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tkCanvArc.c

/* 
 * tkCanvArc.c --
 *
 *    This file implements arc items for canvas widgets.
 *
 * Copyright (c) 1992-1994 The Regents of the University of California.
 * Copyright (c) 1994-1995 Sun Microsystems, Inc.
 *
 * See the file "license.terms" for information on usage and redistribution
 * of this file, and for a DISCLAIMER OF ALL WARRANTIES.
 *
 * RCS: @(#) $Id: tkCanvArc.c,v 1.3 1998/09/14 18:23:04 stanton Exp $
 */

#include <stdio.h>
#include "tkPort.h"
#include "tkInt.h"

/*
 * The structure below defines the record for each arc item.
 */

typedef struct ArcItem  {
    Tk_Item header;           /* Generic stuff that's the same for all
                         * types.  MUST BE FIRST IN STRUCTURE. */
    double bbox[4];           /* Coordinates (x1, y1, x2, y2) of bounding
                         * box for oval of which arc is a piece. */
    double start;       /* Angle at which arc begins, in degrees
                         * between 0 and 360. */
    double extent;            /* Extent of arc (angular distance from
                         * start to end of arc) in degrees between
                         * -360 and 360. */
    double *outlinePtr;       /* Points to (x,y) coordinates for points
                         * that define one or two closed polygons
                         * representing the portion of the outline
                         * that isn't part of the arc (the V-shape
                         * for a pie slice or a line-like segment
                         * for a chord).  Malloc'ed. */
    int numOutlinePoints;     /* Number of points at outlinePtr.  Zero
                         * means no space allocated. */
    int width;                /* Width of outline (in pixels). */
    XColor *outlineColor;     /* Color for outline.  NULL means don't
                         * draw outline. */
    XColor *fillColor;        /* Color for filling arc (used for drawing
                         * outline too when style is "arc").  NULL
                         * means don't fill arc. */
    Pixmap fillStipple;       /* Stipple bitmap for filling item. */
    Pixmap outlineStipple;    /* Stipple bitmap for outline. */
    Tk_Uid style;       /* How to draw arc: arc, chord, or pieslice. */
    GC outlineGC;       /* Graphics context for outline. */
    GC fillGC;                /* Graphics context for filling item. */
    double center1[2];        /* Coordinates of center of arc outline at
                         * start (see ComputeArcOutline). */
    double center2[2];        /* Coordinates of center of arc outline at
                         * start+extent (see ComputeArcOutline). */
} ArcItem;

/*
 * The definitions below define the sizes of the polygons used to
 * display outline information for various styles of arcs:
 */

#define CHORD_OUTLINE_PTS     7
#define PIE_OUTLINE1_PTS      6
#define PIE_OUTLINE2_PTS      7

/*
 * Information used for parsing configuration specs:
 */

static Tk_CustomOption tagsOption = {Tk_CanvasTagsParseProc,
    Tk_CanvasTagsPrintProc, (ClientData) NULL
};

static Tk_ConfigSpec configSpecs[] = {
    {TK_CONFIG_DOUBLE, "-extent", (char *) NULL, (char *) NULL,
      "90", Tk_Offset(ArcItem, extent), TK_CONFIG_DONT_SET_DEFAULT},
    {TK_CONFIG_COLOR, "-fill", (char *) NULL, (char *) NULL,
      (char *) NULL, Tk_Offset(ArcItem, fillColor), TK_CONFIG_NULL_OK},
    {TK_CONFIG_COLOR, "-outline", (char *) NULL, (char *) NULL,
      "black", Tk_Offset(ArcItem, outlineColor), TK_CONFIG_NULL_OK},
    {TK_CONFIG_BITMAP, "-outlinestipple", (char *) NULL, (char *) NULL,
      (char *) NULL, Tk_Offset(ArcItem, outlineStipple), TK_CONFIG_NULL_OK},
    {TK_CONFIG_DOUBLE, "-start", (char *) NULL, (char *) NULL,
      "0", Tk_Offset(ArcItem, start), TK_CONFIG_DONT_SET_DEFAULT},
    {TK_CONFIG_BITMAP, "-stipple", (char *) NULL, (char *) NULL,
      (char *) NULL, Tk_Offset(ArcItem, fillStipple), TK_CONFIG_NULL_OK},
    {TK_CONFIG_UID, "-style", (char *) NULL, (char *) NULL,
      "pieslice", Tk_Offset(ArcItem, style), TK_CONFIG_DONT_SET_DEFAULT},
    {TK_CONFIG_CUSTOM, "-tags", (char *) NULL, (char *) NULL,
      (char *) NULL, 0, TK_CONFIG_NULL_OK, &tagsOption},
    {TK_CONFIG_PIXELS, "-width", (char *) NULL, (char *) NULL,
      "1", Tk_Offset(ArcItem, width), TK_CONFIG_DONT_SET_DEFAULT},
    {TK_CONFIG_END, (char *) NULL, (char *) NULL, (char *) NULL,
      (char *) NULL, 0, 0}
};

/*
 * Prototypes for procedures defined in this file:
 */

static void       ComputeArcBbox _ANSI_ARGS_((Tk_Canvas canvas,
                      ArcItem *arcPtr));
static int        ConfigureArc _ANSI_ARGS_((Tcl_Interp *interp,
                      Tk_Canvas canvas, Tk_Item *itemPtr, int argc,
                      char **argv, int flags));
static int        CreateArc _ANSI_ARGS_((Tcl_Interp *interp,
                      Tk_Canvas canvas, struct Tk_Item *itemPtr,
                      int argc, char **argv));
static void       DeleteArc _ANSI_ARGS_((Tk_Canvas canvas,
                      Tk_Item *itemPtr, Display *display));
static void       DisplayArc _ANSI_ARGS_((Tk_Canvas canvas,
                      Tk_Item *itemPtr, Display *display, Drawable dst,
                      int x, int y, int width, int height));
static int        ArcCoords _ANSI_ARGS_((Tcl_Interp *interp,
                      Tk_Canvas canvas, Tk_Item *itemPtr, int argc,
                      char **argv));
static int        ArcToArea _ANSI_ARGS_((Tk_Canvas canvas,
                      Tk_Item *itemPtr, double *rectPtr));
static double           ArcToPoint _ANSI_ARGS_((Tk_Canvas canvas,
                      Tk_Item *itemPtr, double *coordPtr));
static int        ArcToPostscript _ANSI_ARGS_((Tcl_Interp *interp,
                      Tk_Canvas canvas, Tk_Item *itemPtr, int prepass));
static void       ScaleArc _ANSI_ARGS_((Tk_Canvas canvas,
                      Tk_Item *itemPtr, double originX, double originY,
                      double scaleX, double scaleY));
static void       TranslateArc _ANSI_ARGS_((Tk_Canvas canvas,
                      Tk_Item *itemPtr, double deltaX, double deltaY));
static int        AngleInRange _ANSI_ARGS_((double x, double y,
                      double start, double extent));
static void       ComputeArcOutline _ANSI_ARGS_((ArcItem *arcPtr));
static int        HorizLineToArc _ANSI_ARGS_((double x1, double x2,
                      double y, double rx, double ry,
                      double start, double extent));
static int        VertLineToArc _ANSI_ARGS_((double x, double y1,
                      double y2, double rx, double ry,
                      double start, double extent));

/*
 * The structures below defines the arc item types by means of procedures
 * that can be invoked by generic item code.
 */

Tk_ItemType tkArcType = {
    "arc",                    /* name */
    sizeof(ArcItem),                /* itemSize */
    CreateArc,                      /* createProc */
    configSpecs,              /* configSpecs */
    ConfigureArc,             /* configureProc */
    ArcCoords,                      /* coordProc */
    DeleteArc,                      /* deleteProc */
    DisplayArc,                     /* displayProc */
    0,                              /* alwaysRedraw */
    ArcToPoint,                     /* pointProc */
    ArcToArea,                      /* areaProc */
    ArcToPostscript,                /* postscriptProc */
    ScaleArc,                       /* scaleProc */
    TranslateArc,             /* translateProc */
    (Tk_ItemIndexProc *) NULL,            /* indexProc */
    (Tk_ItemCursorProc *) NULL,           /* icursorProc */
    (Tk_ItemSelectionProc *) NULL,  /* selectionProc */
    (Tk_ItemInsertProc *) NULL,           /* insertProc */
    (Tk_ItemDCharsProc *) NULL,           /* dTextProc */
    (Tk_ItemType *) NULL            /* nextPtr */
};

#ifndef PI
#    define PI 3.14159265358979323846
#endif

/*
 * The uid's below comprise the legal values for the "-style"
 * option for arcs.
 */

static Tk_Uid arcUid =  NULL;
static Tk_Uid chordUid =  NULL;
static Tk_Uid pieSliceUid = NULL;

/*
 *--------------------------------------------------------------
 *
 * CreateArc --
 *
 *    This procedure is invoked to create a new arc item in
 *    a canvas.
 *
 * Results:
 *    A standard Tcl return value.  If an error occurred in
 *    creating the item, then an error message is left in
 *    interp->result;  in this case itemPtr is
 *    left uninitialized, so it can be safely freed by the
 *    caller.
 *
 * Side effects:
 *    A new arc item is created.
 *
 *--------------------------------------------------------------
 */

static int
CreateArc(interp, canvas, itemPtr, argc, argv)
    Tcl_Interp *interp;             /* Interpreter for error reporting. */
    Tk_Canvas canvas;               /* Canvas to hold new item. */
    Tk_Item *itemPtr;               /* Record to hold new item;  header
                               * has been initialized by caller. */
    int argc;                       /* Number of arguments in argv. */
    char **argv;              /* Arguments describing arc. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;

    if (argc < 4) {
      Tcl_AppendResult(interp, "wrong # args: should be \"",
            Tk_PathName(Tk_CanvasTkwin(canvas)), " create ",
            itemPtr->typePtr->name, " x1 y1 x2 y2 ?options?\"",
            (char *) NULL);
      return TCL_ERROR;
    }

    /*
     * Carry out once-only initialization.
     */

    if (arcUid == NULL) {
      arcUid = Tk_GetUid("arc");
      chordUid = Tk_GetUid("chord");
      pieSliceUid = Tk_GetUid("pieslice");
    }

    /*
     * Carry out initialization that is needed in order to clean
     * up after errors during the the remainder of this procedure.
     */

    arcPtr->start = 0;
    arcPtr->extent = 90;
    arcPtr->outlinePtr = NULL;
    arcPtr->numOutlinePoints = 0;
    arcPtr->width = 1;
    arcPtr->outlineColor = NULL;
    arcPtr->fillColor = NULL;
    arcPtr->fillStipple = None;
    arcPtr->outlineStipple = None;
    arcPtr->style = pieSliceUid;
    arcPtr->outlineGC = None;
    arcPtr->fillGC = None;

    /*
     * Process the arguments to fill in the item record.
     */

    if ((Tk_CanvasGetCoord(interp, canvas, argv[0], &arcPtr->bbox[0]) != TCL_OK)
          || (Tk_CanvasGetCoord(interp, canvas, argv[1],
            &arcPtr->bbox[1]) != TCL_OK)
          || (Tk_CanvasGetCoord(interp, canvas, argv[2],
                &arcPtr->bbox[2]) != TCL_OK)
          || (Tk_CanvasGetCoord(interp, canvas, argv[3],
                &arcPtr->bbox[3]) != TCL_OK)) {
      return TCL_ERROR;
    }

    if (ConfigureArc(interp, canvas, itemPtr, argc-4, argv+4, 0) != TCL_OK) {
      DeleteArc(canvas, itemPtr, Tk_Display(Tk_CanvasTkwin(canvas)));
      return TCL_ERROR;
    }
    return TCL_OK;
}

/*
 *--------------------------------------------------------------
 *
 * ArcCoords --
 *
 *    This procedure is invoked to process the "coords" widget
 *    command on arcs.  See the user documentation for details
 *    on what it does.
 *
 * Results:
 *    Returns TCL_OK or TCL_ERROR, and sets interp->result.
 *
 * Side effects:
 *    The coordinates for the given item may be changed.
 *
 *--------------------------------------------------------------
 */

static int
ArcCoords(interp, canvas, itemPtr, argc, argv)
    Tcl_Interp *interp;             /* Used for error reporting. */
    Tk_Canvas canvas;               /* Canvas containing item. */
    Tk_Item *itemPtr;               /* Item whose coordinates are to be
                               * read or modified. */
    int argc;                       /* Number of coordinates supplied in
                               * argv. */
    char **argv;              /* Array of coordinates: x1, y1,
                               * x2, y2, ... */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;
    char c0[TCL_DOUBLE_SPACE], c1[TCL_DOUBLE_SPACE];
    char c2[TCL_DOUBLE_SPACE], c3[TCL_DOUBLE_SPACE];

    if (argc == 0) {
      Tcl_PrintDouble(interp, arcPtr->bbox[0], c0);
      Tcl_PrintDouble(interp, arcPtr->bbox[1], c1);
      Tcl_PrintDouble(interp, arcPtr->bbox[2], c2);
      Tcl_PrintDouble(interp, arcPtr->bbox[3], c3);
      Tcl_AppendResult(interp, c0, " ", c1, " ", c2, " ", c3,
            (char *) NULL);
    } else if (argc == 4) {
      if ((Tk_CanvasGetCoord(interp, canvas, argv[0],
                &arcPtr->bbox[0]) != TCL_OK)
            || (Tk_CanvasGetCoord(interp, canvas, argv[1],
                &arcPtr->bbox[1]) != TCL_OK)
            || (Tk_CanvasGetCoord(interp, canvas, argv[2],
                  &arcPtr->bbox[2]) != TCL_OK)
            || (Tk_CanvasGetCoord(interp, canvas, argv[3],
                  &arcPtr->bbox[3]) != TCL_OK)) {
          return TCL_ERROR;
      }
      ComputeArcBbox(canvas, arcPtr);
    } else {
      sprintf(interp->result,
            "wrong # coordinates: expected 0 or 4, got %d",
            argc);
      return TCL_ERROR;
    }
    return TCL_OK;
}

/*
 *--------------------------------------------------------------
 *
 * ConfigureArc --
 *
 *    This procedure is invoked to configure various aspects
 *    of a arc item, such as its outline and fill colors.
 *
 * Results:
 *    A standard Tcl result code.  If an error occurs, then
 *    an error message is left in interp->result.
 *
 * Side effects:
 *    Configuration information, such as colors and stipple
 *    patterns, may be set for itemPtr.
 *
 *--------------------------------------------------------------
 */

static int
ConfigureArc(interp, canvas, itemPtr, argc, argv, flags)
    Tcl_Interp *interp;       /* Used for error reporting. */
    Tk_Canvas canvas;         /* Canvas containing itemPtr. */
    Tk_Item *itemPtr;         /* Arc item to reconfigure. */
    int argc;                 /* Number of elements in argv.  */
    char **argv;        /* Arguments describing things to configure. */
    int flags;                /* Flags to pass to Tk_ConfigureWidget. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;
    XGCValues gcValues;
    GC newGC;
    unsigned long mask;
    int i;
    Tk_Window tkwin;

    tkwin = Tk_CanvasTkwin(canvas);
    if (Tk_ConfigureWidget(interp, tkwin, configSpecs, argc, argv,
          (char *) arcPtr, flags) != TCL_OK) {
      return TCL_ERROR;
    }

    /*
     * A few of the options require additional processing, such as
     * style and graphics contexts.
     */

    i = (int) (arcPtr->start/360.0);
    arcPtr->start -= i*360.0;
    if (arcPtr->start < 0) {
      arcPtr->start += 360.0;
    }
    i = (int) (arcPtr->extent/360.0);
    arcPtr->extent -= i*360.0;

    if ((arcPtr->style != arcUid) && (arcPtr->style != chordUid)
          && (arcPtr->style != pieSliceUid)) {
      Tcl_AppendResult(interp, "bad -style option \"",
            arcPtr->style, "\": must be arc, chord, or pieslice",
            (char *) NULL);
      arcPtr->style = pieSliceUid;
      return TCL_ERROR;
    }

    if (arcPtr->width < 0) {
      arcPtr->width = 1;
    }
    if (arcPtr->outlineColor == NULL) {
      newGC = None;
    } else {
      gcValues.foreground = arcPtr->outlineColor->pixel;
      gcValues.cap_style = CapButt;
      gcValues.line_width = arcPtr->width;
      mask = GCForeground|GCCapStyle|GCLineWidth;
      if (arcPtr->outlineStipple != None) {
          gcValues.stipple = arcPtr->outlineStipple;
          gcValues.fill_style = FillStippled;
          mask |= GCStipple|GCFillStyle;
      }
      newGC = Tk_GetGC(tkwin, mask, &gcValues);
    }
    if (arcPtr->outlineGC != None) {
      Tk_FreeGC(Tk_Display(tkwin), arcPtr->outlineGC);
    }
    arcPtr->outlineGC = newGC;

    if ((arcPtr->fillColor == NULL) || (arcPtr->style == arcUid)) {
      newGC = None;
    } else {
      gcValues.foreground = arcPtr->fillColor->pixel;
      if (arcPtr->style == chordUid) {
          gcValues.arc_mode = ArcChord;
      } else {
          gcValues.arc_mode = ArcPieSlice;
      }
      mask = GCForeground|GCArcMode;
      if (arcPtr->fillStipple != None) {
          gcValues.stipple = arcPtr->fillStipple;
          gcValues.fill_style = FillStippled;
          mask |= GCStipple|GCFillStyle;
      }
      newGC = Tk_GetGC(tkwin, mask, &gcValues);
    }
    if (arcPtr->fillGC != None) {
      Tk_FreeGC(Tk_Display(tkwin), arcPtr->fillGC);
    }
    arcPtr->fillGC = newGC;

    ComputeArcBbox(canvas, arcPtr);
    return TCL_OK;
}

/*
 *--------------------------------------------------------------
 *
 * DeleteArc --
 *
 *    This procedure is called to clean up the data structure
 *    associated with a arc item.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    Resources associated with itemPtr are released.
 *
 *--------------------------------------------------------------
 */

static void
DeleteArc(canvas, itemPtr, display)
    Tk_Canvas canvas;               /* Info about overall canvas. */
    Tk_Item *itemPtr;               /* Item that is being deleted. */
    Display *display;               /* Display containing window for
                               * canvas. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;

    if (arcPtr->numOutlinePoints != 0) {
      ckfree((char *) arcPtr->outlinePtr);
    }
    if (arcPtr->outlineColor != NULL) {
      Tk_FreeColor(arcPtr->outlineColor);
    }
    if (arcPtr->fillColor != NULL) {
      Tk_FreeColor(arcPtr->fillColor);
    }
    if (arcPtr->fillStipple != None) {
      Tk_FreeBitmap(display, arcPtr->fillStipple);
    }
    if (arcPtr->outlineStipple != None) {
      Tk_FreeBitmap(display, arcPtr->outlineStipple);
    }
    if (arcPtr->outlineGC != None) {
      Tk_FreeGC(display, arcPtr->outlineGC);
    }
    if (arcPtr->fillGC != None) {
      Tk_FreeGC(display, arcPtr->fillGC);
    }
}

/*
 *--------------------------------------------------------------
 *
 * ComputeArcBbox --
 *
 *    This procedure is invoked to compute the bounding box of
 *    all the pixels that may be drawn as part of an arc.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    The fields x1, y1, x2, and y2 are updated in the header
 *    for itemPtr.
 *
 *--------------------------------------------------------------
 */

      /* ARGSUSED */
static void
ComputeArcBbox(canvas, arcPtr)
    Tk_Canvas canvas;               /* Canvas that contains item. */
    ArcItem *arcPtr;                /* Item whose bbox is to be
                               * recomputed. */
{
    double tmp, center[2], point[2];

    /*
     * Make sure that the first coordinates are the lowest ones.
     */

    if (arcPtr->bbox[1] > arcPtr->bbox[3]) {
      double tmp;
      tmp = arcPtr->bbox[3];
      arcPtr->bbox[3] = arcPtr->bbox[1];
      arcPtr->bbox[1] = tmp;
    }
    if (arcPtr->bbox[0] > arcPtr->bbox[2]) {
      double tmp;
      tmp = arcPtr->bbox[2];
      arcPtr->bbox[2] = arcPtr->bbox[0];
      arcPtr->bbox[0] = tmp;
    }

    ComputeArcOutline(arcPtr);

    /*
     * To compute the bounding box, start with the the bbox formed
     * by the two endpoints of the arc.  Then add in the center of
     * the arc's oval (if relevant) and the 3-o'clock, 6-o'clock,
     * 9-o'clock, and 12-o'clock positions, if they are relevant.
     */

    arcPtr->header.x1 = arcPtr->header.x2 = (int) arcPtr->center1[0];
    arcPtr->header.y1 = arcPtr->header.y2 = (int) arcPtr->center1[1];
    TkIncludePoint((Tk_Item *) arcPtr, arcPtr->center2);
    center[0] = (arcPtr->bbox[0] + arcPtr->bbox[2])/2;
    center[1] = (arcPtr->bbox[1] + arcPtr->bbox[3])/2;
    if (arcPtr->style == pieSliceUid) {
      TkIncludePoint((Tk_Item *) arcPtr, center);
    }

    tmp = -arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      point[0] = arcPtr->bbox[2];
      point[1] = center[1];
      TkIncludePoint((Tk_Item *) arcPtr, point);
    }
    tmp = 90.0 - arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      point[0] = center[0];
      point[1] = arcPtr->bbox[1];
      TkIncludePoint((Tk_Item *) arcPtr, point);
    }
    tmp = 180.0 - arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      point[0] = arcPtr->bbox[0];
      point[1] = center[1];
      TkIncludePoint((Tk_Item *) arcPtr, point);
    }
    tmp = 270.0 - arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      point[0] = center[0];
      point[1] = arcPtr->bbox[3];
      TkIncludePoint((Tk_Item *) arcPtr, point);
    }

    /*
     * Lastly, expand by the width of the arc (if the arc's outline is
     * being drawn) and add one extra pixel just for safety.
     */

    if (arcPtr->outlineColor == NULL) {
      tmp = 1;
    } else {
      tmp = (arcPtr->width + 1)/2 + 1;
    }
    arcPtr->header.x1 -= (int) tmp;
    arcPtr->header.y1 -= (int) tmp;
    arcPtr->header.x2 += (int) tmp;
    arcPtr->header.y2 += (int) tmp;
}

/*
 *--------------------------------------------------------------
 *
 * DisplayArc --
 *
 *    This procedure is invoked to draw an arc item in a given
 *    drawable.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    ItemPtr is drawn in drawable using the transformation
 *    information in canvas.
 *
 *--------------------------------------------------------------
 */

static void
DisplayArc(canvas, itemPtr, display, drawable, x, y, width, height)
    Tk_Canvas canvas;               /* Canvas that contains item. */
    Tk_Item *itemPtr;               /* Item to be displayed. */
    Display *display;               /* Display on which to draw item. */
    Drawable drawable;              /* Pixmap or window in which to draw
                               * item. */
    int x, y, width, height;        /* Describes region of canvas that
                               * must be redisplayed (not used). */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;
    short x1, y1, x2, y2;
    int start, extent;

    /*
     * Compute the screen coordinates of the bounding box for the item,
     * plus integer values for the angles.
     */

    Tk_CanvasDrawableCoords(canvas, arcPtr->bbox[0], arcPtr->bbox[1],
          &x1, &y1);
    Tk_CanvasDrawableCoords(canvas, arcPtr->bbox[2], arcPtr->bbox[3],
          &x2, &y2);
    if (x2 <= x1) {
      x2 = x1+1;
    }
    if (y2 <= y1) {
      y2 = y1+1;
    }
    start = (int) ((64*arcPtr->start) + 0.5);
    extent = (int) ((64*arcPtr->extent) + 0.5);

    /*
     * Display filled arc first (if wanted), then outline.  If the extent
     * is zero then don't invoke XFillArc or XDrawArc, since this causes
     * some window servers to crash and should be a no-op anyway.
     */

    if ((arcPtr->fillGC != None) && (extent != 0)) {
      if (arcPtr->fillStipple != None) {
          Tk_CanvasSetStippleOrigin(canvas, arcPtr->fillGC);
      }
      XFillArc(display, drawable, arcPtr->fillGC, x1, y1, (unsigned) (x2-x1),
            (unsigned) (y2-y1), start, extent);
      if (arcPtr->fillStipple != None) {
          XSetTSOrigin(display, arcPtr->fillGC, 0, 0);
      }
    }
    if (arcPtr->outlineGC != None) {
      if (arcPtr->outlineStipple != None) {
          Tk_CanvasSetStippleOrigin(canvas, arcPtr->outlineGC);
      }
      if (extent != 0) {
          XDrawArc(display, drawable, arcPtr->outlineGC, x1, y1,
                (unsigned) (x2-x1), (unsigned) (y2-y1), start, extent);
      }

      /*
       * If the outline width is very thin, don't use polygons to draw
       * the linear parts of the outline (this often results in nothing
       * being displayed); just draw lines instead.
       */

      if (arcPtr->width <= 2) {
          Tk_CanvasDrawableCoords(canvas, arcPtr->center1[0],
                arcPtr->center1[1], &x1, &y1);
          Tk_CanvasDrawableCoords(canvas, arcPtr->center2[0],
                arcPtr->center2[1], &x2, &y2);

          if (arcPtr->style == chordUid) {
            XDrawLine(display, drawable, arcPtr->outlineGC,
                  x1, y1, x2, y2);
          } else if (arcPtr->style == pieSliceUid) {
            short cx, cy;

            Tk_CanvasDrawableCoords(canvas,
                  (arcPtr->bbox[0] + arcPtr->bbox[2])/2.0,
                  (arcPtr->bbox[1] + arcPtr->bbox[3])/2.0, &cx, &cy);
            XDrawLine(display, drawable, arcPtr->outlineGC,
                  cx, cy, x1, y1);
            XDrawLine(display, drawable, arcPtr->outlineGC,
                  cx, cy, x2, y2);
          }
      } else {
          if (arcPtr->style == chordUid) {
            TkFillPolygon(canvas, arcPtr->outlinePtr, CHORD_OUTLINE_PTS,
                  display, drawable, arcPtr->outlineGC, None);
          } else if (arcPtr->style == pieSliceUid) {
            TkFillPolygon(canvas, arcPtr->outlinePtr, PIE_OUTLINE1_PTS,
                  display, drawable, arcPtr->outlineGC, None);
            TkFillPolygon(canvas, arcPtr->outlinePtr + 2*PIE_OUTLINE1_PTS,
                  PIE_OUTLINE2_PTS, display, drawable, arcPtr->outlineGC,
                  None);
          }
      }
      if (arcPtr->outlineStipple != None) {
          XSetTSOrigin(display, arcPtr->outlineGC, 0, 0);
      }
    }
}

/*
 *--------------------------------------------------------------
 *
 * ArcToPoint --
 *
 *    Computes the distance from a given point to a given
 *    arc, in canvas units.
 *
 * Results:
 *    The return value is 0 if the point whose x and y coordinates
 *    are coordPtr[0] and coordPtr[1] is inside the arc.  If the
 *    point isn't inside the arc then the return value is the
 *    distance from the point to the arc.  If itemPtr is filled,
 *    then anywhere in the interior is considered "inside"; if
 *    itemPtr isn't filled, then "inside" means only the area
 *    occupied by the outline.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

      /* ARGSUSED */
static double
ArcToPoint(canvas, itemPtr, pointPtr)
    Tk_Canvas canvas;         /* Canvas containing item. */
    Tk_Item *itemPtr;         /* Item to check against point. */
    double *pointPtr;         /* Pointer to x and y coordinates. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;
    double vertex[2], pointAngle, diff, dist, newDist;
    double poly[8], polyDist, width, t1, t2;
    int filled, angleInRange;

    /*
     * See if the point is within the angular range of the arc.
     * Remember, X angles are backwards from the way we'd normally
     * think of them.  Also, compensate for any eccentricity of
     * the oval.
     */

    vertex[0] = (arcPtr->bbox[0] + arcPtr->bbox[2])/2.0;
    vertex[1] = (arcPtr->bbox[1] + arcPtr->bbox[3])/2.0;
    t1 = (pointPtr[1] - vertex[1])/(arcPtr->bbox[3] - arcPtr->bbox[1]);
    t2 = (pointPtr[0] - vertex[0])/(arcPtr->bbox[2] - arcPtr->bbox[0]);
    if ((t1 == 0.0) && (t2 == 0.0)) {
      pointAngle = 0;
    } else {
      pointAngle = -atan2(t1, t2)*180/PI;
    }
    diff = pointAngle - arcPtr->start;
    diff -= ((int) (diff/360.0) * 360.0);
    if (diff < 0) {
      diff += 360.0;
    }
    angleInRange = (diff <= arcPtr->extent) ||
          ((arcPtr->extent < 0) && ((diff - 360.0) >= arcPtr->extent));

    /*
     * Now perform different tests depending on what kind of arc
     * we're dealing with.
     */

    if (arcPtr->style == arcUid) {
      if (angleInRange) {
          return TkOvalToPoint(arcPtr->bbox, (double) arcPtr->width,
                0, pointPtr);
      }
      dist = hypot(pointPtr[0] - arcPtr->center1[0],
            pointPtr[1] - arcPtr->center1[1]);
      newDist = hypot(pointPtr[0] - arcPtr->center2[0],
            pointPtr[1] - arcPtr->center2[1]);
      if (newDist < dist) {
          return newDist;
      }
      return dist;
    }

    if ((arcPtr->fillGC != None) || (arcPtr->outlineGC == None)) {
      filled = 1;
    } else {
      filled = 0;
    }
    if (arcPtr->outlineGC == None) {
      width = 0.0;
    } else {
      width = arcPtr->width;
    }

    if (arcPtr->style == pieSliceUid) {
      if (width > 1.0) {
          dist = TkPolygonToPoint(arcPtr->outlinePtr, PIE_OUTLINE1_PTS,
                pointPtr);
          newDist = TkPolygonToPoint(arcPtr->outlinePtr + 2*PIE_OUTLINE1_PTS,
                  PIE_OUTLINE2_PTS, pointPtr);
      } else {
          dist = TkLineToPoint(vertex, arcPtr->center1, pointPtr);
          newDist = TkLineToPoint(vertex, arcPtr->center2, pointPtr);
      }
      if (newDist < dist) {
          dist = newDist;
      }
      if (angleInRange) {
          newDist = TkOvalToPoint(arcPtr->bbox, width, filled, pointPtr);
          if (newDist < dist) {
            dist = newDist;
          }
      }
      return dist;
    }

    /*
     * This is a chord-style arc.  We have to deal specially with the
     * triangular piece that represents the difference between a
     * chord-style arc and a pie-slice arc (for small angles this piece
     * is excluded here where it would be included for pie slices;
     * for large angles the piece is included here but would be
     * excluded for pie slices).
     */

    if (width > 1.0) {
      dist = TkPolygonToPoint(arcPtr->outlinePtr, CHORD_OUTLINE_PTS,
                pointPtr);
    } else {
      dist = TkLineToPoint(arcPtr->center1, arcPtr->center2, pointPtr);
    }
    poly[0] = poly[6] = vertex[0];
    poly[1] = poly[7] = vertex[1];
    poly[2] = arcPtr->center1[0];
    poly[3] = arcPtr->center1[1];
    poly[4] = arcPtr->center2[0];
    poly[5] = arcPtr->center2[1];
    polyDist = TkPolygonToPoint(poly, 4, pointPtr);
    if (angleInRange) {
      if ((arcPtr->extent < -180.0) || (arcPtr->extent > 180.0)
            || (polyDist > 0.0)) {
          newDist = TkOvalToPoint(arcPtr->bbox, width, filled, pointPtr);
          if (newDist < dist) {
            dist = newDist;
          }
      }
    } else {
      if ((arcPtr->extent < -180.0) || (arcPtr->extent > 180.0)) {
          if (filled && (polyDist < dist)) {
            dist = polyDist;
          }
      }
    }
    return dist;
}

/*
 *--------------------------------------------------------------
 *
 * ArcToArea --
 *
 *    This procedure is called to determine whether an item
 *    lies entirely inside, entirely outside, or overlapping
 *    a given area.
 *
 * Results:
 *    -1 is returned if the item is entirely outside the area
 *    given by rectPtr, 0 if it overlaps, and 1 if it is entirely
 *    inside the given area.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

      /* ARGSUSED */
static int
ArcToArea(canvas, itemPtr, rectPtr)
    Tk_Canvas canvas;         /* Canvas containing item. */
    Tk_Item *itemPtr;         /* Item to check against arc. */
    double *rectPtr;          /* Pointer to array of four coordinates
                         * (x1, y1, x2, y2) describing rectangular
                         * area.  */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;
    double rx, ry;            /* Radii for transformed oval:  these define
                         * an oval centered at the origin. */
    double tRect[4];          /* Transformed version of x1, y1, x2, y2,
                         * for coord. system where arc is centered
                         * on the origin. */
    double center[2], width, angle, tmp;
    double points[20], *pointPtr;
    int numPoints, filled;
    int inside;               /* Non-zero means every test so far suggests
                         * that arc is inside rectangle.  0 means
                         * every test so far shows arc to be outside
                         * of rectangle. */
    int newInside;

    if ((arcPtr->fillGC != None) || (arcPtr->outlineGC == None)) {
      filled = 1;
    } else {
      filled = 0;
    }
    if (arcPtr->outlineGC == None) {
      width = 0.0;
    } else {
      width = arcPtr->width;
    }

    /*
     * Transform both the arc and the rectangle so that the arc's oval
     * is centered on the origin.
     */

    center[0] = (arcPtr->bbox[0] + arcPtr->bbox[2])/2.0;
    center[1] = (arcPtr->bbox[1] + arcPtr->bbox[3])/2.0;
    tRect[0] = rectPtr[0] - center[0];
    tRect[1] = rectPtr[1] - center[1];
    tRect[2] = rectPtr[2] - center[0];
    tRect[3] = rectPtr[3] - center[1];
    rx = arcPtr->bbox[2] - center[0] + width/2.0;
    ry = arcPtr->bbox[3] - center[1] + width/2.0;

    /*
     * Find the extreme points of the arc and see whether these are all
     * inside the rectangle (in which case we're done), partly in and
     * partly out (in which case we're done), or all outside (in which
     * case we have more work to do).  The extreme points include the
     * following, which are checked in order:
     *
     * 1. The outside points of the arc, corresponding to start and
     *        extent.
     * 2. The center of the arc (but only in pie-slice mode).
     * 3. The 12, 3, 6, and 9-o'clock positions (but only if the arc
     *    includes those angles).
     */

    pointPtr = points;
    angle = -arcPtr->start*(PI/180.0);
    pointPtr[0] = rx*cos(angle);
    pointPtr[1] = ry*sin(angle);
    angle += -arcPtr->extent*(PI/180.0);
    pointPtr[2] = rx*cos(angle);
    pointPtr[3] = ry*sin(angle);
    numPoints = 2;
    pointPtr += 4;

    if ((arcPtr->style == pieSliceUid) && (arcPtr->extent < 180.0)) {
      pointPtr[0] = 0.0;
      pointPtr[1] = 0.0;
      numPoints++;
      pointPtr += 2;
    }

    tmp = -arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      pointPtr[0] = rx;
      pointPtr[1] = 0.0;
      numPoints++;
      pointPtr += 2;
    }
    tmp = 90.0 - arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      pointPtr[0] = 0.0;
      pointPtr[1] = -ry;
      numPoints++;
      pointPtr += 2;
    }
    tmp = 180.0 - arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      pointPtr[0] = -rx;
      pointPtr[1] = 0.0;
      numPoints++;
      pointPtr += 2;
    }
    tmp = 270.0 - arcPtr->start;
    if (tmp < 0) {
      tmp += 360.0;
    }
    if ((tmp < arcPtr->extent) || ((tmp-360) > arcPtr->extent)) {
      pointPtr[0] = 0.0;
      pointPtr[1] = ry;
      numPoints++;
    }

    /*
     * Now that we've located the extreme points, loop through them all
     * to see which are inside the rectangle.
     */

    inside = (points[0] > tRect[0]) && (points[0] < tRect[2])
          && (points[1] > tRect[1]) && (points[1] < tRect[3]);
    for (pointPtr = points+2; numPoints > 1; pointPtr += 2, numPoints--) {
      newInside = (pointPtr[0] > tRect[0]) && (pointPtr[0] < tRect[2])
            && (pointPtr[1] > tRect[1]) && (pointPtr[1] < tRect[3]);
      if (newInside != inside) {
          return 0;
      }
    }

    if (inside) {
      return 1;
    }

    /*
     * So far, oval appears to be outside rectangle, but can't yet tell
     * for sure.  Next, test each of the four sides of the rectangle
     * against the bounding region for the arc.  If any intersections
     * are found, then return "overlapping".  First, test against the
     * polygon(s) forming the sides of a chord or pie-slice.
     */

    if (arcPtr->style == pieSliceUid) {
      if (width >= 1.0) {
          if (TkPolygonToArea(arcPtr->outlinePtr, PIE_OUTLINE1_PTS,
                rectPtr) != -1)  {
            return 0;
          }
          if (TkPolygonToArea(arcPtr->outlinePtr + 2*PIE_OUTLINE1_PTS,
                PIE_OUTLINE2_PTS, rectPtr) != -1) {
            return 0;
          }
      } else {
          if ((TkLineToArea(center, arcPtr->center1, rectPtr) != -1) ||
                (TkLineToArea(center, arcPtr->center2, rectPtr) != -1)) {
            return 0;
          }
      }
    } else if (arcPtr->style == chordUid) {
      if (width >= 1.0) {
          if (TkPolygonToArea(arcPtr->outlinePtr, CHORD_OUTLINE_PTS,
                rectPtr) != -1) {
            return 0;
          }
      } else {
          if (TkLineToArea(arcPtr->center1, arcPtr->center2,
                rectPtr) != -1) {
            return 0;
          }
      }
    }

    /*
     * Next check for overlap between each of the four sides and the
     * outer perimiter of the arc.  If the arc isn't filled, then also
     * check the inner perimeter of the arc.
     */

    if (HorizLineToArc(tRect[0], tRect[2], tRect[1], rx, ry, arcPtr->start,
            arcPtr->extent)
          || HorizLineToArc(tRect[0], tRect[2], tRect[3], rx, ry,
            arcPtr->start, arcPtr->extent)
          || VertLineToArc(tRect[0], tRect[1], tRect[3], rx, ry,
            arcPtr->start, arcPtr->extent)
          || VertLineToArc(tRect[2], tRect[1], tRect[3], rx, ry,
            arcPtr->start, arcPtr->extent)) {
      return 0;
    }
    if ((width > 1.0) && !filled) {
      rx -= width;
      ry -= width;
      if (HorizLineToArc(tRect[0], tRect[2], tRect[1], rx, ry, arcPtr->start,
                arcPtr->extent)
            || HorizLineToArc(tRect[0], tRect[2], tRect[3], rx, ry,
                arcPtr->start, arcPtr->extent)
            || VertLineToArc(tRect[0], tRect[1], tRect[3], rx, ry,
                arcPtr->start, arcPtr->extent)
            || VertLineToArc(tRect[2], tRect[1], tRect[3], rx, ry,
                arcPtr->start, arcPtr->extent)) {
          return 0;
      }
    }

    /*
     * The arc still appears to be totally disjoint from the rectangle,
     * but it's also possible that the rectangle is totally inside the arc.
     * Do one last check, which is to check one point of the rectangle
     * to see if it's inside the arc.  If it is, we've got overlap.  If
     * it isn't, the arc's really outside the rectangle.
     */

    if (ArcToPoint(canvas, itemPtr, rectPtr) == 0.0) {
      return 0;
    }
    return -1;
}

/*
 *--------------------------------------------------------------
 *
 * ScaleArc --
 *
 *    This procedure is invoked to rescale an arc item.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    The arc referred to by itemPtr is rescaled so that the
 *    following transformation is applied to all point
 *    coordinates:
 *          x' = originX + scaleX*(x-originX)
 *          y' = originY + scaleY*(y-originY)
 *
 *--------------------------------------------------------------
 */

static void
ScaleArc(canvas, itemPtr, originX, originY, scaleX, scaleY)
    Tk_Canvas canvas;               /* Canvas containing arc. */
    Tk_Item *itemPtr;               /* Arc to be scaled. */
    double originX, originY;        /* Origin about which to scale rect. */
    double scaleX;                  /* Amount to scale in X direction. */
    double scaleY;                  /* Amount to scale in Y direction. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;

    arcPtr->bbox[0] = originX + scaleX*(arcPtr->bbox[0] - originX);
    arcPtr->bbox[1] = originY + scaleY*(arcPtr->bbox[1] - originY);
    arcPtr->bbox[2] = originX + scaleX*(arcPtr->bbox[2] - originX);
    arcPtr->bbox[3] = originY + scaleY*(arcPtr->bbox[3] - originY);
    ComputeArcBbox(canvas, arcPtr);
}

/*
 *--------------------------------------------------------------
 *
 * TranslateArc --
 *
 *    This procedure is called to move an arc by a given amount.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    The position of the arc is offset by (xDelta, yDelta), and
 *    the bounding box is updated in the generic part of the item
 *    structure.
 *
 *--------------------------------------------------------------
 */

static void
TranslateArc(canvas, itemPtr, deltaX, deltaY)
    Tk_Canvas canvas;               /* Canvas containing item. */
    Tk_Item *itemPtr;               /* Item that is being moved. */
    double deltaX, deltaY;          /* Amount by which item is to be
                               * moved. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;

    arcPtr->bbox[0] += deltaX;
    arcPtr->bbox[1] += deltaY;
    arcPtr->bbox[2] += deltaX;
    arcPtr->bbox[3] += deltaY;
    ComputeArcBbox(canvas, arcPtr);
}

/*
 *--------------------------------------------------------------
 *
 * ComputeArcOutline --
 *
 *    This procedure creates a polygon describing everything in
 *    the outline for an arc except what's in the curved part.
 *    For a "pie slice" arc this is a V-shaped chunk, and for
 *    a "chord" arc this is a linear chunk (with cutaway corners).
 *    For "arc" arcs, this stuff isn't relevant.
 *
 * Results:
 *    None.
 *
 * Side effects:
 *    The information at arcPtr->outlinePtr gets modified, and
 *    storage for arcPtr->outlinePtr may be allocated or freed.
 *
 *--------------------------------------------------------------
 */

static void
ComputeArcOutline(arcPtr)
    ArcItem *arcPtr;                /* Information about arc. */
{
    double sin1, cos1, sin2, cos2, angle, halfWidth;
    double boxWidth, boxHeight;
    double vertex[2], corner1[2], corner2[2];
    double *outlinePtr;

    /*
     * Make sure that the outlinePtr array is large enough to hold
     * either a chord or pie-slice outline.
     */

    if (arcPtr->numOutlinePoints == 0) {
      arcPtr->outlinePtr = (double *) ckalloc((unsigned)
            (26 * sizeof(double)));
      arcPtr->numOutlinePoints = 22;
    }
    outlinePtr = arcPtr->outlinePtr;

    /*
     * First compute the two points that lie at the centers of
     * the ends of the curved arc segment, which are marked with
     * X's in the figure below:
     *
     *
     *                          * * *
     *                        *          *
     *                     *      * *      *
     *                   *    *         *    *
     *                  *   *             *   *
     *                   X *               * X
     *
     * The code is tricky because the arc can be ovular in shape.
     * It computes the position for a unit circle, and then
     * scales to fit the shape of the arc's bounding box.
     *
     * Also, watch out because angles go counter-clockwise like you
     * might expect, but the y-coordinate system is inverted.  To
     * handle this, just negate the angles in all the computations.
     */

    boxWidth = arcPtr->bbox[2] - arcPtr->bbox[0];
    boxHeight = arcPtr->bbox[3] - arcPtr->bbox[1];
    angle = -arcPtr->start*PI/180.0;
    sin1 = sin(angle);
    cos1 = cos(angle);
    angle -= arcPtr->extent*PI/180.0;
    sin2 = sin(angle);
    cos2 = cos(angle);
    vertex[0] = (arcPtr->bbox[0] + arcPtr->bbox[2])/2.0;
    vertex[1] = (arcPtr->bbox[1] + arcPtr->bbox[3])/2.0;
    arcPtr->center1[0] = vertex[0] + cos1*boxWidth/2.0;
    arcPtr->center1[1] = vertex[1] + sin1*boxHeight/2.0;
    arcPtr->center2[0] = vertex[0] + cos2*boxWidth/2.0;
    arcPtr->center2[1] = vertex[1] + sin2*boxHeight/2.0;

    /*
     * Next compute the "outermost corners" of the arc, which are
     * marked with X's in the figure below:
     *
     *                          * * *
     *                        *          *
     *                     *      * *      *
     *                   *    *         *    *
     *                  X   *             *   X
     *                     *               *
     *
     * The code below is tricky because it has to handle eccentricity
     * in the shape of the oval.  The key in the code below is to
     * realize that the slope of the line from arcPtr->center1 to corner1
     * is (boxWidth*sin1)/(boxHeight*cos1), and similarly for arcPtr->center2
     * and corner2.  These formulas can be computed from the formula for
     * the oval.
     */

    halfWidth = arcPtr->width/2.0;
    if (((boxWidth*sin1) == 0.0) && ((boxHeight*cos1) == 0.0)) {
      angle = 0.0;
    } else {
      angle = atan2(boxWidth*sin1, boxHeight*cos1);
    }
    corner1[0] = arcPtr->center1[0] + cos(angle)*halfWidth;
    corner1[1] = arcPtr->center1[1] + sin(angle)*halfWidth;
    if (((boxWidth*sin2) == 0.0) && ((boxHeight*cos2) == 0.0)) {
      angle = 0.0;
    } else {
      angle = atan2(boxWidth*sin2, boxHeight*cos2);
    }
    corner2[0] = arcPtr->center2[0] + cos(angle)*halfWidth;
    corner2[1] = arcPtr->center2[1] + sin(angle)*halfWidth;

    /*
     * For a chord outline, generate a six-sided polygon with three
     * points for each end of the chord.  The first and third points
     * for each end are butt points generated on either side of the
     * center point.  The second point is the corner point.
     */

    if (arcPtr->style == chordUid) {
      outlinePtr[0] = outlinePtr[12] = corner1[0];
      outlinePtr[1] = outlinePtr[13] = corner1[1];
      TkGetButtPoints(arcPtr->center2, arcPtr->center1,
            (double) arcPtr->width, 0, outlinePtr+10, outlinePtr+2);
      outlinePtr[4] = arcPtr->center2[0] + outlinePtr[2]
            - arcPtr->center1[0];
      outlinePtr[5] = arcPtr->center2[1] + outlinePtr[3]
            - arcPtr->center1[1];
      outlinePtr[6] = corner2[0];
      outlinePtr[7] = corner2[1];
      outlinePtr[8] = arcPtr->center2[0] + outlinePtr[10]
            - arcPtr->center1[0];
      outlinePtr[9] = arcPtr->center2[1] + outlinePtr[11]
            - arcPtr->center1[1];
    } else if (arcPtr->style == pieSliceUid) {
      /*
       * For pie slices, generate two polygons, one for each side
       * of the pie slice.  The first arm has a shape like this,
       * where the center of the oval is X, arcPtr->center1 is at Y, and
       * corner1 is at Z:
       *
       *     _____________________
       *    |                 \
       *    |                  \
       *    X                Y  Z
       *    |                  /
       *    |_____________________/
       *
       */

      TkGetButtPoints(arcPtr->center1, vertex, (double) arcPtr->width, 0,
            outlinePtr, outlinePtr+2);
      outlinePtr[4] = arcPtr->center1[0] + outlinePtr[2] - vertex[0];
      outlinePtr[5] = arcPtr->center1[1] + outlinePtr[3] - vertex[1];
      outlinePtr[6] = corner1[0];
      outlinePtr[7] = corner1[1];
      outlinePtr[8] = arcPtr->center1[0] + outlinePtr[0] - vertex[0];
      outlinePtr[9] = arcPtr->center1[1] + outlinePtr[1] - vertex[1];
      outlinePtr[10] = outlinePtr[0];
      outlinePtr[11] = outlinePtr[1];

      /*
       * The second arm has a shape like this:
       *
       *
       *       ______________________
       *      /                 \
       *     /                   \
       *    Z  Y              X  /
       *     \                  /
       *      \______________________/
       *
       * Similar to above X is the center of the oval/circle, Y is
       * arcPtr->center2, and Z is corner2.  The extra jog out to the left
       * of X is needed in or to produce a butted joint with the
       * first arm;  the corner to the right of X is one of the
       * first two points of the first arm, depending on extent.
       */

      TkGetButtPoints(arcPtr->center2, vertex, (double) arcPtr->width, 0,
            outlinePtr+12, outlinePtr+16);
      if ((arcPtr->extent > 180) ||
            ((arcPtr->extent < 0) && (arcPtr->extent > -180))) {
          outlinePtr[14] = outlinePtr[0];
          outlinePtr[15] = outlinePtr[1];
      } else {
          outlinePtr[14] = outlinePtr[2];
          outlinePtr[15] = outlinePtr[3];
      }
      outlinePtr[18] = arcPtr->center2[0] + outlinePtr[16] - vertex[0];
      outlinePtr[19] = arcPtr->center2[1] + outlinePtr[17] - vertex[1];
      outlinePtr[20] = corner2[0];
      outlinePtr[21] = corner2[1];
      outlinePtr[22] = arcPtr->center2[0] + outlinePtr[12] - vertex[0];
      outlinePtr[23] = arcPtr->center2[1] + outlinePtr[13] - vertex[1];
      outlinePtr[24] = outlinePtr[12];
      outlinePtr[25] = outlinePtr[13];
    }
}

/*
 *--------------------------------------------------------------
 *
 * HorizLineToArc --
 *
 *    Determines whether a horizontal line segment intersects
 *    a given arc.
 *
 * Results:
 *    The return value is 1 if the given line intersects the
 *    infinitely-thin arc section defined by rx, ry, start,
 *    and extent, and 0 otherwise.  Only the perimeter of the
 *    arc is checked: interior areas (e.g. pie-slice or chord)
 *    are not checked.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

static int
HorizLineToArc(x1, x2, y, rx, ry, start, extent)
    double x1, x2;            /* X-coords of endpoints of line segment. 
                         * X1 must be <= x2. */
    double y;                 /* Y-coordinate of line segment. */
    double rx, ry;            /* These x- and y-radii define an oval
                         * centered at the origin. */
    double start, extent;     /* Angles that define extent of arc, in
                         * the standard fashion for this module. */
{
    double tmp;
    double tx, ty;            /* Coordinates of intersection point in
                         * transformed coordinate system. */
    double x;

    /*
     * Compute the x-coordinate of one possible intersection point
     * between the arc and the line.  Use a transformed coordinate
     * system where the oval is a unit circle centered at the origin.
     * Then scale back to get actual x-coordinate.
     */

    ty = y/ry;
    tmp = 1 - ty*ty;
    if (tmp < 0) {
      return 0;
    }
    tx = sqrt(tmp);
    x = tx*rx;

    /*
     * Test both intersection points.
     */

    if ((x >= x1) && (x <= x2) && AngleInRange(tx, ty, start, extent)) {
      return 1;
    }
    if ((-x >= x1) && (-x <= x2) && AngleInRange(-tx, ty, start, extent)) {
      return 1;
    }
    return 0;
}

/*
 *--------------------------------------------------------------
 *
 * VertLineToArc --
 *
 *    Determines whether a vertical line segment intersects
 *    a given arc.
 *
 * Results:
 *    The return value is 1 if the given line intersects the
 *    infinitely-thin arc section defined by rx, ry, start,
 *    and extent, and 0 otherwise.  Only the perimeter of the
 *    arc is checked: interior areas (e.g. pie-slice or chord)
 *    are not checked.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

static int
VertLineToArc(x, y1, y2, rx, ry, start, extent)
    double x;                 /* X-coordinate of line segment. */
    double y1, y2;            /* Y-coords of endpoints of line segment. 
                         * Y1 must be <= y2. */
    double rx, ry;            /* These x- and y-radii define an oval
                         * centered at the origin. */
    double start, extent;     /* Angles that define extent of arc, in
                         * the standard fashion for this module. */
{
    double tmp;
    double tx, ty;            /* Coordinates of intersection point in
                         * transformed coordinate system. */
    double y;

    /*
     * Compute the y-coordinate of one possible intersection point
     * between the arc and the line.  Use a transformed coordinate
     * system where the oval is a unit circle centered at the origin.
     * Then scale back to get actual y-coordinate.
     */

    tx = x/rx;
    tmp = 1 - tx*tx;
    if (tmp < 0) {
      return 0;
    }
    ty = sqrt(tmp);
    y = ty*ry;

    /*
     * Test both intersection points.
     */

    if ((y > y1) && (y < y2) && AngleInRange(tx, ty, start, extent)) {
      return 1;
    }
    if ((-y > y1) && (-y < y2) && AngleInRange(tx, -ty, start, extent)) {
      return 1;
    }
    return 0;
}

/*
 *--------------------------------------------------------------
 *
 * AngleInRange --
 *
 *    Determine whether the angle from the origin to a given
 *    point is within a given range.
 *
 * Results:
 *    The return value is 1 if the angle from (0,0) to (x,y)
 *    is in the range given by start and extent, where angles
 *    are interpreted in the standard way for ovals (meaning
 *    backwards from normal interpretation).  Otherwise the
 *    return value is 0.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

static int
AngleInRange(x, y, start, extent)
    double x, y;        /* Coordinate of point;  angle measured
                         * from origin to here, relative to x-axis. */
    double start;       /* First angle, degrees, >=0, <=360. */
    double extent;            /* Size of arc in degrees >=-360, <=360. */
{
    double diff;

    if ((x == 0.0) && (y == 0.0)) {
      return 1;
    }
    diff = -atan2(y, x);
    diff = diff*(180.0/PI) - start;
    while (diff > 360.0) {
      diff -= 360.0;
    }
    while (diff < 0.0) {
      diff += 360.0;
    }
    if (extent >= 0) {
      return diff <= extent;
    }
    return (diff-360.0) >= extent;
}

/*
 *--------------------------------------------------------------
 *
 * ArcToPostscript --
 *
 *    This procedure is called to generate Postscript for
 *    arc items.
 *
 * Results:
 *    The return value is a standard Tcl result.  If an error
 *    occurs in generating Postscript then an error message is
 *    left in interp->result, replacing whatever used
 *    to be there.  If no error occurs, then Postscript for the
 *    item is appended to the result.
 *
 * Side effects:
 *    None.
 *
 *--------------------------------------------------------------
 */

static int
ArcToPostscript(interp, canvas, itemPtr, prepass)
    Tcl_Interp *interp;             /* Leave Postscript or error message
                               * here. */
    Tk_Canvas canvas;               /* Information about overall canvas. */
    Tk_Item *itemPtr;               /* Item for which Postscript is
                               * wanted. */
    int prepass;              /* 1 means this is a prepass to
                               * collect font information;  0 means
                               * final Postscript is being created. */
{
    ArcItem *arcPtr = (ArcItem *) itemPtr;
    char buffer[400];
    double y1, y2, ang1, ang2;

    y1 = Tk_CanvasPsY(canvas, arcPtr->bbox[1]);
    y2 = Tk_CanvasPsY(canvas, arcPtr->bbox[3]);
    ang1 = arcPtr->start;
    ang2 = ang1 + arcPtr->extent;
    if (ang2 < ang1) {
      ang1 = ang2;
      ang2 = arcPtr->start;
    }

    /*
     * If the arc is filled, output Postscript for the interior region
     * of the arc.
     */

    if (arcPtr->fillGC != None) {
      sprintf(buffer, "matrix currentmatrix\n%.15g %.15g translate %.15g %.15g scale\n",
            (arcPtr->bbox[0] + arcPtr->bbox[2])/2, (y1 + y2)/2,
            (arcPtr->bbox[2] - arcPtr->bbox[0])/2, (y1 - y2)/2);
      Tcl_AppendResult(interp, buffer, (char *) NULL);
      if (arcPtr->style == chordUid) {
          sprintf(buffer, "0 0 1 %.15g %.15g arc closepath\nsetmatrix\n",
                ang1, ang2);
      } else {
          sprintf(buffer,
                "0 0 moveto 0 0 1 %.15g %.15g arc closepath\nsetmatrix\n",
                ang1, ang2);
      }
      Tcl_AppendResult(interp, buffer, (char *) NULL);
      if (Tk_CanvasPsColor(interp, canvas, arcPtr->fillColor) != TCL_OK) {
          return TCL_ERROR;
      };
      if (arcPtr->fillStipple != None) {
          Tcl_AppendResult(interp, "clip ", (char *) NULL);
          if (Tk_CanvasPsStipple(interp, canvas, arcPtr->fillStipple)
                != TCL_OK) {
            return TCL_ERROR;
          }
          if (arcPtr->outlineGC != None) {
            Tcl_AppendResult(interp, "grestore gsave\n", (char *) NULL);
          }
      } else {
          Tcl_AppendResult(interp, "fill\n", (char *) NULL);
      }
    }

    /*
     * If there's an outline for the arc, draw it.
     */

    if (arcPtr->outlineGC != None) {
      sprintf(buffer, "matrix currentmatrix\n%.15g %.15g translate %.15g %.15g scale\n",
            (arcPtr->bbox[0] + arcPtr->bbox[2])/2, (y1 + y2)/2,
            (arcPtr->bbox[2] - arcPtr->bbox[0])/2, (y1 - y2)/2);
      Tcl_AppendResult(interp, buffer, (char *) NULL);
      sprintf(buffer, "0 0 1 %.15g %.15g arc\nsetmatrix\n", ang1, ang2);
      Tcl_AppendResult(interp, buffer, (char *) NULL);
      sprintf(buffer, "%d setlinewidth\n0 setlinecap\n", arcPtr->width);
      Tcl_AppendResult(interp, buffer, (char *) NULL);
      if (Tk_CanvasPsColor(interp, canvas, arcPtr->outlineColor)
            != TCL_OK) {
          return TCL_ERROR;
      }
      if (arcPtr->outlineStipple != None) {
          Tcl_AppendResult(interp, "StrokeClip ", (char *) NULL);
          if (Tk_CanvasPsStipple(interp, canvas,
                arcPtr->outlineStipple) != TCL_OK) {
            return TCL_ERROR;
          }
      } else {
          Tcl_AppendResult(interp, "stroke\n", (char *) NULL);
      }
      if (arcPtr->style != arcUid) {
          Tcl_AppendResult(interp, "grestore gsave\n", (char *) NULL);
          if (arcPtr->style == chordUid) {
            Tk_CanvasPsPath(interp, canvas, arcPtr->outlinePtr,
                  CHORD_OUTLINE_PTS);
          } else {
            Tk_CanvasPsPath(interp, canvas, arcPtr->outlinePtr,
                  PIE_OUTLINE1_PTS);
            if (Tk_CanvasPsColor(interp, canvas, arcPtr->outlineColor)
                  != TCL_OK) {
                return TCL_ERROR;
            }
            if (arcPtr->outlineStipple != None) {
                Tcl_AppendResult(interp, "clip ", (char *) NULL);
                if (Tk_CanvasPsStipple(interp, canvas,
                      arcPtr->outlineStipple) != TCL_OK) {
                  return TCL_ERROR;
                }
            } else {
                Tcl_AppendResult(interp, "fill\n", (char *) NULL);
            }
            Tcl_AppendResult(interp, "grestore gsave\n", (char *) NULL);
            Tk_CanvasPsPath(interp, canvas,
                  arcPtr->outlinePtr + 2*PIE_OUTLINE1_PTS,
                  PIE_OUTLINE2_PTS);
          }
          if (Tk_CanvasPsColor(interp, canvas, arcPtr->outlineColor)
                != TCL_OK) {
            return TCL_ERROR;
          }
          if (arcPtr->outlineStipple != None) {
            Tcl_AppendResult(interp, "clip ", (char *) NULL);
            if (Tk_CanvasPsStipple(interp, canvas,
                  arcPtr->outlineStipple) != TCL_OK) {
                return TCL_ERROR;
            }
          } else {
            Tcl_AppendResult(interp, "fill\n", (char *) NULL);
          }
      }
    }

    return TCL_OK;
}

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