ {
+ *mustFree = FALSE;
+ cent = lastCacheHit;
+ if (cent->lw == lw &&
+ cent->width == parc->width && cent->height == parc->height)
+ {
+ cent->lrustamp = ++lrustamp;
+ return cent->spdata;
+ }
+ lruent = &arcCache[0];
+ for (k = CACHESIZE, cent = lruent; --k >= 0; cent++)
+ {
+ if (cent->lw == lw &&
+ cent->width == parc->width && cent->height == parc->height)
+ {
+ cent->lrustamp = ++lrustamp;
+ lastCacheHit = cent;
+ return cent->spdata;
+ }
+ if (cent->lrustamp < lruent->lrustamp)
+ lruent = cent;
+ }
+ if (!cacheType)
+ {
+ cacheType = CreateNewResourceType(miFreeArcCache);
+ (void) AddResource(FakeClientID(0), cacheType, NULL);
+ }
+ } else {
+ lruent = &fakeent;
+ lruent->spdata = NULL;
+ *mustFree = TRUE;
+ }
+ k = (parc->height >> 1) + ((lw - 1) >> 1);
+ spdata = lruent->spdata;
+ if (!spdata || spdata->k != k)
+ {
+ if (spdata)
+ xfree(spdata);
+ spdata = (miArcSpanData *)xalloc(sizeof(miArcSpanData) +
+ sizeof(miArcSpan) * (k + 2));
+ lruent->spdata = spdata;
+ if (!spdata)
+ {
+ lruent->lrustamp = 0;
+ lruent->lw = 0;
+ return spdata;
+ }
+ spdata->spans = (miArcSpan *)(spdata + 1);
+ spdata->k = k;
+ }
+ spdata->top = !(lw & 1) && !(parc->width & 1);
+ spdata->bot = !(parc->height & 1);
+ lruent->lrustamp = ++lrustamp;
+ lruent->lw = lw;
+ lruent->width = parc->width;
+ lruent->height = parc->height;
+ if (lruent != &fakeent)
+ lastCacheHit = lruent;
+ if (parc->width == parc->height)
+ miComputeCircleSpans(lw, parc, spdata);
+ else
+ miComputeEllipseSpans(lw, parc, spdata);
+ return spdata;
+}
+
+static void
+miFillWideEllipse(pDraw, pGC, parc)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ xArc *parc;
+{
+ DDXPointPtr points;
+ register DDXPointPtr pts;
+ int *widths;
+ register int *wids;
+ miArcSpanData *spdata;
+ Bool mustFree;
+ register miArcSpan *span;
+ register int xorg, yorgu, yorgl;
+ register int n;
+
+ yorgu = parc->height + pGC->lineWidth;
+ n = (sizeof(int) * 2) * yorgu;
+ widths = (int *)ALLOCATE_LOCAL(n + (sizeof(DDXPointRec) * 2) * yorgu);
+ if (!widths)
+ return;
+ points = (DDXPointPtr)((char *)widths + n);
+ spdata = miComputeWideEllipse((int)pGC->lineWidth, parc, &mustFree);
+ if (!spdata)
+ {
+ DEALLOCATE_LOCAL(widths);
+ return;
+ }
+ pts = points;
+ wids = widths;
+ span = spdata->spans;
+ xorg = parc->x + (parc->width >> 1);
+ yorgu = parc->y + (parc->height >> 1);
+ yorgl = yorgu + (parc->height & 1);
+ if (pGC->miTranslate)
+ {
+ xorg += pDraw->x;
+ yorgu += pDraw->y;
+ yorgl += pDraw->y;
+ }
+ yorgu -= spdata->k;
+ yorgl += spdata->k;
+ if (spdata->top)
+ {
+ pts->x = xorg;
+ pts->y = yorgu - 1;
+ pts++;
+ *wids++ = 1;
+ span++;
+ }
+ for (n = spdata->count1; --n >= 0; )
+ {
+ pts[0].x = xorg + span->lx;
+ pts[0].y = yorgu;
+ wids[0] = span->lw;
+ pts[1].x = pts[0].x;
+ pts[1].y = yorgl;
+ wids[1] = wids[0];
+ yorgu++;
+ yorgl--;
+ pts += 2;
+ wids += 2;
+ span++;
+ }
+ if (spdata->hole)
+ {
+ pts[0].x = xorg;
+ pts[0].y = yorgl;
+ wids[0] = 1;
+ pts++;
+ wids++;
+ }
+ for (n = spdata->count2; --n >= 0; )
+ {
+ pts[0].x = xorg + span->lx;
+ pts[0].y = yorgu;
+ wids[0] = span->lw;
+ pts[1].x = xorg + span->rx;
+ pts[1].y = pts[0].y;
+ wids[1] = span->rw;
+ pts[2].x = pts[0].x;
+ pts[2].y = yorgl;
+ wids[2] = wids[0];
+ pts[3].x = pts[1].x;
+ pts[3].y = pts[2].y;
+ wids[3] = wids[1];
+ yorgu++;
+ yorgl--;
+ pts += 4;
+ wids += 4;
+ span++;
+ }
+ if (spdata->bot)
+ {
+ if (span->rw <= 0)
+ {
+ pts[0].x = xorg + span->lx;
+ pts[0].y = yorgu;
+ wids[0] = span->lw;
+ pts++;
+ wids++;
+ }
+ else
+ {
+ pts[0].x = xorg + span->lx;
+ pts[0].y = yorgu;
+ wids[0] = span->lw;
+ pts[1].x = xorg + span->rx;
+ pts[1].y = pts[0].y;
+ wids[1] = span->rw;
+ pts += 2;
+ wids += 2;
+ }
+ }
+ if (mustFree)
+ xfree(spdata);
+ (*pGC->ops->FillSpans)(pDraw, pGC, pts - points, points, widths, FALSE);
+
+ DEALLOCATE_LOCAL(widths);
+}
+
+/*
+ * miPolyArc strategy:
+ *
+ * If arc is zero width and solid, we don't have to worry about the rasterop
+ * or join styles. For wide solid circles, we use a fast integer algorithm.
+ * For wide solid ellipses, we use special case floating point code.
+ * Otherwise, we set up pDrawTo and pGCTo according to the rasterop, then
+ * draw using pGCTo and pDrawTo. If the raster-op was "tricky," that is,
+ * if it involves the destination, then we use PushPixels to move the bits
+ * from the scratch drawable to pDraw. (See the wide line code for a
+ * fuller explanation of this.)
+ */
+
+void
+miPolyArc(pDraw, pGC, narcs, parcs)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ int narcs;
+ xArc *parcs;
+{
+ register int i;
+ xArc *parc;
+ int xMin, xMax, yMin, yMax;
+ int pixmapWidth, pixmapHeight;
+ int xOrg, yOrg;
+ int width;
+ Bool fTricky;
+ DrawablePtr pDrawTo;
+ CARD32 fg, bg;
+ GCPtr pGCTo;
+ miPolyArcPtr polyArcs;
+ int cap[2], join[2];
+ int iphase;
+ int halfWidth;
+
+ width = pGC->lineWidth;
+ if(width == 0 && pGC->lineStyle == LineSolid)
+ {
+ for(i = narcs, parc = parcs; --i >= 0; parc++)
+ miArcSegment( pDraw, pGC, *parc,
+ (miArcFacePtr) 0, (miArcFacePtr) 0 );
+ fillSpans (pDraw, pGC);
+ }
+ else
+ {
+ if ((pGC->lineStyle == LineSolid) && narcs)
+ {
+ while (parcs->width && parcs->height &&
+ (parcs->angle2 >= FULLCIRCLE ||
+ parcs->angle2 <= -FULLCIRCLE))
+ {
+ miFillWideEllipse(pDraw, pGC, parcs);
+ if (!--narcs)
+ return;
+ parcs++;
+ }
+ }
+
+ /* Set up pDrawTo and pGCTo based on the rasterop */
+ switch(pGC->alu)
+ {
+ case GXclear: /* 0 */
+ case GXcopy: /* src */
+ case GXcopyInverted: /* NOT src */
+ case GXset: /* 1 */
+ fTricky = FALSE;
+ pDrawTo = pDraw;
+ pGCTo = pGC;
+ break;
+ default:
+ fTricky = TRUE;
+
+ /* find bounding box around arcs */
+ xMin = yMin = MAXSHORT;
+ xMax = yMax = MINSHORT;
+
+ for(i = narcs, parc = parcs; --i >= 0; parc++)
+ {
+ xMin = min (xMin, parc->x);
+ yMin = min (yMin, parc->y);
+ xMax = max (xMax, (parc->x + (int) parc->width));
+ yMax = max (yMax, (parc->y + (int) parc->height));
+ }
+
+ /* expand box to deal with line widths */
+ halfWidth = (width + 1)/2;
+ xMin -= halfWidth;
+ yMin -= halfWidth;
+ xMax += halfWidth;
+ yMax += halfWidth;
+
+ /* compute pixmap size; limit it to size of drawable */
+ xOrg = max(xMin, 0);
+ yOrg = max(yMin, 0);
+ pixmapWidth = min(xMax, pDraw->width) - xOrg;
+ pixmapHeight = min(yMax, pDraw->height) - yOrg;
+
+ /* if nothing left, return */
+ if ( (pixmapWidth <= 0) || (pixmapHeight <= 0) ) return;
+
+ for(i = narcs, parc = parcs; --i >= 0; parc++)
+ {
+ parc->x -= xOrg;
+ parc->y -= yOrg;
+ }
+ if (pGC->miTranslate)
+ {
+ xOrg += pDraw->x;
+ yOrg += pDraw->y;
+ }
+
+ /* set up scratch GC */
+
+ pGCTo = GetScratchGC(1, pDraw->pScreen);
+ if (!pGCTo)
+ return;
+ gcvals[GCValsFunction] = GXcopy;
+ gcvals[GCValsForeground] = 1;
+ gcvals[GCValsBackground] = 0;
+ gcvals[GCValsLineWidth] = pGC->lineWidth;
+ gcvals[GCValsCapStyle] = pGC->capStyle;
+ gcvals[GCValsJoinStyle] = pGC->joinStyle;
+ dixChangeGC(NullClient, pGCTo, GCValsMask, gcvals, NULL);
+
+ /* allocate a 1 bit deep pixmap of the appropriate size, and
+ * validate it */
+ pDrawTo = (DrawablePtr)(*pDraw->pScreen->CreatePixmap)
+ (pDraw->pScreen, pixmapWidth, pixmapHeight, 1);
+ if (!pDrawTo)
+ {
+ FreeScratchGC(pGCTo);
+ return;
+ }
+ ValidateGC(pDrawTo, pGCTo);
+ miClearDrawable(pDrawTo, pGCTo);
+ }
+
+ fg = pGC->fgPixel;
+ bg = pGC->bgPixel;
+ if ((pGC->fillStyle == FillTiled) ||
+ (pGC->fillStyle == FillOpaqueStippled))
+ bg = fg; /* the protocol sez these don't cause color changes */
+
+ polyArcs = miComputeArcs (parcs, narcs, pGC);
+
+ if (!polyArcs)
+ {
+ if (fTricky) {
+ (*pDraw->pScreen->DestroyPixmap) ((PixmapPtr)pDrawTo);
+ FreeScratchGC (pGCTo);
+ }
+ return;
+ }
+
+ cap[0] = cap[1] = 0;
+ join[0] = join[1] = 0;
+ for (iphase = ((pGC->lineStyle == LineDoubleDash) ? 1 : 0);
+ iphase >= 0;
+ iphase--)
+ {
+ if (iphase == 1) {
+ dixChangeGC (NullClient, pGC, GCForeground, &bg, NULL);
+ ValidateGC (pDraw, pGC);
+ } else if (pGC->lineStyle == LineDoubleDash) {
+ dixChangeGC (NullClient, pGC, GCForeground, &fg, NULL);
+ ValidateGC (pDraw, pGC);
+ }
+ for (i = 0; i < polyArcs[iphase].narcs; i++) {
+ miArcDataPtr arcData;
+
+ arcData = &polyArcs[iphase].arcs[i];
+ miArcSegment(pDrawTo, pGCTo, arcData->arc,
+ &arcData->bounds[RIGHT_END],
+ &arcData->bounds[LEFT_END]);
+ if (polyArcs[iphase].arcs[i].render) {
+ fillSpans (pDrawTo, pGCTo);
+ /*
+ * don't cap self-joining arcs
+ */
+ if (polyArcs[iphase].arcs[i].selfJoin &&
+ cap[iphase] < polyArcs[iphase].arcs[i].cap)
+ cap[iphase]++;
+ while (cap[iphase] < polyArcs[iphase].arcs[i].cap) {
+ int arcIndex, end;
+ miArcDataPtr arcData0;
+
+ arcIndex = polyArcs[iphase].caps[cap[iphase]].arcIndex;
+ end = polyArcs[iphase].caps[cap[iphase]].end;
+ arcData0 = &polyArcs[iphase].arcs[arcIndex];
+ miArcCap (pDrawTo, pGCTo,
+ &arcData0->bounds[end], end,
+ arcData0->arc.x, arcData0->arc.y,
+ (double) arcData0->arc.width / 2.0,
+ (double) arcData0->arc.height / 2.0);
+ ++cap[iphase];
+ }
+ while (join[iphase] < polyArcs[iphase].arcs[i].join) {
+ int arcIndex0, arcIndex1, end0, end1;
+ int phase0, phase1;
+ miArcDataPtr arcData0, arcData1;
+ miArcJoinPtr joinp;
+
+ joinp = &polyArcs[iphase].joins[join[iphase]];
+ arcIndex0 = joinp->arcIndex0;
+ end0 = joinp->end0;
+ arcIndex1 = joinp->arcIndex1;
+ end1 = joinp->end1;
+ phase0 = joinp->phase0;
+ phase1 = joinp->phase1;
+ arcData0 = &polyArcs[phase0].arcs[arcIndex0];
+ arcData1 = &polyArcs[phase1].arcs[arcIndex1];
+ miArcJoin (pDrawTo, pGCTo,
+ &arcData0->bounds[end0],
+ &arcData1->bounds[end1],
+ arcData0->arc.x, arcData0->arc.y,
+ (double) arcData0->arc.width / 2.0,
+ (double) arcData0->arc.height / 2.0,
+ arcData1->arc.x, arcData1->arc.y,
+ (double) arcData1->arc.width / 2.0,
+ (double) arcData1->arc.height / 2.0);
+ ++join[iphase];
+ }
+ if (fTricky) {
+ if (pGC->serialNumber != pDraw->serialNumber)
+ ValidateGC (pDraw, pGC);
+ (*pGC->ops->PushPixels) (pGC, (PixmapPtr)pDrawTo,
+ pDraw, pixmapWidth, pixmapHeight, xOrg, yOrg);
+ miClearDrawable ((DrawablePtr) pDrawTo, pGCTo);
+ }
+ }
+ }
+ }
+ miFreeArcs(polyArcs, pGC);
+
+ if(fTricky)
+ {
+ (*pGCTo->pScreen->DestroyPixmap)((PixmapPtr)pDrawTo);
+ FreeScratchGC(pGCTo);
+ }
+ }
+}
+
+static double
+angleBetween (center, point1, point2)
+ SppPointRec center, point1, point2;
+{
+ double a1, a2, a;
+
+ /*
+ * reflect from X coordinates back to ellipse
+ * coordinates -- y increasing upwards
+ */
+ a1 = miDatan2 (- (point1.y - center.y), point1.x - center.x);
+ a2 = miDatan2 (- (point2.y - center.y), point2.x - center.x);
+ a = a2 - a1;
+ if (a <= -180.0)
+ a += 360.0;
+ else if (a > 180.0)
+ a -= 360.0;
+ return a;
+}
+
+static void
+translateBounds (b, x, y, fx, fy)
+miArcFacePtr b;
+int x, y;
+double fx, fy;
+{
+ fx += x;
+ fy += y;
+ b->clock.x -= fx;
+ b->clock.y -= fy;
+ b->center.x -= fx;
+ b->center.y -= fy;
+ b->counterClock.x -= fx;
+ b->counterClock.y -= fy;
+}
+
+static void
+miArcJoin (pDraw, pGC, pLeft, pRight,
+ xOrgLeft, yOrgLeft, xFtransLeft, yFtransLeft,
+ xOrgRight, yOrgRight, xFtransRight, yFtransRight)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ miArcFacePtr pRight, pLeft;
+ int xOrgRight, yOrgRight;
+ double xFtransRight, yFtransRight;
+ int xOrgLeft, yOrgLeft;
+ double xFtransLeft, yFtransLeft;
+{
+ SppPointRec center, corner, otherCorner;
+ SppPointRec poly[5], e;
+ SppPointPtr pArcPts;
+ int cpt;
+ SppArcRec arc;
+ miArcFaceRec Right, Left;
+ int polyLen;
+ int xOrg, yOrg;
+ double xFtrans, yFtrans;
+ double a;
+ double ae, ac2, ec2, bc2, de;
+ double width;
+
+ xOrg = (xOrgRight + xOrgLeft) / 2;
+ yOrg = (yOrgRight + yOrgLeft) / 2;
+ xFtrans = (xFtransLeft + xFtransRight) / 2;
+ yFtrans = (yFtransLeft + yFtransRight) / 2;
+ Right = *pRight;
+ translateBounds (&Right, xOrg - xOrgRight, yOrg - yOrgRight,
+ xFtrans - xFtransRight, yFtrans - yFtransRight);
+ Left = *pLeft;
+ translateBounds (&Left, xOrg - xOrgLeft, yOrg - yOrgLeft,
+ xFtrans - xFtransLeft, yFtrans - yFtransLeft);
+ pRight = &Right;
+ pLeft = &Left;
+
+ if (pRight->clock.x == pLeft->counterClock.x &&
+ pRight->clock.y == pLeft->counterClock.y)
+ return;
+ center = pRight->center;
+ if (0 <= (a = angleBetween (center, pRight->clock, pLeft->counterClock))
+ && a <= 180.0)
+ {
+ corner = pRight->clock;
+ otherCorner = pLeft->counterClock;
+ } else {
+ a = angleBetween (center, pLeft->clock, pRight->counterClock);
+ corner = pLeft->clock;
+ otherCorner = pRight->counterClock;
+ }
+ switch (pGC->joinStyle) {
+ case JoinRound:
+ width = (pGC->lineWidth ? (double)pGC->lineWidth : (double)1);
+
+ arc.x = center.x - width/2;
+ arc.y = center.y - width/2;
+ arc.width = width;
+ arc.height = width;
+ arc.angle1 = -miDatan2 (corner.y - center.y, corner.x - center.x);
+ arc.angle2 = a;
+ pArcPts = (SppPointPtr) xalloc (3 * sizeof (SppPointRec));
+ if (!pArcPts)
+ return;
+ pArcPts[0].x = otherCorner.x;
+ pArcPts[0].y = otherCorner.y;
+ pArcPts[1].x = center.x;
+ pArcPts[1].y = center.y;
+ pArcPts[2].x = corner.x;
+ pArcPts[2].y = corner.y;
+ if( (cpt = miGetArcPts(&arc, 3, &pArcPts)) )
+ {
+ /* by drawing with miFillSppPoly and setting the endpoints of the arc
+ * to be the corners, we assure that the cap will meet up with the
+ * rest of the line */
+ miFillSppPoly(pDraw, pGC, cpt, pArcPts, xOrg, yOrg, xFtrans, yFtrans);
+ }
+ xfree(pArcPts);
+ return;
+ case JoinMiter:
+ /*
+ * don't miter arcs with less than 11 degrees between them
+ */
+ if (a < 169.0) {
+ poly[0] = corner;
+ poly[1] = center;
+ poly[2] = otherCorner;
+ bc2 = (corner.x - otherCorner.x) * (corner.x - otherCorner.x) +
+ (corner.y - otherCorner.y) * (corner.y - otherCorner.y);
+ ec2 = bc2 / 4;
+ ac2 = (corner.x - center.x) * (corner.x - center.x) +
+ (corner.y - center.y) * (corner.y - center.y);
+ ae = sqrt (ac2 - ec2);
+ de = ec2 / ae;
+ e.x = (corner.x + otherCorner.x) / 2;
+ e.y = (corner.y + otherCorner.y) / 2;
+ poly[3].x = e.x + de * (e.x - center.x) / ae;
+ poly[3].y = e.y + de * (e.y - center.y) / ae;
+ poly[4] = corner;
+ polyLen = 5;
+ break;
+ }
+ case JoinBevel:
+ poly[0] = corner;
+ poly[1] = center;
+ poly[2] = otherCorner;
+ poly[3] = corner;
+ polyLen = 4;
+ break;
+ }
+ miFillSppPoly (pDraw, pGC, polyLen, poly, xOrg, yOrg, xFtrans, yFtrans);
+}
+
+/*ARGSUSED*/
+static void
+miArcCap (pDraw, pGC, pFace, end, xOrg, yOrg, xFtrans, yFtrans)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ miArcFacePtr pFace;
+ int end;
+ int xOrg, yOrg;
+ double xFtrans, yFtrans;
+{
+ SppPointRec corner, otherCorner, center, endPoint, poly[5];
+
+ corner = pFace->clock;
+ otherCorner = pFace->counterClock;
+ center = pFace->center;
+ switch (pGC->capStyle) {
+ case CapProjecting:
+ poly[0].x = otherCorner.x;
+ poly[0].y = otherCorner.y;
+ poly[1].x = corner.x;
+ poly[1].y = corner.y;
+ poly[2].x = corner.x -
+ (center.y - corner.y);
+ poly[2].y = corner.y +
+ (center.x - corner.x);
+ poly[3].x = otherCorner.x -
+ (otherCorner.y - center.y);
+ poly[3].y = otherCorner.y +
+ (otherCorner.x - center.x);
+ poly[4].x = otherCorner.x;
+ poly[4].y = otherCorner.y;
+ miFillSppPoly (pDraw, pGC, 5, poly, xOrg, yOrg, xFtrans, yFtrans);
+ break;
+ case CapRound:
+ /*
+ * miRoundCap just needs these to be unequal.
+ */
+ endPoint = center;
+ endPoint.x = endPoint.x + 100;
+ miRoundCap (pDraw, pGC, center, endPoint, corner, otherCorner, 0,
+ -xOrg, -yOrg, xFtrans, yFtrans);
+ break;
+ }
+}
+
+/* MIROUNDCAP -- a private helper function
+ * Put Rounded cap on end. pCenter is the center of this end of the line
+ * pEnd is the center of the other end of the line. pCorner is one of the
+ * two corners at this end of the line.
+ * NOTE: pOtherCorner must be counter-clockwise from pCorner.
+ */
+/*ARGSUSED*/
+static void
+miRoundCap(pDraw, pGC, pCenter, pEnd, pCorner, pOtherCorner, fLineEnd,
+ xOrg, yOrg, xFtrans, yFtrans)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ SppPointRec pCenter, pEnd;
+ SppPointRec pCorner, pOtherCorner;
+ int fLineEnd, xOrg, yOrg;
+ double xFtrans, yFtrans;
+{
+ int cpt;
+ double width;
+ double miDatan2 ();
+ SppArcRec arc;
+ SppPointPtr pArcPts;
+
+ width = (pGC->lineWidth ? (double)pGC->lineWidth : (double)1);
+
+ arc.x = pCenter.x - width/2;
+ arc.y = pCenter.y - width/2;
+ arc.width = width;
+ arc.height = width;
+ arc.angle1 = -miDatan2 (pCorner.y - pCenter.y, pCorner.x - pCenter.x);
+ if(PTISEQUAL(pCenter, pEnd))
+ arc.angle2 = - 180.0;
+ else {
+ arc.angle2 = -miDatan2 (pOtherCorner.y - pCenter.y, pOtherCorner.x - pCenter.x) - arc.angle1;
+ if (arc.angle2 < 0)
+ arc.angle2 += 360.0;
+ }
+ pArcPts = (SppPointPtr) NULL;
+ if( (cpt = miGetArcPts(&arc, 0, &pArcPts)) )
+ {
+ /* by drawing with miFillSppPoly and setting the endpoints of the arc
+ * to be the corners, we assure that the cap will meet up with the
+ * rest of the line */
+ miFillSppPoly(pDraw, pGC, cpt, pArcPts, -xOrg, -yOrg, xFtrans, yFtrans);
+ }
+ xfree(pArcPts);
+}
+
+/*
+ * To avoid inaccuracy at the cardinal points, use trig functions
+ * which are exact for those angles
+ */
+
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+#ifndef M_PI_2
+#define M_PI_2 1.57079632679489661923
+#endif
+
+# define Dsin(d) ((d) == 0.0 ? 0.0 : ((d) == 90.0 ? 1.0 : sin(d*M_PI/180.0)))
+# define Dcos(d) ((d) == 0.0 ? 1.0 : ((d) == 90.0 ? 0.0 : cos(d*M_PI/180.0)))
+# define mod(a,b) ((a) >= 0 ? (a) % (b) : (b) - (-a) % (b))
+
+static double
+miDcos (a)
+double a;
+{
+ int i;
+
+ if (floor (a/90) == a/90) {
+ i = (int) (a/90.0);
+ switch (mod (i, 4)) {
+ case 0: return 1;
+ case 1: return 0;
+ case 2: return -1;
+ case 3: return 0;
+ }
+ }
+ return cos (a * M_PI / 180.0);
+}
+
+static double
+miDsin (a)
+double a;
+{
+ int i;
+
+ if (floor (a/90) == a/90) {
+ i = (int) (a/90.0);
+ switch (mod (i, 4)) {
+ case 0: return 0;
+ case 1: return 1;
+ case 2: return 0;
+ case 3: return -1;
+ }
+ }
+ return sin (a * M_PI / 180.0);
+}
+
+static double
+miDasin (v)
+double v;
+{
+ if (v == 0)
+ return 0.0;
+ if (v == 1.0)
+ return 90.0;
+ if (v == -1.0)
+ return -90.0;
+ return asin(v) * (180.0 / M_PI);
+}
+
+static double
+miDatan2 (dy, dx)
+double dy, dx;
+{
+ if (dy == 0) {
+ if (dx >= 0)
+ return 0.0;
+ return 180.0;
+ } else if (dx == 0) {
+ if (dy > 0)
+ return 90.0;
+ return -90.0;
+ } else if (Fabs (dy) == Fabs (dx)) {
+ if (dy > 0) {
+ if (dx > 0)
+ return 45.0;
+ return 135.0;
+ } else {
+ if (dx > 0)
+ return 315.0;
+ return 225.0;
+ }
+ } else {
+ return atan2 (dy, dx) * (180.0 / M_PI);
+ }
+}
+
+/* MIGETARCPTS -- Converts an arc into a set of line segments -- a helper
+ * routine for filled arc and line (round cap) code.
+ * Returns the number of points in the arc. Note that it takes a pointer
+ * to a pointer to where it should put the points and an index (cpt).
+ * This procedure allocates the space necessary to fit the arc points.
+ * Sometimes it's convenient for those points to be at the end of an existing
+ * array. (For example, if we want to leave a spare point to make sectors
+ * instead of segments.) So we pass in the Xalloc()ed chunk that contains the
+ * array and an index saying where we should start stashing the points.
+ * If there isn't an array already, we just pass in a null pointer and
+ * count on Xrealloc() to handle the null pointer correctly.
+ */
+static int
+miGetArcPts(parc, cpt, ppPts)
+ SppArcPtr parc; /* points to an arc */
+ int cpt; /* number of points already in arc list */
+ SppPointPtr *ppPts; /* pointer to pointer to arc-list -- modified */
+{
+ double st, /* Start Theta, start angle */
+ et, /* End Theta, offset from start theta */
+ dt, /* Delta Theta, angle to sweep ellipse */
+ cdt, /* Cos Delta Theta, actually 2 cos(dt) */
+ x0, y0, /* the recurrence formula needs two points to start */
+ x1, y1,
+ x2, y2, /* this will be the new point generated */
+ xc, yc; /* the center point */
+ int count, i;
+ SppPointPtr poly;
+ DDXPointRec last; /* last point on integer boundaries */
+
+ /* The spec says that positive angles indicate counterclockwise motion.
+ * Given our coordinate system (with 0,0 in the upper left corner),
+ * the screen appears flipped in Y. The easiest fix is to negate the
+ * angles given */
+
+ st = - parc->angle1;
+
+ et = - parc->angle2;
+
+ /* Try to get a delta theta that is within 1/2 pixel. Then adjust it
+ * so that it divides evenly into the total.
+ * I'm just using cdt 'cause I'm lazy.
+ */
+ cdt = parc->width;
+ if (parc->height > cdt)
+ cdt = parc->height;
+ cdt /= 2.0;
+ if(cdt <= 0)
+ return 0;
+ if (cdt < 1.0)
+ cdt = 1.0;
+ dt = miDasin ( 1.0 / cdt ); /* minimum step necessary */
+ count = et/dt;
+ count = abs(count) + 1;
+ dt = et/count;
+ count++;
+
+ cdt = 2 * miDcos(dt);
+ if (!(poly = (SppPointPtr) xrealloc((pointer)*ppPts,
+ (cpt + count) * sizeof(SppPointRec))))
+ return(0);
+ *ppPts = poly;
+
+ xc = parc->width/2.0; /* store half width and half height */
+ yc = parc->height/2.0;
+
+ x0 = xc * miDcos(st);
+ y0 = yc * miDsin(st);
+ x1 = xc * miDcos(st + dt);
+ y1 = yc * miDsin(st + dt);
+ xc += parc->x; /* by adding initial point, these become */
+ yc += parc->y; /* the center point */
+
+ poly[cpt].x = (xc + x0);
+ poly[cpt].y = (yc + y0);
+ last.x = ROUNDTOINT( poly[cpt + 1].x = (xc + x1) );
+ last.y = ROUNDTOINT( poly[cpt + 1].y = (yc + y1) );
+
+ for(i = 2; i < count; i++)
+ {
+ x2 = cdt * x1 - x0;
+ y2 = cdt * y1 - y0;
+
+ poly[cpt + i].x = (xc + x2);
+ poly[cpt + i].y = (yc + y2);
+
+ x0 = x1; y0 = y1;
+ x1 = x2; y1 = y2;
+ }
+ /* adjust the last point */
+ if (abs(parc->angle2) >= 360.0)
+ poly[cpt +i -1] = poly[0];
+ else {
+ poly[cpt +i -1].x = (miDcos(st + et) * parc->width/2.0 + xc);
+ poly[cpt +i -1].y = (miDsin(st + et) * parc->height/2.0 + yc);
+ }
+
+ return(count);
+}
+
+struct arcData {
+ double x0, y0, x1, y1;
+ int selfJoin;
+};
+
+# define ADD_REALLOC_STEP 20
+
+static void
+addCap (capsp, ncapsp, sizep, end, arcIndex)
+ miArcCapPtr *capsp;
+ int *ncapsp, *sizep;
+ int end, arcIndex;
+{
+ int newsize;
+ miArcCapPtr cap;
+
+ if (*ncapsp == *sizep)
+ {
+ newsize = *sizep + ADD_REALLOC_STEP;
+ cap = (miArcCapPtr) xrealloc (*capsp,
+ newsize * sizeof (**capsp));
+ if (!cap)
+ return;
+ *sizep = newsize;
+ *capsp = cap;
+ }
+ cap = &(*capsp)[*ncapsp];
+ cap->end = end;
+ cap->arcIndex = arcIndex;
+ ++*ncapsp;
+}
+
+static void
+addJoin (joinsp, njoinsp, sizep, end0, index0, phase0, end1, index1, phase1)
+ miArcJoinPtr *joinsp;
+ int *njoinsp, *sizep;
+ int end0, index0, phase0, end1, index1, phase1;
+{
+ int newsize;
+ miArcJoinPtr join;
+
+ if (*njoinsp == *sizep)
+ {
+ newsize = *sizep + ADD_REALLOC_STEP;
+ join = (miArcJoinPtr) xrealloc (*joinsp,
+ newsize * sizeof (**joinsp));
+ if (!join)
+ return;
+ *sizep = newsize;
+ *joinsp = join;
+ }
+ join = &(*joinsp)[*njoinsp];
+ join->end0 = end0;
+ join->arcIndex0 = index0;
+ join->phase0 = phase0;
+ join->end1 = end1;
+ join->arcIndex1 = index1;
+ join->phase1 = phase1;
+ ++*njoinsp;
+}
+
+static miArcDataPtr
+addArc (arcsp, narcsp, sizep, xarc)
+ miArcDataPtr *arcsp;
+ int *narcsp, *sizep;
+ xArc *xarc;
+{
+ int newsize;
+ miArcDataPtr arc;
+
+ if (*narcsp == *sizep)
+ {
+ newsize = *sizep + ADD_REALLOC_STEP;
+ arc = (miArcDataPtr) xrealloc (*arcsp,
+ newsize * sizeof (**arcsp));
+ if (!arc)
+ return (miArcDataPtr)NULL;
+ *sizep = newsize;
+ *arcsp = arc;
+ }
+ arc = &(*arcsp)[*narcsp];
+ arc->arc = *xarc;
+ ++*narcsp;
+ return arc;
+}
+
+static void
+miFreeArcs(arcs, pGC)
+ miPolyArcPtr arcs;
+ GCPtr pGC;
+{
+ int iphase;
+
+ for (iphase = ((pGC->lineStyle == LineDoubleDash) ? 1 : 0);
+ iphase >= 0;
+ iphase--)
+ {
+ if (arcs[iphase].narcs > 0)
+ xfree(arcs[iphase].arcs);
+ if (arcs[iphase].njoins > 0)
+ xfree(arcs[iphase].joins);
+ if (arcs[iphase].ncaps > 0)
+ xfree(arcs[iphase].caps);
+ }
+ xfree(arcs);
+}
+
+/*
+ * map angles to radial distance. This only deals with the first quadrant
+ */
+
+/*
+ * a polygonal approximation to the arc for computing arc lengths
+ */
+
+# define DASH_MAP_SIZE 91
+
+# define dashIndexToAngle(di) ((((double) (di)) * 90.0) / ((double) DASH_MAP_SIZE - 1))
+# define xAngleToDashIndex(xa) ((((long) (xa)) * (DASH_MAP_SIZE - 1)) / (90 * 64))
+# define dashIndexToXAngle(di) ((((long) (di)) * (90 * 64)) / (DASH_MAP_SIZE - 1))
+# define dashXAngleStep (((double) (90 * 64)) / ((double) (DASH_MAP_SIZE - 1)))
+
+typedef struct {
+ double map[DASH_MAP_SIZE];
+} dashMap;
+
+static void
+computeDashMap (arcp, map)
+ xArc *arcp;
+ dashMap *map;
+{
+ int di;
+ double a, x, y, prevx, prevy, dist;
+
+ for (di = 0; di < DASH_MAP_SIZE; di++) {
+ a = dashIndexToAngle (di);
+ x = ((double) arcp->width / 2.0) * miDcos (a);
+ y = ((double) arcp->height / 2.0) * miDsin (a);
+ if (di == 0) {
+ map->map[di] = 0.0;
+ } else {
+ dist = hypot (x - prevx, y - prevy);
+ map->map[di] = map->map[di - 1] + dist;
+ }
+ prevx = x;
+ prevy = y;
+ }
+}
+
+typedef enum {HORIZONTAL, VERTICAL, OTHER} arcTypes;
+
+/* this routine is a bit gory */
+
+static miPolyArcPtr
+miComputeArcs (parcs, narcs, pGC)
+ xArc *parcs;
+ int narcs;
+ GCPtr pGC;
+{
+ int isDashed, isDoubleDash;
+ int dashOffset;
+ miPolyArcPtr arcs;
+ int start, i, j, k, nexti, nextk;
+ int joinSize[2];
+ int capSize[2];
+ int arcSize[2];
+ int angle2;
+ double a0, a1;
+ struct arcData *data;
+ miArcDataPtr arc;
+ xArc xarc;
+ int iphase, prevphase, joinphase;
+ int arcsJoin;
+ int selfJoin;
+
+ int iDash, dashRemaining;
+ int iDashStart, dashRemainingStart, iphaseStart;
+ int startAngle, spanAngle, endAngle, backwards;
+ int prevDashAngle, dashAngle;
+ dashMap map;
+
+ isDashed = !(pGC->lineStyle == LineSolid);
+ isDoubleDash = (pGC->lineStyle == LineDoubleDash);
+ dashOffset = pGC->dashOffset;
+
+ data = (struct arcData *) ALLOCATE_LOCAL (narcs * sizeof (struct arcData));
+ if (!data)
+ return (miPolyArcPtr)NULL;
+ arcs = (miPolyArcPtr) xalloc (sizeof (*arcs) * (isDoubleDash ? 2 : 1));
+ if (!arcs)
+ {
+ DEALLOCATE_LOCAL(data);
+ return (miPolyArcPtr)NULL;
+ }
+ for (i = 0; i < narcs; i++) {
+ a0 = todeg (parcs[i].angle1);
+ angle2 = parcs[i].angle2;
+ if (angle2 > FULLCIRCLE)
+ angle2 = FULLCIRCLE;
+ else if (angle2 < -FULLCIRCLE)
+ angle2 = -FULLCIRCLE;
+ data[i].selfJoin = angle2 == FULLCIRCLE || angle2 == -FULLCIRCLE;
+ a1 = todeg (parcs[i].angle1 + angle2);
+ data[i].x0 = parcs[i].x + (double) parcs[i].width / 2 * (1 + miDcos (a0));
+ data[i].y0 = parcs[i].y + (double) parcs[i].height / 2 * (1 - miDsin (a0));
+ data[i].x1 = parcs[i].x + (double) parcs[i].width / 2 * (1 + miDcos (a1));
+ data[i].y1 = parcs[i].y + (double) parcs[i].height / 2 * (1 - miDsin (a1));
+ }
+
+ for (iphase = 0; iphase < (isDoubleDash ? 2 : 1); iphase++) {
+ arcs[iphase].njoins = 0;
+ arcs[iphase].joins = 0;
+ joinSize[iphase] = 0;
+
+ arcs[iphase].ncaps = 0;
+ arcs[iphase].caps = 0;
+ capSize[iphase] = 0;
+
+ arcs[iphase].narcs = 0;
+ arcs[iphase].arcs = 0;
+ arcSize[iphase] = 0;
+ }
+
+ iphase = 0;
+ if (isDashed) {
+ iDash = 0;
+ dashRemaining = pGC->dash[0];
+ while (dashOffset > 0) {
+ if (dashOffset >= dashRemaining) {
+ dashOffset -= dashRemaining;
+ iphase = iphase ? 0 : 1;
+ iDash++;
+ if (iDash == pGC->numInDashList)
+ iDash = 0;
+ dashRemaining = pGC->dash[iDash];
+ } else {
+ dashRemaining -= dashOffset;
+ dashOffset = 0;
+ }
+ }
+ iDashStart = iDash;
+ dashRemainingStart = dashRemaining;
+ }
+ iphaseStart = iphase;
+
+ for (i = narcs - 1; i >= 0; i--) {
+ j = i + 1;
+ if (j == narcs)
+ j = 0;
+ if (data[i].selfJoin || i == j ||
+ (UNEQUAL (data[i].x1, data[j].x0) ||
+ UNEQUAL (data[i].y1, data[j].y0)))
+ {
+ if (iphase == 0 || isDoubleDash)
+ addCap (&arcs[iphase].caps, &arcs[iphase].ncaps,
+ &capSize[iphase], RIGHT_END, 0);
+ break;
+ }
+ }
+ start = i + 1;
+ if (start == narcs)
+ start = 0;
+ i = start;
+ for (;;) {
+ j = i + 1;
+ if (j == narcs)
+ j = 0;
+ nexti = i+1;
+ if (nexti == narcs)
+ nexti = 0;
+ if (isDashed) {
+ /*
+ ** deal with dashed arcs. Use special rules for certain 0 area arcs.
+ ** Presumably, the other 0 area arcs still aren't done right.
+ */
+ arcTypes arcType = OTHER;
+ CARD16 thisLength;
+
+ if (parcs[i].height == 0
+ && (parcs[i].angle1 % FULLCIRCLE) == 0x2d00
+ && parcs[i].angle2 == 0x2d00)
+ arcType = HORIZONTAL;
+ else if (parcs[i].width == 0
+ && (parcs[i].angle1 % FULLCIRCLE) == 0x1680
+ && parcs[i].angle2 == 0x2d00)
+ arcType = VERTICAL;
+ if (arcType == OTHER) {
+ /*
+ * precompute an approximation map
+ */
+ computeDashMap (&parcs[i], &map);
+ /*
+ * compute each individual dash segment using the path
+ * length function
+ */
+ startAngle = parcs[i].angle1;
+ spanAngle = parcs[i].angle2;
+ if (spanAngle > FULLCIRCLE)
+ spanAngle = FULLCIRCLE;
+ else if (spanAngle < -FULLCIRCLE)
+ spanAngle = -FULLCIRCLE;
+ if (startAngle < 0)
+ startAngle = FULLCIRCLE - (-startAngle) % FULLCIRCLE;
+ if (startAngle >= FULLCIRCLE)
+ startAngle = startAngle % FULLCIRCLE;
+ endAngle = startAngle + spanAngle;
+ backwards = spanAngle < 0;
+ } else {
+ xarc = parcs[i];
+ if (arcType == VERTICAL) {
+ xarc.angle1 = 0x1680;
+ startAngle = parcs[i].y;
+ endAngle = startAngle + parcs[i].height;
+ } else {
+ xarc.angle1 = 0x2d00;
+ startAngle = parcs[i].x;
+ endAngle = startAngle + parcs[i].width;
+ }
+ }
+ dashAngle = startAngle;
+ selfJoin = data[i].selfJoin &&
+ (iphase == 0 || isDoubleDash);
+ /*
+ * add dashed arcs to each bucket
+ */
+ arc = 0;
+ while (dashAngle != endAngle) {
+ prevDashAngle = dashAngle;
+ if (arcType == OTHER) {
+ dashAngle = computeAngleFromPath (prevDashAngle, endAngle,
+ &map, &dashRemaining, backwards);
+ /* avoid troubles with huge arcs and small dashes */
+ if (dashAngle == prevDashAngle) {
+ if (backwards)
+ dashAngle--;
+ else
+ dashAngle++;
+ }
+ } else {
+ thisLength = (dashAngle + dashRemaining <= endAngle) ?
+ dashRemaining : endAngle - dashAngle;
+ if (arcType == VERTICAL) {
+ xarc.y = dashAngle;
+ xarc.height = thisLength;
+ } else {
+ xarc.x = dashAngle;
+ xarc.width = thisLength;
+ }
+ dashAngle += thisLength;
+ dashRemaining -= thisLength;
+ }
+ if (iphase == 0 || isDoubleDash) {
+ if (arcType == OTHER) {
+ xarc = parcs[i];
+ spanAngle = prevDashAngle;
+ if (spanAngle < 0)
+ spanAngle = FULLCIRCLE - (-spanAngle) % FULLCIRCLE;
+ if (spanAngle >= FULLCIRCLE)
+ spanAngle = spanAngle % FULLCIRCLE;
+ xarc.angle1 = spanAngle;
+ spanAngle = dashAngle - prevDashAngle;
+ if (backwards) {
+ if (dashAngle > prevDashAngle)
+ spanAngle = - FULLCIRCLE + spanAngle;
+ } else {
+ if (dashAngle < prevDashAngle)
+ spanAngle = FULLCIRCLE + spanAngle;
+ }
+ if (spanAngle > FULLCIRCLE)
+ spanAngle = FULLCIRCLE;
+ if (spanAngle < -FULLCIRCLE)
+ spanAngle = -FULLCIRCLE;
+ xarc.angle2 = spanAngle;
+ }
+ arc = addArc (&arcs[iphase].arcs, &arcs[iphase].narcs,
+ &arcSize[iphase], &xarc);
+ if (!arc)
+ goto arcfail;
+ /*
+ * cap each end of an on/off dash
+ */
+ if (!isDoubleDash) {
+ if (prevDashAngle != startAngle) {
+ addCap (&arcs[iphase].caps,
+ &arcs[iphase].ncaps,
+ &capSize[iphase], RIGHT_END,
+ arc - arcs[iphase].arcs);
+
+ }
+ if (dashAngle != endAngle) {
+ addCap (&arcs[iphase].caps,
+ &arcs[iphase].ncaps,
+ &capSize[iphase], LEFT_END,
+ arc - arcs[iphase].arcs);
+ }
+ }
+ arc->cap = arcs[iphase].ncaps;
+ arc->join = arcs[iphase].njoins;
+ arc->render = 0;
+ arc->selfJoin = 0;
+ if (dashAngle == endAngle)
+ arc->selfJoin = selfJoin;
+ }
+ prevphase = iphase;
+ if (dashRemaining <= 0) {
+ ++iDash;
+ if (iDash == pGC->numInDashList)
+ iDash = 0;
+ iphase = iphase ? 0:1;
+ dashRemaining = pGC->dash[iDash];
+ }
+ }
+ /*
+ * make sure a place exists for the position data when
+ * drawing a zero-length arc
+ */
+ if (startAngle == endAngle) {
+ prevphase = iphase;
+ if (!isDoubleDash && iphase == 1)
+ prevphase = 0;
+ arc = addArc (&arcs[prevphase].arcs, &arcs[prevphase].narcs,
+ &arcSize[prevphase], &parcs[i]);
+ if (!arc)
+ goto arcfail;
+ arc->join = arcs[prevphase].njoins;
+ arc->cap = arcs[prevphase].ncaps;
+ arc->selfJoin = data[i].selfJoin;
+ }
+ } else {
+ arc = addArc (&arcs[iphase].arcs, &arcs[iphase].narcs,
+ &arcSize[iphase], &parcs[i]);
+ if (!arc)
+ goto arcfail;
+ arc->join = arcs[iphase].njoins;
+ arc->cap = arcs[iphase].ncaps;
+ arc->selfJoin = data[i].selfJoin;
+ prevphase = iphase;
+ }
+ if (prevphase == 0 || isDoubleDash)
+ k = arcs[prevphase].narcs - 1;
+ if (iphase == 0 || isDoubleDash)
+ nextk = arcs[iphase].narcs;
+ if (nexti == start) {
+ nextk = 0;
+ if (isDashed) {
+ iDash = iDashStart;
+ iphase = iphaseStart;
+ dashRemaining = dashRemainingStart;
+ }
+ }
+ arcsJoin = narcs > 1 && i != j &&
+ ISEQUAL (data[i].x1, data[j].x0) &&
+ ISEQUAL (data[i].y1, data[j].y0) &&
+ !data[i].selfJoin && !data[j].selfJoin;
+ if (arc)
+ {
+ if (arcsJoin)
+ arc->render = 0;
+ else
+ arc->render = 1;
+ }
+ if (arcsJoin &&
+ (prevphase == 0 || isDoubleDash) &&
+ (iphase == 0 || isDoubleDash))
+ {
+ joinphase = iphase;
+ if (isDoubleDash) {
+ if (nexti == start)
+ joinphase = iphaseStart;
+ /*
+ * if the join is right at the dash,
+ * draw the join in foreground
+ * This is because the foreground
+ * arcs are computed second, the results
+ * of which are needed to draw the join
+ */
+ if (joinphase != prevphase)
+ joinphase = 0;
+ }
+ if (joinphase == 0 || isDoubleDash) {
+ addJoin (&arcs[joinphase].joins,
+ &arcs[joinphase].njoins,
+ &joinSize[joinphase],
+ LEFT_END, k, prevphase,
+ RIGHT_END, nextk, iphase);
+ arc->join = arcs[prevphase].njoins;
+ }
+ } else {
+ /*
+ * cap the left end of this arc
+ * unless it joins itself
+ */
+ if ((prevphase == 0 || isDoubleDash) &&
+ !arc->selfJoin)
+ {
+ addCap (&arcs[prevphase].caps, &arcs[prevphase].ncaps,
+ &capSize[prevphase], LEFT_END, k);
+ arc->cap = arcs[prevphase].ncaps;
+ }
+ if (isDashed && !arcsJoin) {
+ iDash = iDashStart;
+ iphase = iphaseStart;
+ dashRemaining = dashRemainingStart;
+ }
+ nextk = arcs[iphase].narcs;
+ if (nexti == start) {
+ nextk = 0;
+ iDash = iDashStart;
+ iphase = iphaseStart;
+ dashRemaining = dashRemainingStart;
+ }
+ /*
+ * cap the right end of the next arc. If the
+ * next arc is actually the first arc, only
+ * cap it if it joins with this arc. This
+ * case will occur when the final dash segment
+ * of an on/off dash is off. Of course, this
+ * cap will be drawn at a strange time, but that
+ * hardly matters...
+ */
+ if ((iphase == 0 || isDoubleDash) &&
+ (nexti != start || (arcsJoin && isDashed)))
+ addCap (&arcs[iphase].caps, &arcs[iphase].ncaps,
+ &capSize[iphase], RIGHT_END, nextk);
+ }
+ i = nexti;
+ if (i == start)
+ break;
+ }
+ /*
+ * make sure the last section is rendered
+ */
+ for (iphase = 0; iphase < (isDoubleDash ? 2 : 1); iphase++)
+ if (arcs[iphase].narcs > 0) {
+ arcs[iphase].arcs[arcs[iphase].narcs-1].render = 1;
+ arcs[iphase].arcs[arcs[iphase].narcs-1].join =
+ arcs[iphase].njoins;
+ arcs[iphase].arcs[arcs[iphase].narcs-1].cap =
+ arcs[iphase].ncaps;
+ }
+ DEALLOCATE_LOCAL(data);
+ return arcs;
+arcfail:
+ miFreeArcs(arcs, pGC);
+ DEALLOCATE_LOCAL(data);
+ return (miPolyArcPtr)NULL;
+}
+
+static double
+angleToLength (angle, map)
+ int angle;
+ dashMap *map;
+{
+ double len, excesslen, sidelen = map->map[DASH_MAP_SIZE - 1], totallen;
+ int di;
+ int excess;
+ Bool oddSide = FALSE;
+
+ totallen = 0;
+ if (angle >= 0) {
+ while (angle >= 90 * 64) {
+ angle -= 90 * 64;
+ totallen += sidelen;
+ oddSide = !oddSide;
+ }
+ } else {
+ while (angle < 0) {
+ angle += 90 * 64;
+ totallen -= sidelen;
+ oddSide = !oddSide;
+ }
+ }
+ if (oddSide)
+ angle = 90 * 64 - angle;
+
+ di = xAngleToDashIndex (angle);
+ excess = angle - dashIndexToXAngle (di);
+
+ len = map->map[di];
+ /*
+ * linearly interpolate between this point and the next
+ */
+ if (excess > 0) {
+ excesslen = (map->map[di + 1] - map->map[di]) *
+ ((double) excess) / dashXAngleStep;
+ len += excesslen;
+ }
+ if (oddSide)
+ totallen += (sidelen - len);
+ else
+ totallen += len;
+ return totallen;
+}
+
+/*
+ * len is along the arc, but may be more than one rotation
+ */
+
+static int
+lengthToAngle (len, map)
+ double len;
+ dashMap *map;
+{
+ double sidelen = map->map[DASH_MAP_SIZE - 1];
+ int angle, angleexcess;
+ Bool oddSide = FALSE;
+ int a0, a1, a;
+
+ angle = 0;
+ /*
+ * step around the ellipse, subtracting sidelens and
+ * adding 90 degrees. oddSide will tell if the
+ * map should be interpolated in reverse
+ */
+ if (len >= 0) {
+ if (sidelen == 0)
+ return 2 * FULLCIRCLE; /* infinity */
+ while (len >= sidelen) {
+ angle += 90 * 64;
+ len -= sidelen;
+ oddSide = !oddSide;
+ }
+ } else {
+ if (sidelen == 0)
+ return -2 * FULLCIRCLE; /* infinity */
+ while (len < 0) {
+ angle -= 90 * 64;
+ len += sidelen;
+ oddSide = !oddSide;
+ }
+ }
+ if (oddSide)
+ len = sidelen - len;
+ a0 = 0;
+ a1 = DASH_MAP_SIZE - 1;
+ /*
+ * binary search for the closest pre-computed length
+ */
+ while (a1 - a0 > 1) {
+ a = (a0 + a1) / 2;
+ if (len > map->map[a])
+ a0 = a;
+ else
+ a1 = a;
+ }
+ angleexcess = dashIndexToXAngle (a0);
+ /*
+ * linearly interpolate to the next point
+ */
+ angleexcess += (len - map->map[a0]) /
+ (map->map[a0+1] - map->map[a0]) * dashXAngleStep;
+ if (oddSide)
+ angle += (90 * 64) - angleexcess;
+ else
+ angle += angleexcess;
+ return angle;
+}
+
+/*
+ * compute the angle of an ellipse which cooresponds to
+ * the given path length. Note that the correct solution
+ * to this problem is an eliptic integral, we'll punt and
+ * approximate (it's only for dashes anyway). This
+ * approximation uses a polygon.
+ *
+ * The remaining portion of len is stored in *lenp -
+ * this will be negative if the arc extends beyond
+ * len and positive if len extends beyond the arc.
+ */
+
+static int
+computeAngleFromPath (startAngle, endAngle, map, lenp, backwards)
+ int startAngle, endAngle; /* normalized absolute angles in *64 degrees */
+ dashMap *map;
+ int *lenp;
+ int backwards;
+{
+ int a0, a1, a;
+ double len0;
+ int len;
+
+ a0 = startAngle;
+ a1 = endAngle;
+ len = *lenp;
+ if (backwards) {
+ /*
+ * flip the problem around to always be
+ * forwards
+ */
+ a0 = FULLCIRCLE - a0;
+ a1 = FULLCIRCLE - a1;
+ }
+ if (a1 < a0)
+ a1 += FULLCIRCLE;
+ len0 = angleToLength (a0, map);
+ a = lengthToAngle (len0 + len, map);
+ if (a > a1) {
+ a = a1;
+ len -= angleToLength (a1, map) - len0;
+ } else
+ len = 0;
+ if (backwards)
+ a = FULLCIRCLE - a;
+ *lenp = len;
+ return a;
+}
+
+/*
+ * scan convert wide arcs.
+ */
+
+/*
+ * draw zero width/height arcs
+ */
+
+static void
+drawZeroArc (pDraw, pGC, tarc, lw, left, right)
+ DrawablePtr pDraw;
+ GCPtr pGC;
+ xArc *tarc;
+ int lw;
+ miArcFacePtr right, left;
+{
+ double x0, y0, x1, y1, w, h, x, y;
+ double xmax, ymax, xmin, ymin;
+ int a0, a1;
+ double a, startAngle, endAngle;
+ double l, lx, ly;
+
+ l = lw / 2.0;
+ a0 = tarc->angle1;
+ a1 = tarc->angle2;
+ if (a1 > FULLCIRCLE)
+ a1 = FULLCIRCLE;
+ else if (a1 < -FULLCIRCLE)
+ a1 = -FULLCIRCLE;
+ w = (double)tarc->width / 2.0;
+ h = (double)tarc->height / 2.0;
+ /*
+ * play in X coordinates right away
+ */
+ startAngle = - ((double) a0 / 64.0);
+ endAngle = - ((double) (a0 + a1) / 64.0);
+
+ xmax = -w;
+ xmin = w;
+ ymax = -h;
+ ymin = h;
+ a = startAngle;
+ for (;;)
+ {
+ x = w * miDcos(a);
+ y = h * miDsin(a);
+ if (a == startAngle)
+ {
+ x0 = x;
+ y0 = y;
+ }
+ if (a == endAngle)
+ {
+ x1 = x;
+ y1 = y;
+ }
+ if (x > xmax)
+ xmax = x;
+ if (x < xmin)
+ xmin = x;
+ if (y > ymax)
+ ymax = y;
+ if (y < ymin)
+ ymin = y;
+ if (a == endAngle)
+ break;
+ if (a1 < 0) /* clockwise */
+ {
+ if (floor (a / 90.0) == floor (endAngle / 90.0))
+ a = endAngle;
+ else
+ a = 90 * (floor (a/90.0) + 1);
+ }
+ else
+ {
+ if (ceil (a / 90.0) == ceil (endAngle / 90.0))
+ a = endAngle;
+ else
+ a = 90 * (ceil (a/90.0) - 1);
+ }
+ }
+ lx = ly = l;
+ if ((x1 - x0) + (y1 - y0) < 0)
+ lx = ly = -l;
+ if (h)
+ {
+ ly = 0.0;
+ lx = -lx;
+ }
+ else
+ lx = 0.0;
+ if (right)
+ {
+ right->center.x = x0;
+ right->center.y = y0;
+ right->clock.x = x0 - lx;
+ right->clock.y = y0 - ly;
+ right->counterClock.x = x0 + lx;
+ right->counterClock.y = y0 + ly;
+ }
+ if (left)
+ {
+ left->center.x = x1;
+ left->center.y = y1;
+ left->clock.x = x1 + lx;
+ left->clock.y = y1 + ly;
+ left->counterClock.x = x1 - lx;
+ left->counterClock.y = y1 - ly;
+ }
+
+ x0 = xmin;
+ x1 = xmax;
+ y0 = ymin;
+ y1 = ymax;
+ if (ymin != y1) {
+ xmin = -l;
+ xmax = l;
+ } else {
+ ymin = -l;
+ ymax = l;
+ }
+ if (xmax != xmin && ymax != ymin) {
+ int minx, maxx, miny, maxy;
+ xRectangle rect;
+
+ minx = ICEIL (xmin + w) + tarc->x;
+ maxx = ICEIL (xmax + w) + tarc->x;
+ miny = ICEIL (ymin + h) + tarc->y;
+ maxy = ICEIL (ymax + h) + tarc->y;
+ rect.x = minx;
+ rect.y = miny;
+ rect.width = maxx - minx;
+ rect.height = maxy - miny;
+ (*pGC->ops->PolyFillRect) (pDraw, pGC, 1, &rect);
+ }
+}
+
+/*
+ * this computes the ellipse y value associated with the
+ * bottom of the tail.
+ */
+
+static void
+tailEllipseY (def, acc)
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ double t;
+
+ acc->tail_y = 0.0;
+ if (def->w == def->h)
+ return;
+ t = def->l * def->w;
+ if (def->w > def->h) {
+ if (t < acc->h2)
+ return;
+ } else {
+ if (t > acc->h2)
+ return;
+ }
+ t = 2.0 * def->h * t;
+ t = (CUBED_ROOT_4 * acc->h2 - cbrt(t * t)) / acc->h2mw2;
+ if (t > 0.0)
+ acc->tail_y = def->h / CUBED_ROOT_2 * sqrt(t);
+}
+
+/*
+ * inverse functions -- compute edge coordinates
+ * from the ellipse
+ */
+
+static double
+outerXfromXY (x, y, def, acc)
+ double x, y;
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ return x + (x * acc->h2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
+}
+
+static double
+outerYfromXY (x, y, def, acc)
+ double x, y;
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ return y + (y * acc->w2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
+}
+
+static double
+innerXfromXY (x, y, def, acc)
+ double x, y;
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ return x - (x * acc->h2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
+}
+
+static double
+innerYfromXY (x, y, def, acc)
+ double x, y;
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ return y - (y * acc->w2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
+}
+
+static double
+innerYfromY (y, def, acc)
+ double y;
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ double x;
+
+ x = (def->w / def->h) * sqrt (acc->h2 - y*y);
+
+ return y - (y * acc->w2l) / sqrt (x*x * acc->h4 + y*y * acc->w4);
+}
+
+static void
+computeLine (x1, y1, x2, y2, line)
+ double x1, y1, x2, y2;
+ struct line *line;
+{
+ if (y1 == y2)
+ line->valid = 0;
+ else {
+ line->m = (x1 - x2) / (y1 - y2);
+ line->b = x1 - y1 * line->m;
+ line->valid = 1;
+ }
+}
+
+/*
+ * compute various accelerators for an ellipse. These
+ * are simply values that are used repeatedly in
+ * the computations
+ */
+
+static void
+computeAcc (tarc, lw, def, acc)
+ xArc *tarc;
+ int lw;
+ struct arc_def *def;
+ struct accelerators *acc;
+{
+ def->w = ((double) tarc->width) / 2.0;
+ def->h = ((double) tarc->height) / 2.0;
+ def->l = ((double) lw) / 2.0;
+ acc->h2 = def->h * def->h;
+ acc->w2 = def->w * def->w;
+ acc->h4 = acc->h2 * acc->h2;
+ acc->w4 = acc->w2 * acc->w2;
+ acc->h2l = acc->h2 * def->l;
+ acc->w2l = acc->w2 * def->l;
+ acc->h2mw2 = acc->h2 - acc->w2;
+ acc->fromIntX = (tarc->width & 1) ? 0.5 : 0.0;
+ acc->fromIntY = (tarc->height & 1) ? 0.5 : 0.0;
+ acc->xorg = tarc->x + (tarc->width >> 1);
+ acc->yorgu = tarc->y + (tarc->height >> 1);
+ acc->yorgl = acc->yorgu + (tarc->height & 1);
+ tailEllipseY (def, acc);
+}
+
+/*
+ * compute y value bounds of various portions of the arc,
+ * the outer edge, the ellipse and the inner edge.
+ */
+
+static void
+computeBound (def, bound, acc, right, left)
+ struct arc_def *def;
+ struct arc_bound *bound;
+ struct accelerators *acc;
+ miArcFacePtr right, left;
+{
+ double t;
+ double innerTaily;
+ double tail_y;
+ struct bound innerx, outerx;
+ struct bound ellipsex;
+
+ bound->ellipse.min = Dsin (def->a0) * def->h;
+ bound->ellipse.max = Dsin (def->a1) * def->h;
+ if (def->a0 == 45 && def->w == def->h)
+ ellipsex.min = bound->ellipse.min;
+ else
+ ellipsex.min = Dcos (def->a0) * def->w;
+ if (def->a1 == 45 && def->w == def->h)
+ ellipsex.max = bound->ellipse.max;
+ else
+ ellipsex.max = Dcos (def->a1) * def->w;
+ bound->outer.min = outerYfromXY (ellipsex.min, bound->ellipse.min, def, acc);
+ bound->outer.max = outerYfromXY (ellipsex.max, bound->ellipse.max, def, acc);
+ bound->inner.min = innerYfromXY (ellipsex.min, bound->ellipse.min, def, acc);
+ bound->inner.max = innerYfromXY (ellipsex.max, bound->ellipse.max, def, acc);
+
+ outerx.min = outerXfromXY (ellipsex.min, bound->ellipse.min, def, acc);
+ outerx.max = outerXfromXY (ellipsex.max, bound->ellipse.max, def, acc);
+ innerx.min = innerXfromXY (ellipsex.min, bound->ellipse.min, def, acc);
+ innerx.max = innerXfromXY (ellipsex.max, bound->ellipse.max, def, acc);
+
+ /*
+ * save the line end points for the
+ * cap code to use. Careful here, these are
+ * in cartesean coordinates (y increasing upwards)
+ * while the cap code uses inverted coordinates
+ * (y increasing downwards)
+ */
+
+ if (right) {
+ right->counterClock.y = bound->outer.min;
+ right->counterClock.x = outerx.min;
+ right->center.y = bound->ellipse.min;
+ right->center.x = ellipsex.min;
+ right->clock.y = bound->inner.min;
+ right->clock.x = innerx.min;
+ }
+
+ if (left) {
+ left->clock.y = bound->outer.max;
+ left->clock.x = outerx.max;
+ left->center.y = bound->ellipse.max;
+ left->center.x = ellipsex.max;
+ left->counterClock.y = bound->inner.max;
+ left->counterClock.x = innerx.max;
+ }
+
+ bound->left.min = bound->inner.max;
+ bound->left.max = bound->outer.max;
+ bound->right.min = bound->inner.min;
+ bound->right.max = bound->outer.min;
+
+ computeLine (innerx.min, bound->inner.min, outerx.min, bound->outer.min,
+ &acc->right);
+ computeLine (innerx.max, bound->inner.max, outerx.max, bound->outer.max,
+ &acc->left);
+
+ if (bound->inner.min > bound->inner.max) {
+ t = bound->inner.min;
+ bound->inner.min = bound->inner.max;
+ bound->inner.max = t;
+ }
+ tail_y = acc->tail_y;
+ if (tail_y > bound->ellipse.max)
+ tail_y = bound->ellipse.max;
+ else if (tail_y < bound->ellipse.min)
+ tail_y = bound->ellipse.min;
+ innerTaily = innerYfromY (tail_y, def, acc);
+ if (bound->inner.min > innerTaily)
+ bound->inner.min = innerTaily;
+ if (bound->inner.max < innerTaily)
+ bound->inner.max = innerTaily;
+ bound->inneri.min = ICEIL(bound->inner.min - acc->fromIntY);
+ bound->inneri.max = floor(bound->inner.max - acc->fromIntY);
+ bound->outeri.min = ICEIL(bound->outer.min - acc->fromIntY);
+ bound->outeri.max = floor(bound->outer.max - acc->fromIntY);
+}
+
+/*
+ * this section computes the x value of the span at y
+ * intersected with the specified face of the ellipse.
+ *
+ * this is the min/max X value over the set of normal
+ * lines to the entire ellipse, the equation of the
+ * normal lines is:
+ *
+ * ellipse_x h^2 h^2
+ * x = ------------ y + ellipse_x (1 - --- )
+ * ellipse_y w^2 w^2
+ *
+ * compute the derivative with-respect-to ellipse_y and solve
+ * for zero:
+ *
+ * (w^2 - h^2) ellipse_y^3 + h^4 y
+ * 0 = - ----------------------------------
+ * h w ellipse_y^2 sqrt (h^2 - ellipse_y^2)
+ *
+ * ( h^4 y )
+ * ellipse_y = ( ---------- ) ^ (1/3)
+ * ( (h^2 - w^2) )
+ *
+ * The other two solutions to the equation are imaginary.
+ *
+ * This gives the position on the ellipse which generates
+ * the normal with the largest/smallest x intersection point.
+ *
+ * Now compute the second derivative to check whether
+ * the intersection is a minimum or maximum:
+ *
+ * h (y0^3 (w^2 - h^2) + h^2 y (3y0^2 - 2h^2))
+ * - -------------------------------------------
+ * w y0^3 (sqrt (h^2 - y^2)) ^ 3
+ *
+ * as we only care about the sign,
+ *
+ * - (y0^3 (w^2 - h^2) + h^2 y (3y0^2 - 2h^2))
+ *
+ * or (to use accelerators),
+ *
+ * y0^3 (h^2 - w^2) - h^2 y (3y0^2 - 2h^2)
+ *
+ */
+
+/*
+ * computes the position on the ellipse whose normal line
+ * intersects the given scan line maximally
+ */
+
+static double
+hookEllipseY (scan_y, bound, acc, left)
+ double scan_y;
+ struct arc_bound *bound;
+ struct accelerators *acc;
+ int left;
+{
+ double ret;
+
+ if (acc->h2mw2 == 0) {
+ if ( (scan_y > 0 && !left) || (scan_y < 0 && left) )
+ return bound->ellipse.min;
+ return bound->ellipse.max;
+ }
+ ret = (acc->h4 * scan_y) / (acc->h2mw2);
+ if (ret >= 0)
+ return cbrt (ret);
+ else
+ return -cbrt (-ret);
+}
+
+/*
+ * computes the X value of the intersection of the
+ * given scan line with the right side of the lower hook
+ */
+
+static double
+hookX (scan_y, def, bound, acc, left)
+ double scan_y;
+ struct arc_def *def;
+ struct arc_bound *bound;
+ struct accelerators *acc;
+ int left;
+{
+ double ellipse_y, x;
+ double maxMin;
+
+ if (def->w != def->h) {
+ ellipse_y = hookEllipseY (scan_y, bound, acc, left);
+ if (boundedLe (ellipse_y, bound->ellipse)) {
+ /*
+ * compute the value of the second
+ * derivative
+ */
+ maxMin = ellipse_y*ellipse_y*ellipse_y * acc->h2mw2 -
+ acc->h2 * scan_y * (3 * ellipse_y*ellipse_y - 2*acc->h2);
+ if ((left && maxMin > 0) || (!left && maxMin < 0)) {
+ if (ellipse_y == 0)
+ return def->w + left ? -def->l : def->l;
+ x = (acc->h2 * scan_y - ellipse_y * acc->h2mw2) *
+ sqrt (acc->h2 - ellipse_y * ellipse_y) /
+ (def->h * def->w * ellipse_y);
+ return x;
+ }
+ }
+ }
+ if (left) {
+ if (acc->left.valid && boundedLe (scan_y, bound->left)) {
+ x = intersectLine (scan_y, acc->left);
+ } else {
+ if (acc->right.valid)
+ x = intersectLine (scan_y, acc->right);
+ else
+ x = def->w - def->l;
+ }
+ } else {
+ if (acc->right.valid && boundedLe (scan_y, bound->right)) {
+ x = intersectLine (scan_y, acc->right);
+ } else {
+ if (acc->left.valid)
+ x = intersectLine (scan_y, acc->left);
+ else
+ x = def->w - def->l;
+ }
+ }
+ return x;
+}
+
+/*
+ * generate the set of spans with
+ * the given y coordinate
+ */
+
+static void
+arcSpan (y, lx, lw, rx, rw, def, bounds, acc, mask)
+ int y;
+ int lx;
+ int lw;
+ int rx;
+ int rw;
+ struct arc_def *def;
+ struct arc_bound *bounds;
+ struct accelerators *acc;
+ int mask;
+{
+ int linx, loutx, rinx, routx;
+ double x, altx;
+
+ if (boundedLe (y, bounds->inneri)) {
+ linx = -(lx + lw);
+ rinx = rx;
+ } else {
+ /*
+ * intersection with left face
+ */
+ x = hookX (y + acc->fromIntY, def, bounds, acc, 1);
+ if (acc->right.valid &&
+ boundedLe (y + acc->fromIntY, bounds->right))
+ {
+ altx = intersectLine (y + acc->fromIntY, acc->right);
+ if (altx < x)
+ x = altx;
+ }
+ linx = -ICEIL(acc->fromIntX - x);
+ rinx = ICEIL(acc->fromIntX + x);
+ }
+ if (boundedLe (y, bounds->outeri)) {
+ loutx = -lx;
+ routx = rx + rw;
+ } else {
+ /*
+ * intersection with right face
+ */
+ x = hookX (y + acc->fromIntY, def, bounds, acc, 0);
+ if (acc->left.valid &&
+ boundedLe (y + acc->fromIntY, bounds->left))
+ {
+ altx = x;
+ x = intersectLine (y + acc->fromIntY, acc->left);
+ if (x < altx)
+ x = altx;
+ }
+ loutx = -ICEIL(acc->fromIntX - x);
+ routx = ICEIL(acc->fromIntX + x);
+ }
+ if (routx > rinx) {
+ if (mask & 1)
+ newFinalSpan (acc->yorgu - y,
+ acc->xorg + rinx, acc->xorg + routx);
+ if (mask & 8)
+ newFinalSpan (acc->yorgl + y,
+ acc->xorg + rinx, acc->xorg + routx);
+ }
+ if (loutx > linx) {
+ if (mask & 2)
+ newFinalSpan (acc->yorgu - y,
+ acc->xorg - loutx, acc->xorg - linx);
+ if (mask & 4)
+ newFinalSpan (acc->yorgl + y,
+ acc->xorg - loutx, acc->xorg - linx);
+ }
+}
+
+static void
+arcSpan0 (lx, lw, rx, rw, def, bounds, acc, mask)
+ int lx;
+ int lw;
+ int rx;
+ int rw;
+ struct arc_def *def;
+ struct arc_bound *bounds;
+ struct accelerators *acc;
+ int mask;
+{
+ double x;
+
+ if (boundedLe (0, bounds->inneri) &&
+ acc->left.valid && boundedLe (0, bounds->left) &&
+ acc->left.b > 0)
+ {
+ x = def->w - def->l;
+ if (acc->left.b < x)
+ x = acc->left.b;
+ lw = ICEIL(acc->fromIntX - x) - lx;
+ rw += rx;
+ rx = ICEIL(acc->fromIntX + x);
+ rw -= rx;
+ }
+ arcSpan (0, lx, lw, rx, rw, def, bounds, acc, mask);
+}
+
+static void
+tailSpan (y, lw, rw, def, bounds, acc, mask)
+ int y;
+ int lw;
+ int rw;
+ struct arc_def *def;
+ struct arc_bound *bounds;
+ struct accelerators *acc;
+ int mask;
+{
+ double yy, xalt, x, lx, rx;
+ int n;
+
+ if (boundedLe(y, bounds->outeri))
+ arcSpan (y, 0, lw, -rw, rw, def, bounds, acc, mask);
+ else if (def->w != def->h) {
+ yy = y + acc->fromIntY;
+ x = tailX(yy, def, bounds, acc);
+ if (yy == 0.0 && x == -rw - acc->fromIntX)
+ return;
+ if (acc->right.valid && boundedLe (yy, bounds->right)) {
+ rx = x;
+ lx = -x;
+ xalt = intersectLine (yy, acc->right);
+ if (xalt >= -rw - acc->fromIntX && xalt <= rx)
+ rx = xalt;
+ n = ICEIL(acc->fromIntX + lx);
+ if (lw > n) {
+ if (mask & 2)
+ newFinalSpan (acc->yorgu - y,
+ acc->xorg + n, acc->xorg + lw);
+ if (mask & 4)
+ newFinalSpan (acc->yorgl + y,
+ acc->xorg + n, acc->xorg + lw);
+ }
+ n = ICEIL(acc->fromIntX + rx);
+ if (n > -rw) {
+ if (mask & 1)
+ newFinalSpan (acc->yorgu - y,
+ acc->xorg - rw, acc->xorg + n);
+ if (mask & 8)
+ newFinalSpan (acc->yorgl + y,
+ acc->xorg - rw, acc->xorg + n);
+ }
+ }
+ arcSpan (y,
+ ICEIL(acc->fromIntX - x), 0,
+ ICEIL(acc->fromIntX + x), 0,
+ def, bounds, acc, mask);
+ }
+}
+
+/*
+ * create whole arcs out of pieces. This code is
+ * very bad.
+ */
+
+static struct finalSpan **finalSpans = NULL;
+static int finalMiny = 0, finalMaxy = -1;
+static int finalSize = 0;
+
+static int nspans = 0; /* total spans, not just y coords */
+
+struct finalSpan {
+ struct finalSpan *next;
+ int min, max; /* x values */
+};
+
+static struct finalSpan *freeFinalSpans, *tmpFinalSpan;
+
+# define allocFinalSpan() (freeFinalSpans ?\
+ ((tmpFinalSpan = freeFinalSpans), \
+ (freeFinalSpans = freeFinalSpans->next), \
+ (tmpFinalSpan->next = 0), \
+ tmpFinalSpan) : \
+ realAllocSpan ())
+
+# define SPAN_CHUNK_SIZE 128
+
+struct finalSpanChunk {
+ struct finalSpan data[SPAN_CHUNK_SIZE];
+ struct finalSpanChunk *next;
+};
+
+static struct finalSpanChunk *chunks;
+
+struct finalSpan *
+realAllocSpan ()
+{
+ register struct finalSpanChunk *newChunk;
+ register struct finalSpan *span;
+ register int i;
+
+ newChunk = (struct finalSpanChunk *) xalloc (sizeof (struct finalSpanChunk));
+ if (!newChunk)
+ return (struct finalSpan *) NULL;
+ newChunk->next = chunks;
+ chunks = newChunk;
+ freeFinalSpans = span = newChunk->data + 1;
+ for (i = 1; i < SPAN_CHUNK_SIZE-1; i++) {
+ span->next = span+1;
+ span++;
+ }
+ span->next = 0;
+ span = newChunk->data;
+ span->next = 0;
+ return span;
+}
+
+static void
+disposeFinalSpans ()
+{
+ struct finalSpanChunk *chunk, *next;
+
+ for (chunk = chunks; chunk; chunk = next) {
+ next = chunk->next;
+ xfree (chunk);
+ }
+ chunks = 0;
+ freeFinalSpans = 0;
+ xfree(finalSpans);
+ finalSpans = 0;
+}
+
+static void
+fillSpans (pDrawable, pGC)
+ DrawablePtr pDrawable;
+ GCPtr pGC;
+{
+ register struct finalSpan *span;
+ register DDXPointPtr xSpan;
+ register int *xWidth;
+ register int i;
+ register struct finalSpan **f;
+ register int spany;
+ DDXPointPtr xSpans;
+ int *xWidths;
+
+ if (nspans == 0)
+ return;
+ xSpan = xSpans = (DDXPointPtr) xalloc (nspans * sizeof (DDXPointRec));
+ xWidth = xWidths = (int *) xalloc (nspans * sizeof (int));
+ if (xSpans && xWidths)
+ {
+ i = 0;
+ f = finalSpans;
+ for (spany = finalMiny; spany <= finalMaxy; spany++, f++) {
+ for (span = *f; span; span=span->next) {
+ if (span->max <= span->min)
+ continue;
+ xSpan->x = span->min;
+ xSpan->y = spany;
+ ++xSpan;
+ *xWidth++ = span->max - span->min;
+ ++i;
+ }
+ }
+ (*pGC->ops->FillSpans) (pDrawable, pGC, i, xSpans, xWidths, TRUE);
+ }
+ disposeFinalSpans ();
+ xfree (xSpans);
+ xfree (xWidths);
+ finalMiny = 0;
+ finalMaxy = -1;
+ finalSize = 0;
+ nspans = 0;
+}
+
+# define SPAN_REALLOC 100
+
+# define findSpan(y) ((finalMiny <= (y) && (y) <= finalMaxy) ? \
+ &finalSpans[(y) - finalMiny] : \
+ realFindSpan (y))
+
+static struct finalSpan **
+realFindSpan (y)
+ int y;
+{
+ struct finalSpan **newSpans;
+ int newSize, newMiny, newMaxy;
+ int change;
+ int i;
+
+ if (y < finalMiny || y > finalMaxy) {
+ if (!finalSize) {
+ finalMiny = y;
+ finalMaxy = y - 1;
+ }
+ if (y < finalMiny)
+ change = finalMiny - y;
+ else
+ change = y - finalMaxy;
+ if (change >= SPAN_REALLOC)
+ change += SPAN_REALLOC;
+ else
+ change = SPAN_REALLOC;
+ newSize = finalSize + change;
+ newSpans = (struct finalSpan **) xalloc
+ (newSize * sizeof (struct finalSpan *));
+ if (!newSpans)
+ return (struct finalSpan **)NULL;
+ newMiny = finalMiny;
+ newMaxy = finalMaxy;
+ if (y < finalMiny)
+ newMiny = finalMiny - change;
+ else
+ newMaxy = finalMaxy + change;
+ if (finalSpans) {
+ memmove(((char *) newSpans) + (finalMiny-newMiny) * sizeof (struct finalSpan *),
+ (char *) finalSpans,
+ finalSize * sizeof (struct finalSpan *));
+ xfree (finalSpans);
+ }
+ if ((i = finalMiny - newMiny) > 0)
+ bzero ((char *)newSpans, i * sizeof (struct finalSpan *));
+ if ((i = newMaxy - finalMaxy) > 0)
+ bzero ((char *)(newSpans + newSize - i),
+ i * sizeof (struct finalSpan *));
+ finalSpans = newSpans;
+ finalMaxy = newMaxy;
+ finalMiny = newMiny;
+ finalSize = newSize;
+ }
+ return &finalSpans[y - finalMiny];
+}
+
+static void
+newFinalSpan (y, xmin, xmax)
+ int y;
+ register int xmin, xmax;
+{
+ register struct finalSpan *x;
+ register struct finalSpan **f;
+ struct finalSpan *oldx;
+ struct finalSpan *prev;
+
+ f = findSpan (y);
+ if (!f)
+ return;
+ oldx = 0;
+ for (;;) {
+ prev = 0;
+ for (x = *f; x; x=x->next) {
+ if (x == oldx) {
+ prev = x;
+ continue;
+ }
+ if (x->min <= xmax && xmin <= x->max) {
+ if (oldx) {
+ oldx->min = min (x->min, xmin);
+ oldx->max = max (x->max, xmax);
+ if (prev)
+ prev->next = x->next;
+ else
+ *f = x->next;
+ --nspans;
+ } else {
+ x->min = min (x->min, xmin);
+ x->max = max (x->max, xmax);
+ oldx = x;
+ }
+ xmin = oldx->min;
+ xmax = oldx->max;
+ break;
+ }
+ prev = x;
+ }
+ if (!x)
+ break;
+ }
+ if (!oldx) {
+ x = allocFinalSpan ();
+ if (x)
+ {
+ x->min = xmin;
+ x->max = xmax;
+ x->next = *f;
+ *f = x;
+ ++nspans;
+ }
+ }
+}
+
+static void
+mirrorSppPoint (quadrant, sppPoint)
+ int quadrant;
+ SppPointPtr sppPoint;
+{
+ switch (quadrant) {
+ case 0:
+ break;
+ case 1:
+ sppPoint->x = -sppPoint->x;
+ break;
+ case 2:
+ sppPoint->x = -sppPoint->x;
+ sppPoint->y = -sppPoint->y;
+ break;
+ case 3:
+ sppPoint->y = -sppPoint->y;
+ break;
+ }
+ /*
+ * and translate to X coordinate system
+ */
+ sppPoint->y = -sppPoint->y;
+}
+
+/*
+ * split an arc into pieces which are scan-converted
+ * in the first-quadrant and mirrored into position.
+ * This is necessary as the scan-conversion code can
+ * only deal with arcs completely contained in the
+ * first quadrant.
+ */
+
+static void
+drawArc (tarc, l, a0, a1, right, left)
+ xArc *tarc;
+ int l, a0, a1;
+ miArcFacePtr right, left; /* save end line points */
+{
+ struct arc_def def;
+ struct accelerators acc;
+ int startq, endq, curq;
+ int rightq, leftq, righta, lefta;
+ miArcFacePtr passRight, passLeft;
+ int q0, q1, mask;
+ struct band {
+ int a0, a1;
+ int mask;
+ } band[5], sweep[20];
+ int bandno, sweepno;
+ int i, j;
+ int flipRight = 0, flipLeft = 0;
+ int copyEnd = 0;
+ miArcSpanData *spdata;
+ Bool mustFree;
+
+ spdata = miComputeWideEllipse(l, tarc, &mustFree);
+ if (!spdata)
+ return;
+
+ if (a1 < a0)
+ a1 += 360 * 64;
+ startq = a0 / (90 * 64);
+ if (a0 == a1)
+ endq = startq;
+ else
+ endq = (a1-1) / (90 * 64);
+ bandno = 0;
+ curq = startq;
+ rightq = -1;
+ for (;;) {
+ switch (curq) {
+ case 0:
+ if (a0 > 90 * 64)
+ q0 = 0;
+ else
+ q0 = a0;
+ if (a1 < 360 * 64)
+ q1 = min (a1, 90 * 64);
+ else
+ q1 = 90 * 64;
+ if (curq == startq && a0 == q0 && rightq < 0) {
+ righta = q0;
+ rightq = curq;
+ }
+ if (curq == endq && a1 == q1) {
+ lefta = q1;
+ leftq = curq;
+ }
+ break;
+ case 1:
+ if (a1 < 90 * 64)
+ q0 = 0;
+ else
+ q0 = 180 * 64 - min (a1, 180 * 64);
+ if (a0 > 180 * 64)
+ q1 = 90 * 64;
+ else
+ q1 = 180 * 64 - max (a0, 90 * 64);
+ if (curq == startq && 180 * 64 - a0 == q1) {
+ righta = q1;
+ rightq = curq;
+ }
+ if (curq == endq && 180 * 64 - a1 == q0) {
+ lefta = q0;
+ leftq = curq;
+ }
+ break;
+ case 2:
+ if (a0 > 270 * 64)
+ q0 = 0;
+ else
+ q0 = max (a0, 180 * 64) - 180 * 64;
+ if (a1 < 180 * 64)
+ q1 = 90 * 64;
+ else
+ q1 = min (a1, 270 * 64) - 180 * 64;
+ if (curq == startq && a0 - 180*64 == q0) {
+ righta = q0;
+ rightq = curq;
+ }
+ if (curq == endq && a1 - 180 * 64 == q1) {
+ lefta = q1;
+ leftq = curq;
+ }
+ break;
+ case 3:
+ if (a1 < 270 * 64)
+ q0 = 0;
+ else
+ q0 = 360 * 64 - min (a1, 360 * 64);
+ q1 = 360 * 64 - max (a0, 270 * 64);
+ if (curq == startq && 360 * 64 - a0 == q1) {
+ righta = q1;
+ rightq = curq;
+ }
+ if (curq == endq && 360 * 64 - a1 == q0) {
+ lefta = q0;
+ leftq = curq;
+ }
+ break;
+ }
+ band[bandno].a0 = q0;
+ band[bandno].a1 = q1;
+ band[bandno].mask = 1 << curq;
+ bandno++;
+ if (curq == endq)
+ break;
+ curq++;
+ if (curq == 4) {
+ a0 = 0;
+ a1 -= 360 * 64;
+ curq = 0;
+ endq -= 4;
+ }
+ }
+ sweepno = 0;
+ for (;;) {
+ q0 = 90 * 64;
+ mask = 0;
+ /*
+ * find left-most point
+ */
+ for (i = 0; i < bandno; i++)
+ if (band[i].a0 <= q0) {
+ q0 = band[i].a0;
+ q1 = band[i].a1;
+ mask = band[i].mask;
+ }
+ if (!mask)
+ break;
+ /*
+ * locate next point of change
+ */
+ for (i = 0; i < bandno; i++)
+ if (!(mask & band[i].mask)) {
+ if (band[i].a0 == q0) {
+ if (band[i].a1 < q1)
+ q1 = band[i].a1;
+ mask |= band[i].mask;
+ } else if (band[i].a0 < q1)
+ q1 = band[i].a0;
+ }
+ /*
+ * create a new sweep
+ */
+ sweep[sweepno].a0 = q0;
+ sweep[sweepno].a1 = q1;
+ sweep[sweepno].mask = mask;
+ sweepno++;
+ /*
+ * subtract the sweep from the affected bands
+ */
+ for (i = 0; i < bandno; i++)
+ if (band[i].a0 == q0) {
+ band[i].a0 = q1;
+ /*
+ * check if this band is empty
+ */
+ if (band[i].a0 == band[i].a1)
+ band[i].a1 = band[i].a0 = 90 * 64 + 1;
+ }
+ }
+ computeAcc (tarc, l, &def, &acc);
+ for (j = 0; j < sweepno; j++) {
+ mask = sweep[j].mask;
+ passRight = passLeft = 0;
+ if (mask & (1 << rightq)) {
+ if (sweep[j].a0 == righta)
+ passRight = right;
+ else if (sweep[j].a1 == righta) {
+ passLeft = right;
+ flipRight = 1;
+ }
+ }
+ if (mask & (1 << leftq)) {
+ if (sweep[j].a1 == lefta)
+ {
+ if (passLeft)
+ copyEnd = 1;
+ passLeft = left;
+ }
+ else if (sweep[j].a0 == lefta) {
+ if (passRight)
+ copyEnd = 1;
+ passRight = left;
+ flipLeft = 1;
+ }
+ }
+ drawQuadrant (&def, &acc, sweep[j].a0, sweep[j].a1, mask,
+ passRight, passLeft, spdata);
+ }
+ /*
+ * when copyEnd is set, both ends of the arc were computed
+ * at the same time; drawQuadrant only takes one end though,
+ * so the left end will be the only one holding the data. Copy
+ * it from there.
+ */
+ if (copyEnd)
+ *right = *left;
+ /*
+ * mirror the coordinates generated for the
+ * faces of the arc
+ */
+ if (right) {
+ mirrorSppPoint (rightq, &right->clock);
+ mirrorSppPoint (rightq, &right->center);
+ mirrorSppPoint (rightq, &right->counterClock);
+ if (flipRight) {
+ SppPointRec temp;
+
+ temp = right->clock;
+ right->clock = right->counterClock;
+ right->counterClock = temp;
+ }
+ }
+ if (left) {
+ mirrorSppPoint (leftq, &left->counterClock);
+ mirrorSppPoint (leftq, &left->center);
+ mirrorSppPoint (leftq, &left->clock);
+ if (flipLeft) {
+ SppPointRec temp;
+
+ temp = left->clock;
+ left->clock = left->counterClock;
+ left->counterClock = temp;
+ }
+ }
+ if (mustFree)
+ xfree(spdata);
+}
+
+static void
+drawQuadrant (def, acc, a0, a1, mask, right, left, spdata)
+ struct arc_def *def;
+ struct accelerators *acc;
+ int a0, a1;
+ int mask;
+ miArcFacePtr right, left;
+ miArcSpanData *spdata;
+{
+ struct arc_bound bound;
+ double yy, x, xalt;
+ int y, miny, maxy;
+ int n;
+ miArcSpan *span;
+
+ def->a0 = ((double) a0) / 64.0;
+ def->a1 = ((double) a1) / 64.0;
+ computeBound (def, &bound, acc, right, left);
+ yy = bound.inner.min;
+ if (bound.outer.min < yy)
+ yy = bound.outer.min;
+ miny = ICEIL(yy - acc->fromIntY);
+ yy = bound.inner.max;
+ if (bound.outer.max > yy)
+ yy = bound.outer.max;
+ maxy = floor(yy - acc->fromIntY);
+ y = spdata->k;
+ span = spdata->spans;
+ if (spdata->top)
+ {
+ if (a1 == 90 * 64 && (mask & 1))
+ newFinalSpan (acc->yorgu - y - 1, acc->xorg, acc->xorg + 1);
+ span++;
+ }
+ for (n = spdata->count1; --n >= 0; )
+ {
+ if (y < miny)
+ return;
+ if (y <= maxy) {
+ arcSpan (y,
+ span->lx, -span->lx, 0, span->lx + span->lw,
+ def, &bound, acc, mask);
+ if (span->rw + span->rx)
+ tailSpan (y, -span->rw, -span->rx, def, &bound, acc, mask);
+ }
+ y--;
+ span++;
+ }
+ if (y < miny)
+ return;
+ if (spdata->hole)
+ {
+ if (y <= maxy)
+ arcSpan (y, 0, 0, 0, 1, def, &bound, acc, mask & 0xc);
+ }
+ for (n = spdata->count2; --n >= 0; )
+ {
+ if (y < miny)
+ return;
+ if (y <= maxy)
+ arcSpan (y, span->lx, span->lw, span->rx, span->rw,
+ def, &bound, acc, mask);
+ y--;
+ span++;
+ }
+ if (spdata->bot && miny <= y && y <= maxy)
+ {
+ n = mask;
+ if (y == miny)
+ n &= 0xc;
+ if (span->rw <= 0) {
+ arcSpan0 (span->lx, -span->lx, 0, span->lx + span->lw,
+ def, &bound, acc, n);
+ if (span->rw + span->rx)
+ tailSpan (y, -span->rw, -span->rx, def, &bound, acc, n);
+ }
+ else
+ arcSpan0 (span->lx, span->lw, span->rx, span->rw,
+ def, &bound, acc, n);
+ y--;
+ }
+ while (y >= miny) {
+ yy = y + acc->fromIntY;
+ if (def->w == def->h) {
+ xalt = def->w - def->l;
+ x = -sqrt(xalt * xalt - yy * yy);
+ } else {
+ x = tailX(yy, def, &bound, acc);
+ if (acc->left.valid && boundedLe (yy, bound.left)) {
+ xalt = intersectLine (yy, acc->left);
+ if (xalt < x)
+ x = xalt;
+ }
+ if (acc->right.valid && boundedLe (yy, bound.right)) {
+ xalt = intersectLine (yy, acc->right);
+ if (xalt < x)
+ x = xalt;
+ }
+ }
+ arcSpan (y,
+ ICEIL(acc->fromIntX - x), 0,
+ ICEIL(acc->fromIntX + x), 0,
+ def, &bound, acc, mask);
+ y--;
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-22 13:37:58 +0000